PDF - Effects of Forces

1.3 Effects of Forces A small creature such as an insect can fall from a great height and walk away unharmed....

1.3 Effects of Forces A small creature such as an insect can fall from a great height and walk away unharmed. CAN YOU EXPLAIN THE PHENOMENON? © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Spike Mafford/Photodisc/ You have studied how objects moving only under the influence of gravity fall with the same downward acceleration. Yet you know of real-world examples that show more complex motion, such as the fall of a leaf or a sheet of paper. Think about an acorn and an ant, each falling from the same high branch of a tree. As the acorn hits the ground, it produces a sound loud enough to hear. The ant hits almost silently and walks away unharmed. INFER Use the impact of the ant and the acorn with the ground as a way of comparing their motion just before impact. Describe a likely way the ant’s motion differs from the acorn’s motion. Getty Images Evidence Notebook As you explore the lesson, gather evidence to explain the factors that can cause the motion of the falling ant and the acorn in the example to differ. Lesson 3 Effects of Forces 53 EXPLORATION 1 Representing Forces In everyday language, “to force” can mean to cause something to happen; in science, a force is a push or a pull exerted by one object on another. In the International System (SI) 2 of Units, the unit for force is the newton (N), which is equal to 1 kg m/s. Force is a vector quantity because it has direction as well as magnitude. Collaborate With a partner, compare and contrast the everyday and scientific meanings of force. In your discussion, address these questions: Can there be a force if nothing happens? How might the units (kg m/s2) be related to the scientific definition? FIGURE 1: Spring scales are Identifying Forces used to measure force. Think about the downward pull due to gravity. Scientists distinguish between weight, the gravitational force acting on an object, and mass, a measure of the amount of matter. The mass of an object can be measured by comparing it to known masses using a balance; mass is not a force. Weight and other forces can be measured—for example, by how much they push or pull a spring in a spring scale. These tools work because an object’s weight is balanced by another force. A kitchen or bathroom scale can be used to measure the downward force (weight) that is balanced by an upward supporting force, such as from a table or the floor. This supporting force is perpendicular to a surface and is called the normal force. © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Houghton Mifflin Harcourt INFER For each type of force in the table, match the example description with the vector image of the force. Force Description air resistance Air exerts a force against the moving box in a way that increases with the box’s speed. friction Two sliding surfaces produce a force that acts opposite to the direction of the relative motion of the surfaces. gravitational force Earth exerts a force of attraction on the box. normal force An object exerts a force on the box in a direction perpendicular to the surfaces in contact. 54 Unit 1 Physics and Engineering  Cause and Effect Exploring Friction FIGURE 2: The surfaces of the box and When an object is pushed or pulled across another object, small the ramp resist motion between them. points of the surfaces in contact push against each other and resist motion. This effect and several other effects, together, produce friction. Friction is a force that opposes motion between two surfaces that are in contact. The box in Figure 2 stays in place because static friction resists the force that would make it slide down the ramp. Static friction occurs when the two surfaces are not sliding. When the box slides along the surface, kinetic friction resists—but does not prevent—the motion. The force of kinetic friction is less than the maximum value of static friction. Unlike air resistance, static and kinetic friction do not typically depend on speed or on the area of contact. They are each proportional to the force pushing the surfaces together, which is usually characterized by the normal force. The normal force is in a direction perpendicular to a surface, so it is not always vertical. Language Arts Connection Use the two types of friction to describe what happens as you slide a heavy box across a table. You might also research the coefficient of friction. Prepare an explanation to present to the class. Using Diagrams to Analyze Force The normal force and static friction tend to oppose other forces, while forces acting in the same direction produce a greater force. Forces combine as vectors, in the same way velocities or accelerations combine. To make calculations, however, you have to determine which vectors to add together. APPLY Use vector arrows to draw the forces you expect to be present when a car is parked on flat pavement. Treat the car as a single object. © Houghton Mifflin Harcourt Publishing Company Compare the vectors you drew with those of a classmate. Each of you may have represented the car’s weight, for example, in different ways. Perhaps you drew gravitational force pulling down on the car or the heavy car pressing down on the pavement. Look at the forces on a single object: the car. You can combine these forces. It is less useful to combine the forces that act on different objects. Lesson 3 Effects of Forces 55  A free-body diagram is a way to model a situation by looking at only one object and the external forces that act on it. Figure 3a shows some forces on the car and forces on the pavement. Figure 3b includes the car’s weight but not the forces on the pavement. FIGURE 3: The first model (a) shows forces on both the car and the ground. The second, free- body diagram (b) shows only forces on the car. a b In a free-body diagram, each force on an object is represented by a vector arrow. This model treats all forces as if they were acting at a single point, called the center of mass of the object. The center of mass is usually represented as a dot and may not be exactly at the center of the object. In Figure 3b, the free-body diagram of the car, the normal force is shown as a single vector pointing upward from the center of mass. Compare Figure 3a, in which the normal forces from the ground are represented as two vectors at the tires. ANALYZE Select the correct label for each vector in the free-body diagrams. A label can be used more than once. Fgravity Fnormal Fspring Fstring Determining Net Force © Houghton Mifflin Harcourt Publishing Company The net force on an object, Fnet, is the vector sum of all external forces acting on it. You may also see net force written as ΣF, where the capital sigma, Σ, indicates a summation. In each of the free-body diagrams that you labeled, two forces are balanced. When forces on an object are balanced, the net force is zero. The forces may be large or small, but if they balance, the result is as if no force were acting on the object. INFER What can you infer about the net force when an object is unmoving—at rest? Explain your reasoning. 56 Unit 1 Physics and Engineering  PREDICT Next to each diagram, draw a vector to represent the direction and approximate magnitude of the net force. Then describe what you think will happen to the motion of the box. Scenario Free-body diagram Predicted motion box falling in air box on a spring If forces act in one dimension—that is, along a single line—they can be represented as positive and negative numbers. For example, a force of 10 N down and a force 8 N up can be written as −10 N + 8 N = −2 N, a net force of 2 N downward. When forces are in two dimensions, you can look separately at the forces FIGURE 4: Components of the in perpendicular directions, such as vertical and horizontal forces. Because force due to gravity frictional forces are parallel to surfaces in contact and normal forces are perpendicular to the surfaces, you might choose a coordinate system oriented with one axis along the surface. In Figure 4, one axis would be parallel to the ramp and the other would be perpendicular to the rampFand parallel to Fnormal the Ffriction Fnormal friction normal force on the box. You can often determine the normal force by analyzing the other forces. Suppose gravitational force is the only force pressing the object to the surface. Fgravity Fgravity For an object at rest on a horizontal surface, the normal force equals the weight of the object supported by the surface. For a slanted surface, such as a ramp, the normal force equals the component of the force due to gravity perpendicular to the surface. APPLY Suppose you place a coin on a book; the book’s cover acts as a ramp. You open the cover slowly until static friction is overcome. The coin begins to slide. What happens to the forces on the coin as the angle of the cover changes? Select all correct answers. © Houghton Mifflin Harcourt Publishing Company a. A component of the frictional force begins pushing the coin and book together. b. The frictional force decreases suddenly as the coin starts to slide. c. The gravitational force increases. d. The component of gravitational force along the surface increases. e. The component of gravitational force perpendicular to the surface decreases. f. The normal force decreases slowly, which produces a slow decrease in static friction. Evidence Notebook Construct a free-body diagram for the falling ant and the falling acorn in the example, just before each hits the ground. Use the lengths of the vectors to show your estimate of the relative magnitudes. Lesson 3 Effects of Forces 57 EXPLORATION 2 Hands-On Lab Exploring Force and Motion In this lab, you will explore two ways of producing constant forces and the effects of constant forces on motion. Then you will use a more formal setup to determine the effects of constant forces on the motion of objects that are initially at rest and initially moving. RESEARCH QUESTION How is force related to motion? MAKE A CLAIM After completing Part I, use your hypothesis to help you address this question: Suppose the frictionless system shown in Figure 7 is tested with equal masses. What will happen if the system is given a small initial motion—one mass moving upward, one downward? POSSIBLE MATERIALS safety goggles mass set and/or ring stand balance objects of known mass spring scale or other force meter box with a flat bottom mass hangers and stopwatch or other timing device slotted mass set dynamics cart string pulley with clamp for elastic cord or rubber surfaces, assorted table edge band tape, masking SAFETY INFORMATION Wear safety goggles during the setup, hands-on, and takedown segments of the activity. Immediately pick up any items dropped on the floor so that they do not become a slip/fall hazard. Wash your hands with soap and water immediately after completing this activity. © Houghton Mifflin Harcourt Publishing Company PART I: Testing Constant Forces FIGURE 5: Use a spring scale to ensure a steady applied force. CARRY OUT THE INVESTIGATION In Part I, you will first explore the relationship between applied force and net force. Later, you will need to decide which force to use in your hypothesis. Then you will use a setup in which a gravitational force is approximately the same as the net force on a system. As you work, you will need to determine and record details of your procedure based on the materials available, your ongoing results, and your judgment. Use three or more values of an independent variable (such as force applied or mass of the moving object) to make a rough graph as you work. Try to determine whether the variable has no effect (a horizontal line), a linear effect (a straight line), or a nonlinear effect (a curved line). If you can’t tell, gather more or better data before you put away the equipment. 58 Unit 1 Physics and Engineering  Procedure Record details of your procedure and your observations in your Evidence Notebook. You might design tables to record multiple trials and multiple values of independent variables. 1. Record the type and mass of the box you use. Tie a loop of string around the box. Place the box flat on a table or the floor, and hook the force meter to the string loop. Add a known amount of mass to the box. 2. Gently pull the spring scale with different amounts of force but without moving the box. Record the range of forces you can apply and the static friction you infer. 3. Gently pull the box along the table using the spring scale. Try to keep the force constant as the box slides. Optimize the mass in the box and the applied force to find a range for which you can keep your applied force constant. Then describe the relative velocity and acceleration for different applied forces, as well as an estimated net force. You can use the stretch of an elastic cord as another way to estimate the applied force. Vary the sliding surfaces or the mass of the box to increase or reduce friction in order to help you pull the box with a constant force. For example, you can put strips of tape along the surface or the bottom of the box. 4. Set up a low-friction system as shown in Figure 6. The hanging weight FIGURE 6: Use a hanging (b) provides a constant force as it drops. Check that the string’s length weight (b) to provide a steady enables the maximum motion. Prevent the cart and hanging weight from force on the object (a), but hitting anything at the end of each run. include its mass as part of the 5. Experiment with different masses in the cart and different hanging weights system in motion. to find a range that gives good results. Ignore friction and assume the hanging weight is the net force. Then test enough values of force to a b develop a hypothesis about the effect of force on motion. Record your measurements or estimates of velocity and acceleration, along with any qualitative observations of motion for each trial run. ANALYZE 1. List the relationships that were clearly linear or clearly nonlinear. © Houghton Mifflin Harcourt Publishing Company 2. Do you think the applied force, the frictional force, or the net force has the strongest relationship to motion? Use a free-body diagram to help you determine your answer. 3. Think about how varying the force you chose affects velocity and acceleration. Write a hypothesis that summarizes how force affects motion. Lesson 3 Effects of Forces 59  PART II: Testing Your Hypothesis PLAN YOUR INVESTIGATION Use your hypothesis from Part I to make a claim about the setup shown in Figure 7. Then use your experiences from Part I to develop a plan to test your hypothesis about force and motion. Consider these suggestions as you plan your procedure: Use or adapt one of the two setups from Part I. Draw a free-body diagram of the system to help ensure that you will be able to measure or calculate all significant forces. Design a procedure to test and refine your hypothesis about how force affects motion. Plan to determine whether the effect of force has a linear relationship to an object’s velocity or acceleration. If not, find a way to describe the relationship. Test enough values of force to provide evidence of the relationship. Also test several values of mass to ensure that the relationship holds for different objects. If you can, test a setup in which there is zero net force and a small initial velocity. Make sure your teacher approves your procedure and safety plan. Then carry out your procedure and record your observations in your Evidence Notebook. ANALYZE 1. Based on your experiment, is the effect of force more closely related to an object’s velocity or its acceleration? Is the relationship linear? Give details of the relationship. 2. How well does your answer to the first question apply if you use a different mass? DRAW CONCLUSIONS FIGURE 7: A string passing over a pulley supports two objects. Write a conclusion that addresses each of the points below. Claim Suppose the frictionless system shown in Figure 7 is tested with objects of equal mass (zero net force). What will happen if the system is given a small initial motion, such that one mass moves up and the other moves down? © Houghton Mifflin Harcourt Publishing Company Evidence Present your hypothesis tests and other evidence to support your claim. Reasoning Explain how your evidence applies to the system in Figure 7. Evidence Notebook Apply what you have learned about the effect of force on motion to form a hypothesis about the difference between the falling ant and acorn. 60 Unit 1 Physics and Engineering  EXPLORATION 3 Connecting Force and Motion Collaborate With a partner, choose a scenario such as sliding a table across the floor. Discuss the effect of the force you apply, such as by pulling or pushing the object. Then discuss the effect of net force. Which force would you use to predict the object’s motion? Analyzing Force and Motion ANALYZE For each example, describe the car’s motion by determining whether velocity and acceleration are zero, positive, or negative. Then try to do the same for net force. Example Velocity Acceleration Net force A car is parked. A car moves at a constant speed of 100 km/h on a straight roadway. A car slows in a school zone. A car that was stopped at a red light begins to move when the light turns green. A car turns a corner at a constant speed of 10 km/h. When two balanced forces are exerted on an object, such as an object’s weight and the normal force from the floor beneath it, the effects of the forces tend to cancel each other. To predict motion, scientists typically use net force. In Figure 8, two objects hang by a single string that runs over a pulley. The device, called Atwood’s machine, shows how net force affects motion. Each object is pulled down by gravity and up by the string. FIGURE 8: Atwood’s machine EVALUATE Select the correct terms to complete the statements about the © Houghton Mifflin Harcourt Publishing Company forces in Figure 8. The forces from the string, F1,string and F2,string, have magnitudes that are the same | different and directions that are the same | opposite | perpendicular, whether or not the system is in motion. F1,string If the masses are equal and unmoving, the net force on each object must be upward | zero | downward. F1,gravity Suppose the masses of the objects are equal and the masses of the string and F2,string the pulley are small enough to be ignored. If the objects are at rest, they stay at rest. However, if the system is initially moving, it continues moving steadily until something stops it. One object moves up and the other moves down, F2,gravity each at constant velocity, until an object reaches the pulley or the ground. Lesson 3 Effects of Forces 61  Effect of Balanced Forces on Motion In many everyday experiences, moving objects tend to slow down or stop unless something keeps them moving. For example, if you tap a pencil to make it slide along a table, it slows down and comes to a stop. You may not notice that frictional force acts on the pencil; it represents a net force in the direction opposite to the pencil’s velocity. Gravitational force and friction are part of most of your everyday experiences. If you have experiences with objects sliding on ice or other nearly frictionless surfaces, you may have noticed that objects can move at a constant velocity for a long time without anything pushing on them. FIGURE 9: Little or no friction is present between a hockey puck and ice. INFER Draw the free-body diagram for the hockey puck when it is not moving (a), and when it is moving steadily to the right (b). © Houghton Mifflin Harcourt Publishing Company Image Credits: (c) ©francisblack/E+/Getty Images a Not moving, at rest b Moving steadily to the right Apply the idea of net force to everyday experiences in which you exert a force to keep an object moving. Suppose you pull an object just hard enough to oppose friction, so Fnet = 0. If you reduce friction, such as by using a slippery surface, less force is needed to keep the object in motion. If you could reduce friction all the way to zero, an object sliding across the surface would continue to slide at its initial velocity without any applied force. You would not have to continue pulling to keep it moving. The same thing happens with Atwood’s machine and with an ideal hockey puck; an object can move at a constant velocity when Fnet = 0. When a moving object slows, it is because of a net force, such as friction, acting on it. Explore Online You can summarize the two effects of zero net force: An object at rest remains Hands-On Lab at rest and an object in motion continues in motion with constant velocity Exploring Newton’s Laws unless the object is subject to a net external force. This relationship is called Explore the factors that cause a Newton’s first law of motion. Remember that an object at rest has zero velocity. change in the motion of an object. In other words, when net force is zero, an object remains at constant velocity (which may be zero); it does not accelerate. Language Arts Connection Find a video, simulation, or physical situation that shows an example of Newton’s first law of motion. You might instead be able to demonstrate an example. Describe the example and draw a free-body diagram that represents it. 62 Unit 1 Physics and Engineering  Effect of Unbalanced Forces on Motion As you may have inferred, an object’s velocity changes when the net force on it is not zero. The object may slow down, speed up, or turn; the force causes this change in motion. Data Analysis Magnitude of Net Force MODEL Graph the simulated data from the table, which show the effect of different forces on a 2 kg object, or make a graph of data from an experiment or a simulation. Then draw the curve or straight line that best represents the points. Model m (kg) a (m/s2) Fnet (N) 2 2.5 5 2 5 10 2 10 20 2 15 30 Force (N) 0 © Houghton Mifflin Harcourt Publishing Company 0 Acceleration (m/s2) ANALYZE Select the correct terms to complete the statements. The points lie along a straight line | simple curve | complex path, so the relationship between acceleration and force is linear | geometric | exponential. The magnitude of the acceleration a is directly proportional to | inversely proportional to | the inverse square of the magnitude of the force F. The overall slope represents the velocity | rate of change in acceleration | mass. Lesson 3 Effects of Forces 63  If you push on an object at rest, static friction may prevent it from moving: the net force is zero. If you push hard enough, the object starts moving—accelerates—in the direction of the net force. Explore the relationships between net force, velocity, and acceleration when the object does not start from rest. INFER The dots show the car’s position at equal intervals of time. The vectors show the car’s initial and final velocities. For each example, first determine whether the car is speeding up or slowing down, then infer the direction of the net force. speeding up slowing down vi vf vi vi vi vf vf vi Notice how the direction of net force can be different from the direction of an object’s motion. For example, when you slide an object across a floor, the force of kinetic friction is opposite to the velocity and tends to slow the object. © Houghton Mifflin Harcourt Publishing Company APPLY Select the correct terms to complete the statements for an object acted upon by a nonzero net force. The direction of acceleration is the same as | opposite to the direction of net force. A force in the direction of motion causes an object to slow down | speed up | turn. A force opposite the direction of motion causes an object to slow down | speed up | turn. A force at a 90° angle to the direction of motion causes an object to slow down | speed up | turn. 64 Unit 1 Physics and Engineering  Relating Force, Mass, and Acceleration You have seen how acceleration is related to the net force, but it also depends on an object’s mass. Think about how objects of different masses accelerate if pushed with the same force; imagine the objects on ice or another low-friction surface. Data Analysis Effect of Mass on Acceleration MODEL The table shows the results of a simulation in which force is held constant. Graph the results to find out how an increase in mass affects acceleration. Model F (N) 10 10 10 10 10 m (kg) 1 2.5 5 10 15 a (m/s2) 10 4 2 1 2/3 Acceleration (m/s2) 0 Mass (kg) © Houghton Mifflin Harcourt Publishing Company ANALYZE Select the correct terms to complete the statements. A more massive object acted on by the same net force as a less massive object has a smaller | the same | a greater acceleration. The tangent to the curve at each point has positive | zero | negative slope. There is a direct | an inverse | a complex relationship between the mass of an object and its acceleration—a is proportional to m | 1/m. Suppose you gave pushes of equal force to a small child on one swing and an adult on a second swing. The force has less effect on the adult’s greater mass. To achieve the same acceleration of the greater mass, you must apply a greater force. Lesson 3 Effects of Forces 65  SOLVE The relationships between Fnet, acceleration a, and mass m can be summarized in an equation. Place each variable in the equation. a m = × Fnet The equation can be rewritten to show how acceleration depends on both force and mass: a = Fnet/m. This relationship is known as Newton’s second law of motion. Constant acceleration is the result of a constant net force acting on an object, such as when gravity alone acts on a falling object near Earth’s surface. APPLY Match the change in the force or mass to the change in the acceleration of an object. As the net force increases slightly, the acceleration decreases slightly. When the net force doubles, the acceleration doubles. As the mass increases slightly, the acceleration halves. When the mass doubles, the acceleration increases slightly. The mass in the equation is the total mass of the system being accelerated. For two objects connected by a (massless) string over a pulley, both objects contribute to the system’s mass. If you use a descending weight to provide a constant force, or if you set up Atwood’s machine with different masses, the net force is the unbalanced part of the gravitational force. FIGURE 10: The cart has mass m1 and the Language Arts Connection When you make calculations descending weight has mass m2. for the system shown in Figure 10, you might assume that the system is frictionless, that air resistance is zero, and that the m1 string and pulley have zero mass. List advantages and disadvantages of using this model. Think about the conditions under which it is reasonable to use the simplified model. When m2 might you need to include more detail in your calculations? Summarize your conclusions in a flow chart. Think about how this relationship applies to situations with different amounts of friction. On a frictionless surface or in space, an object accelerates as soon any force is applied. In contrast, a heavy object on a high-friction surface does not move until the applied © Houghton Mifflin Harcourt Publishing Company force becomes great enough. It then moves suddenly as the force due to static friction is exceeded and kinetic friction begins. On a frictionless surface or in space, a more massive object takes greater force to speed up, to turn, or to stop. Its mass resists the change in velocity. In situations with significant friction, the amount of friction often depends on an object’s weight, which is proportional to its mass. A more massive object takes greater force to accelerate both because its mass resists acceleration and because its weight produces greater friction. Evidence Notebook Think about the motion of the ant and acorn just before each hits the ground; assume the acorn hits at a greater velocity. Infer the relative accelerations, compare the net forces on the ant and acorn, and then review the free-body diagrams you made. 66 Unit 1 Physics and Engineering  EXPLORATION 4 Analyzing Action and Reaction Language Arts Connection Think about a toy that jumps when a spring FIGURE 11: A jumping toy is released, as in Figure 11. An upward force causes acceleration at the start of the jump, yet the spring presses downward on the table. Use a labeled diagram to identify the unbalanced force that accelerates the toy. Analyzing Paired Forces A free-body diagram models only the forces acting on a single object or system treated as a point. A different model is needed to analyze the forces between objects. The car in the visual exerts a forward force as it hits the wall; this force can be considered an action force. The car’s speed decreases suddenly, so you can infer that the wall pushes backward on the car. This force can be considered a reaction force. Unlike the forces in a free-body diagram, action and reaction forces act on different objects. ANNOTATE Label the action and reaction forces shown. Draw and label vectors for other forces in this situation, such as the force pairs that include friction. © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Houghton Mifflin Harcourt Forces in the universe occur in pairs. For every action force, there is a reaction force of equal magnitude in the opposite direction. This relationship is known as Newton’s third law of motion. Each force in the pair acts on a different object, so these forces cannot balance one another. The forces are equal even when one or both objects accelerate. Collaborate With a partner, make a list of examples of action-reaction force pairs you have observed. Compare your list with other groups. The car slows to a stop because of a reaction force to the left, exerted on the car by the wall. In turn, the wall produces a force to the right on the ground, which produces a reaction force to the left on the wall. You can also model the wall and ground as if they were a single object. Think of a swimmer pushing off the wall of a swimming pool; action and reaction forces are always equal, opposite, and exerted on different objects. Lesson 3 Effects of Forces 67  Scientific Knowledge Assumes an Order and Consistency in Natural Systems Mathematical Models of Newton’s Laws The observations about force discussed in this lesson are collectively known as Newton’s laws of motion. First law: An object will remain at rest or in uniform straight-line motion unless acted on by a net external force. Second law: An object acted on by a net external force will accelerate in the direction of that force according to the equation Fnet = ma. Third law: For every action force, there is an equal and opposite reaction force. Evidence Notebook How do the laws apply to the example of the ant and the acorn? Be careful to distinguish between balanced forces and action-reaction pairs. Analyzing Internal Forces Suppose a cardboard tube from a roll of paper towels is lying on a table. The normal force from the table balances the weight of the tube, and the tube does not accelerate. If you press down on the tube with your hand, then the tube, in turn, presses down on the table. The upward normal force from the table, a reaction force, increases as the total downward force increases. The forces on the cardboard tube remain balanced, and the tube still does not accelerate. However, the downward and upward forces on the tube may cause the cardboard to deform. The cross-section of the tube may become oval rather than round, or a dent in © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Heather Hall/Getty Images the side may form. As the external forces from your hand and the table are transferred through the tube, they produce internal forces. Action-reaction force pairs occur between adjacent particles and are, together, called stress. Stress is also the name of a variable, σ ­ , that has units of force per unit area. Scientists and engineers classify stresses into three types: compression, tension, and shear stress. EVALUATE Use your knowledge of root words to label the three types of stress. The dotted outline shows the shape of an object before the forces were applied. The solid shapes show the deformation, or strain, resulting from each stress. tension shear stress compression Aligned forces Aligned forces Nonaligned forces push inward pull outward may push or pull 68 Unit 1 Physics and Engineering  Hands-On Lab Model Stresses You will explore the deformation and failure of a material from different types of stress. RESEARCH QUESTION How do materials show the effects of balanced external forces? MAKE A CLAIM Describe how you think the material will respond when subject to different stresses produced by balanced external forces. Will the deformations or breaks be symmetric? POSSIBLE MATERIALS safety goggles, nonlatex sticky sand, compressible ruler, metric, or similar tool apron, nonlatex gloves clay, or similar material SAFETY INFORMATION Wear safety goggles, a nonlatex apron, and nonlatex gloves during the setup, hands-on, and takedown segments of the activity. Immediately clean up any water, sand, or clay spilled on the floor so it does not become a slip/fall hazard. CARRY OUT THE INVESTIGATION 1. Wearing gloves, shape the material into blocks. 2. Use gloved hands to produce moderate amounts of stress of each type within a block; reshape the material as needed. Try increasing the stress both quickly and gradually. Record your detailed procedure and observations in your Evidence Notebook. DRAW CONCLUSIONS Write a conclusion that addresses each of the points below. Claim Do materials show symmetry when balanced external forces are applied? © Houghton Mifflin Harcourt Publishing Company Evidence Give specific evidence from your observations to support your claim. Reasoning Explain how your evidence supports your claim. Give details of the connections between the evidence you cited and the argument you are making. Evidence Notebook Think about the force pair between a falling object and air. Take into account that air resistance varies with speed. Construct a diagram showing the force pairs for an ant at the beginning, in the middle, and near the end of its fall. Lesson 3 Effects of Forces 69 EXPLORATION 5 Forces and Stresses in Engineering Collaborate With a partner, choose an item you can examine, such as a retractable pen. Discuss how you would evaluate the forces on and within the object. Analyzing Structures One strategy for analyzing complex systems or structures is to look at one part at a time. An engineer might make a free-body diagram as if a selected part were a separate object. For a structure to be stable, there must be a way for the expected forces on each part to be balanced by reaction forces (Fnet = 0). A supporting column of a bridge must provide an upward force to match the combined downward weight of the bridge and vehicles. An engineer may separate the external forces needed to address the design problem—the load—from the forces due to the structure itself. The weight of vehicles might be a bridge’s main load. A highway bridge must be designed for a greater load than a pedestrian bridge. Horizontal forces due to wind are also part of the load on a bridge. Engineering In a truss—the structure shown—the segments may bend slightly under the weight. The top is typically compressed and the bottom is typically stretched. You can model the weight of each segment as a point mass at the center of the segment. INFER For each of the two locations marked by a dot, draw a free-body diagram of the forces acting at that point (Fnet = 0). Use the space below the diagram. compression tension © Houghton Mifflin Harcourt Publishing Company Evidence Notebook How might you use ideas from the design of a truss to help you test designs for a beam in your unit project? 70 Unit 1 Physics and Engineering  Hands-On Lab Testing a Bridge RESEARCH QUESTION How does the distribution of a load affect the forces and stresses on a structure? MAKE A CLAIM How might the paper bridge in Figure 12 respond differently to a line of pennies across the span of paper and to a stack of pennies in the middle? FIGURE 12: A piece of paper forms a bridge between books. POSSIBLE MATERIALS safety goggles paper, sheets (3) pennies or other small books, matching (2) masses (50) SAFETY INFORMATION Wear safety goggles during the setup, hands-on, and takedown segments of the activity. Immediately pick up any items dropped on the floor so they do not become a slip/fall hazard. Wash your hands with soap and water immediately after completing this activity. CARRY OUT THE INVESTIGATION Fold a piece of paper to make a bridge, such as in Figure 12, and place it on two books. Test the bridge by placing pennies, one at a time, and recording the maximum number © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Houghton Mifflin Harcourt before the bridge fails. Make sure that none of the pennies are resting on the books. After each failure, build a new bridge using fresh paper. Test three distributions of pennies. Center of bridge: Spread along length: One end of bridge: DRAW CONCLUSIONS Write a conclusion that addresses each of the points below. Claim What load distribution is most likely to cause the model bridge to collapse? Evidence Give specific evidence from your observations to support your claim. Reasoning Describe, in detail, how the evidence you cited supports your argument. EXTEND Test different bridge designs, such as a simple flat sheet or a sheet cut to resemble a truss. Lesson 3 Effects of Forces 71  Using Forces in Designs For a structure to stay stable or moving as intended, it must withstand the expected forces. An umbrella, for example, must withstand the weight of precipitation. It must withstand the forces that cause it to open and close. An umbrella should also withstand the forces as a person hangs onto the umbrella during a light gust of wind. APPLY Suppose wind blows on the house in Figure 13 from the FIGURE 13: Use this house design to answer left and also produces an upward force on the roof. What reaction the question. forces are needed to support the weight of the roof and counteract forces from the wind? A designer may first look at the external forces on a structure, such as those shown in a free-body diagram. If wind blows on one side of the house in Figure 13, the reaction force you identified comes from the structure of the house. The structure pushes on the ground on the opposite side, which, in turn, opposes the force. The structure of the house must transfer the force from one side to the other without breaking. A designer might add stiff braces, rigid triangles, or tight wires to the structure to balance possible forces. In any building design, many different forces are involved. An engineer uses equations for balanced forces and action-reaction force pairs to break the problem into solvable parts and then puts the parts together to find an overall design solution. For example, to reduce the forces on a support beam or other structure, a designer might choose components that weigh less. Yet the designer might need to widen a support or add more supports to provide greater reaction forces, and so may have to make tradeoffs. Collaborate Analyze the external forces acting on a chair, such as one in which you sit. Think about how forces are transferred through different parts the chair to the floor. With a partner, discuss ways to add support for someone who likes to rock from side to side. Calculating Stress © Houghton Mifflin Harcourt Publishing Company External forces produce stress inside a material. The effect depends, in part, on the area over which the forces act. Think of poking a balloon with a finger and with a pin using equal forces. The balloon is more likely to break with the pin because the force is concentrated into a smaller area. As the area decreases, the stress increases. Designers often seek ways to distribute forces and to reduce stress. They generally avoid having a large force through one narrow part. They may use larger pieces, use more pieces, change the angles, or use curved pieces. SOLVE How does stress (σ) depend on force (F) and area (A)? a. σ = F A b. σ = _​ ​ 1 ​​ c. σ = _ ​ ​F ​​ d. σ = _ ​ ​A ​​ FA A F 72 Unit 1 Physics and Engineering  Using Stresses in Designs One measure of a material’s strength is the maximum amount of stress that can be applied before the material breaks or deforms an unacceptable amount. Tensile, compressive, and shear strengths describe how a material stands up to tension, compression, and shear stresses, respectively. The megapascal (MPa) is a unit of strength equal to 106 N/m2, roughly equal to the weight of a 10 kg object pressing on 1 cm2. SOLVE An engineer is deciding whether to replace a bar made of an aluminum alloy with steel of tensile strength 500 MPa. A bar of the aluminum alloy 2 cm across (square cross section) can withstand pulling up to about 120 000 N. What is the tensile strength of the aluminum alloy, and how would a steel bar of equal tensile strength compare? a. about 600 MPa; an equivalent steel bar would be thicker b. about 300 MPa; an equivalent steel bar would be thinner c. about 60 MPa; an equivalent steel bar would be much thinner In the example, the steel also has much greater density than the aluminum alloy. A steel replacement bar would also have a greater mass. Other parts would need to support a greater weight. Engineers and other designers must consider tradeoffs among strength, size, and weight as well as other factors such as cost and ease of use. FIGURE 14: Donghai Bridge near Shanghai and a simplified model of stresses in beam bridges tension compression © Houghton Mifflin Harcourt Publishing Company Image Credits: (cl) ©Li Chengjun/Getty Images Think about the tradeoffs for the large beam bridge shown in Figure 14. It has supporting columns that reduce the lengths of the unsupported horizontal parts, or spans. The weight causes each span to bend slightly. A material is needed that can support compression in the top surface and tension in the bottom surface. A choice of material might be good for longer spans but require stronger columns, while a different choice might require shorter spans and more columns. EVALUATE Measurements of strength depend on many factors; example values and ranges are listed in the table. Of the materials listed, recommend a material to use for the beam bridge’s vertical supporting columns and a material to use for the horizontal spans. Material Concrete Steel (structural) Wood (pine) Compressive strength (MPa) 20–40 300 30–50 Tensile strength (MPa) 2–5 400–500 40 Shear strength (MPa) 6–17 300–400 6–10 3 Approximate density (kg/m ) 2400 7900 350–590 Recommended use(s) in a beam bridge Lesson 3 Effects of Forces 73  FIGURE 15: Stresses in truss bridges (Astoria Bridge connecting Oregon and Washington) tension compression A truss bridge typically has a framework of triangles, a shape that can resist stress in different directions. As with a beam bridge, the top is compressed and bottom stretched. Diagonal pieces support compression or tension, as needed. The height or thickness of the truss helps provide these extra reaction forces. The open framework results in less weight and less force from the wind than a solid design. EVALUATE Suspension and cable-stayed bridges have cables under tension, as shown in Figure 16. Study the figure, and select all correct statements. a. Cables are used where the design calls for both compression and tension. b. Vertical columns support the weight of the span through compression. c. Vertical columns are pulled upward by tension from the cables. d. Tension acts horizontally as well as vertically. The curved cables of the Golden Gate Bridge (Figure 16a) change the direction of some forces. A design can be adjusted to produce different stresses. A designer can then make use of different materials, such as those used in the four bridges in Figures 14, 15, and 16. FIGURE 16: Stresses in suspension bridges (a) and cable-stayed bridges (b) © Houghton Mifflin Harcourt Publishing Company Image Credits: (tl) ©Grant Faint/Photolibrary/ Getty Images; (cl) ©Richard Müller/EyeEm/Getty Images; (bl) ©rglinsky/Getty Images tension compression a Golden Gate Bridge, San Francisco tension compression b Vasco da Gama Bridge near Lisbon Evidence Notebook Use the forces you have inferred for the ant in the example to evaluate the stresses. Explain the type(s) of stress you expect as the ant falls. 74 Unit 1 Physics and Engineering  TAKE IT FURTHER Guided Research Accelerometers FIGURE 17: A micromechanical accelerometer, used in vehicle stability systems An accelerometer is a device to measure acceleration. It may consist of a mass suspended in a casing Language Arts Connection Research the on a spring. When the accelerometer is at rest or design of a simple one-dimensional accelerometer © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Volker Steger/Science Photo moving at constant velocity, the mass doesn’t shift. that you can make with household materials. Build and When the device accelerates along the axis of the calibrate a working prototype. Use it to measure acceleration spring, the mass compresses or stretches the spring. in two or more situations, such as the following tests: The displacement of the mass is often measured Ride as a passenger in a bus as it speeds up, slows down, and electronically, such as by compressing a material that makes turns. responds by producing electric current. Use the device in an elevator or on an amusement park ride. Think about your motion when riding in a car, bus, or Move the device upward or downward quickly, such as by other vehicle. When the vehicle accelerates forward standing rapidly or jumping off a step. from rest, you are pressed back in your seat briefly and Explore circular motion, such as turning or moving the device then move at the velocity of the vehicle. When the in an arc. vehicle brakes, you continue forward; when it turns, your body slides in the opposite direction. However, Develop an instruction manual. from a point of view outside of the car, your body Identify the parts of the device. Library/Science Source tends to continue moving in a straight line. Your body Give step-by-step instructions for how to use the device. is acting like the mass in an accelerometer. Explain the physical principles behind its function. Why does Accelerometers are used in many fields to determine it work? changes in motion. For example, they measure the Compare the device you built to a commercial device, such as motion of spacecraft and cars, the orientation of the sensors of a cell phone. How accurate is your device? cell phones, and the motion of artificial limbs. Go online to choose one PULLEYS TYPES OF FRICTION MEASURING IN SPACE of these other paths. Lesson 3 Effects of Forces 75 EVALUATE Lesson Self-Check CAN YOU EXPLAIN THE IT? PHENOMENON? FIGURE 18: An acorn and an ant fall from a branch at the same time. The insect hits the ground more gently. Use these details as evidence when you construct your explanation. The effect of gravity on a steel ball, a rubber ball, and an iron ball is similar—all fall with 2 a constant acceleration of 9.8 m/s. A leaf is also subject to the force due to gravity, yet it may fall with a different pattern of motion. In this lesson, you have learned how forces affect motion. You have also learned some © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Spike Mafford/Photodisc/ of the factors that affect the magnitudes and directions of different types of forces. For example, frictional force depends on the normal force but not on area or speed of the object, while air resistance depends on both the area and the speed of the object moving through air. Apply your knowledge to the example of an acorn and an ant, each falling from the same high branch of a tree. Recall that the acorn makes an audible sound as it hits the ground, while the ant hits almost silently and walks away unharmed. Evidence Notebook Refer to your notes in your Evidence Notebook to explain the factors that affect the motion of falling objects. Your explanation should include a discussion of different forces that can act on a falling object, net force, and acceleration due to force. Claim Explain the factors that can cause the motion of the falling ant and the acorn in the example to differ. Put your claim in terms of physical quantities such as force, mass, and acceleration. Evidence List the information given about the ant and acorn, observations you have made Getty Images in labs and other situations, physical laws, and any other information that you are using as evidence to support your claim. Reasoning Explain how the evidence supports your claim. Use free-body or force-pair diagrams to compare the falling ant and acorn. If either or both depart from an acceleration 2 of 9.8 m/s , explain why. 76 Unit 1 Physics and Engineering  Name Date CHECKPOINTS Check Your Understanding Use the diagram to answer the next two questions. Assume the pulley and string are massless and the Use the following description to answer the next system is frictionless. three questions. FIGURE 19: The cart has mass m1 and the descending A book of mass 0.8 kg is pushed left across a table weight has mass m2. with a force of 2.0 N. Kinetic friction provides a force of magnitude 0.2 N. m1 1. Use a free-body diagram to analyze the forces on the object. In what direction is the net force? a. Net force is down. m2 b. Net force is up. c. Net force is to the left. d. Net force is to the right. e. Net force is at a diagonal. 6. Select the correct terms to complete the 2. What is the magnitude of the net force statements about the diagram. on the book? The tension in the vertical part of the string is a. 0 N d. 2.2 N less than | greater than | the same as the tension in b. 1.8 N e. 7.8 N the horizontal part of the same string. c. 2.0 N The net force on the cart-string-weight system is 3. What is the magnitude of the acceleration m1g | m2 g | (m1 + m2)g | (m2 − m1)g. of the book? 2 2 7. Suppose that for trial 1, m1 = 0.2 kg and a. 0 m/s c. 2.5 m/s m2 = 0.5 kg. For trial 2, m1 = 0.4 kg, double the 2 2 b. 2.3 m/s d. 9.8 m/s initial value. How will the acceleration of trial 2 compare to that measured in trial 1? 4. Select the correct terms to complete the sentence a. Acceleration will double. about force and acceleration. Ignore friction. b. Acceleration will be halved. When a bowling ball hits a bowling pin of lesser c. Acceleration will increase by less than mass, it exerts a forward force on the pin. The pin a factor of 2. exerts a forward | backward force on the ball. This © Houghton Mifflin Harcourt Publishing Company d. Acceleration will decrease by less force is less than | more than | equal to the force than a factor of 2. of the ball on the pin. The ball accelerates 8. An engineer wants to increase the load that the forward | backward, and the magnitude of the legs of a wooden stool can support. Which of the ball’s acceleration is less than | more than | following changes would meet that goal? Select all equal to the magnitude of the pin’s acceleration. correct answers. a. Add more legs. 5. Two ice skaters stand facing each other. The first b. Make the legs thicker (larger skater has a mass of 100 kg and the second has a diameter). mass of 50 kg. They push each other away. During 2 c. Use stronger wood of the same density. this push, the first skater accelerates at 3 m/s to the left. The second skater accelerates at d. Use taller legs. e. Make the stool smaller in every dimension. 2