Physics 110 - Lecture 2 - Forces and Newton's Laws PDF

Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 1 FORCES AND NEWTON’S LAWS Chapters 2,4,5  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 2 Student learning objectives Inertia Force Newton's First Law of Motion Net Force and Vectors T...

Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 1 FORCES AND NEWTON’S LAWS Chapters 2,4,5  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 2 Student learning objectives Inertia Force Newton's First Law of Motion Net Force and Vectors The Equilibrium Rule Support Force Equilibrium of Moving Things Force Causes Acceleration Friction Mass and Weight Newton's Second Law of Motion Free Fall Nonfree Fall Newton’s Third Law of Motion Vectors and the Third Law  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 3 Dynamics Dynamics (the study of forces: why things move) is essentially made up of Newton’s Three Laws of motion. The textbook divides these up into three chapters (2,4,5), but we’re going to compress them into one lecture. We should probably start with “What is a force?”  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 4 Inertia Objects of different weight fall to the ground at the same rate in the absence of air resistance. A moving object needs no force to keep it moving in the absence of friction. Inertia is a property of matter to resist changes in motion. It depends on the amount of matter in an object (its mass).  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 5 Forces A force is any push or pull between two objects. Notice that there must be two objects involved Some examples: Gravitational force (weight) – your book is very sloppy with this terminology. For us, the force of gravity will be synonymous with weight Tension – in ropes and strings and wires Normal force – your book calls this “support force”; it’s the force that a surface exerts to keep you from sinking into it Friction – acts opposite to relative motion due to surfaces Buoyant force – upward force in fluids Electric force  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 6 Forces Forces are vectors, since they have a magnitude and a direction. The SI unit of force is the Newton (N) (in Imperial units, it’s the pound (lb.)) When there are many forces acting on an object, we are usually interested in the total or net force, which is the (vector) sum of all the forces. ⃗ I’ll call the net force Σ𝐹𝐹 𝐹𝐹  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 7 Net Force Since it’s a vector sum, the net force depends on the magnitudes and directions of the applied forces.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 8 Equilibrium When the net force on an object is zero ⃗𝐹𝐹 = 0), we say that the object is in (Σ𝐹𝐹 equilibrium (more specifically, mechanical equilibrium). Things that are in mechanical equilibrium have no change in their motion. An unbalanced (nonzero net) force would be needed to change their state of motion  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 9 Equilibrium When the girl holds the rock with as much force upward as gravity pulls downward, the net force on the rock is zero.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 10 Equilibrium The upward tension in the string has the same magnitude as the weight of the bag, so the net force on the bag is zero. The bag of sugar is attracted to Earth with a gravitational force of 2 pounds or 9 Newtons.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 11 Equilibrium Two forces act on the bag Tension force in string acts upward. Force due to gravity acts downward. Both are equal in magnitude and opposite in direction. When added, they cancel to zero. So, the bag remains at rest.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 12 Vectors vs. Scalars Remember the difference!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 13 Equilibrium The scaffold is suspended by two ropes attached to its left and right end. A painter stands at the left end of the scaffold, to the left of the rope. Another painter stands at the right end, just right of center, and is moving towards the left..  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 14 Equilibrium The sum of the upward vectors equals the sum of the ⃗𝐹𝐹 = 0, and the scaffold is in downward vectors. Σ𝐹𝐹 equilibrium. Two upward force vectors are drawn along the ropes, with a longer one on the left and shorter one on the right. Three downward force vectors are drawn, one at each painter and one at the center of the scaffold. F(upwards) = F(downwards) ⃗𝐹𝐹 = 0 Σ𝐹𝐹  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 15 Normal (Support) Forces In physics, the word “normal” means “perpendicular”, so the normal force of a surface on an object is the force the surface exerts perpendicular to that surface.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 16 Quick Question When you stand on two bathroom scales with one foot on each scale and with your weight evenly distributed, each scale will read A. your weight. B. half your weight. C. zero. D. more than your weight.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 17 Quick Question When you stand on two bathroom scales with one foot on each scale and with your weight evenly distributed, each scale will read A. your weight. B. half your weight. C. zero. D. more than your weight. ⃗𝐹𝐹 = 0 You are at rest, so Σ𝐹𝐹 The sum of the two upward support forces is equal to your weight. Your weight is distributed over the two scales. So, each scale reads half your weight.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 18 Quick Question If the gymnast hangs with her weight evenly divided between the two rings, how would scale readings in both supporting ropes compare with her weight? Suppose she hangs with slightly more of her weight supported by the left ring. How would a scale on the right read?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 19 Quick Question If the gymnast hangs with her weight evenly divided between the two rings, how would scale readings in both supporting ropes compare with her weight? Each half Suppose she hangs with slightly more of her weight supported by the left ring. How would a scale on the right read? Less than half  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 20 Equilibrium So far, we’ve looked at static equilibrium, where the object of interest is at rest. ⃗ = 0, since nothing is moving. It’s clear in that case that Σ𝐹𝐹 𝐹𝐹 However, we may also have dynamic equilibrium, where an object is moving at constant speed in a straight line. This type of motion is also called rectilinear motion, and it means once again that Σ𝐹𝐹 ⃗𝐹𝐹 = 0.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 21 Equilibrium Equilibrium test: whether something undergoes change in motion Static equilibrium: A crate at rest (no change in motion). Dynamic equilibrium: A crate pushed at steady speed (no change in motion).  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 22 Quick Question An airplane flies horizontally at constant speed in a straight-line direction. Its state of motion is unchanging. In other words, it is in equilibrium. Two horizontal forces act on the plane. One is the thrust of the propeller that pulls it forward. The other is the force of air resistance (air friction) that acts in the opposite direction. Which force is greater?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 23 Quick Question An airplane flies horizontally at constant speed in a straight-line direction. Its state of motion is unchanging. In other words, it is in equilibrium. Two horizontal forces act on the plane. One is the thrust of the propeller that pulls it forward. The other is the force of air resistance (air friction) that acts in the opposite direction. Which force is greater? They are the same!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 24 Friction Depends on the kinds of material and how much they are pressed together. Is due to tiny surface bumps and to "stickiness" of the atoms on a material's surface. Example: Friction between a crate on a smooth wooden floor is less than that on a rough floor.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 25 Friction Surfaces can also exert forces parallel to the surface (remember that normal forces are perpendicular). These forces are frictional forces. They come in two types, static friction and kinetic (or dynamic) friction. Static friction exists before an object moves to oppose another force, while kinetic exists when an object is sliding.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 26 Quick Question You push a crate at a steady speed in a straight line. If the friction force is 75 N, how much force must you apply? A. More than 75 N. B. Less than 75 N. C. Equal to 75 N. D. Not enough information.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 27 Quick Question You push a crate at a steady speed in a straight line. If the friction force is 75 N, how much force must you apply? A. More than 75 N. B. Less than 75 N. C. Equal to 75 N. D. Not enough information. The crate is in dynamic equilibrium. So there is no NET force acting on it. So you must apply a force that balances out the force of friction. Applied force must be equal and opposite to the force of friction. So if Friction is 75 N to the left, the Applied Force from you is 75 N to the right.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 28 Dynamic Equilibrium When the push on the desk is the same as the force of friction between the desk and the floor, the net force is zero and the desk slides at an unchanging speed.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 29 Quick Question You are riding in a vehicle at a steady speed and toss a coin straight upward. Where will the coin land? A. Behind you. B. Ahead of you. C. In your hand. D. There is not enough information.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 30 Quick Question You are riding in a vehicle at a steady speed and toss a coin straight upward. Where will the coin land? A. Behind you. B. Ahead of you. C. In your hand. D. There is not enough information. Due to the coin's inertia, it continues sideways with the same speed as the vehicle in its up-and-down motion, which is why it lands in your hand.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 31 Newton’s 1st Law So here it is, Newton’s 1st Law of Motion: An object in equilibrium (static or dynamic) will remain in equilibrium unless the net force on the object differs from zero. You may have heard other similar version, like “An object at rest remains at rest unless acted upon by an outside force”, but remember this holds for dynamic equilibrium too!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 32 Free Body Diagrams When examining forces, it is convenient to make free body diagrams (FBDs), which is a diagram for a given mass that has all forces acting on it labelled with the correct directions. While a picture of the object is nice, forces do not care about the shape or size of the object, so a dot or box will suffice.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 33 FBDs a) The tension in the rope is 300 N, equal to Nellie’s weight. b) The tension in each rope is now 150 N, half of Nellie’s weight. In each case,Σ𝐹𝐹⃗𝐹𝐹 = 0.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 34 Vectors Remember that if the forces are not pointing in the same direction, we need to add them as vectors, which might mean using components! To add graphically, remember the parallelogram rule:  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 35 FBDs and Vectors Nellie’s weight is shown by the downward vertical vector. An equal and opposite vector is needed for equilibrium, shown by the dashed vector. Note that the dashed vector is the diagonal of the parallelogram defined by the dotted lines. Using the parallelogram rule, we find that the tension in each rope is more than half her weight.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 36 FBDs and Vectors As the angle between the ropes increases, tension increases so that the resultant (dashed-line vector) remains at 300 N upward, which is required to support 300-N Nellie.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 37 FBDs and Vectors When the ropes supporting Nellie are at different angles to the vertical, the tensions in the two ropes are unequal. By the parallelogram rule, we see that the right rope bears most of the load and has the greater tension.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 38 FBDs and Vectors You can safely hang from a clothesline hanging vertically, but you will break the clothesline if it is strung horizontally. This is also how you can get your car out of the mud!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 39 Quick Question Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 40 Quick Question Two sets of swings are shown at right. If the children on the swings are of equal weights, the ropes of which swing are more likely to break? Girl on right  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 41 Inertia Newton’s 1st Law (NL1) is also called the “Law of Inertia”. Inertia is a tendency for an object to keep doing what it’s doing. The quantity we use to measure inertia is the object’s mass (measured in kilograms). The more mass an object has, the harder it is to change its motion  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 42 Mass Mass: The quantity of matter in an object. It is also the measure of the inertia Inertia is resistance to change in motion Greater Inertia = Greater Mass The pillow has a larger size (volume) but a smaller mass than the battery. Note that volume is the amount of space an object takes up, not how much mass it has.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 43 Mass vs. Weight Also, be sure not to confuse mass with weight. Weight is the gravitational force on an object (in deep space, your weight would be zero) Standard unit of force is the newton (N) Mass is the amount of stuff inside an object, and doesn’t depend on the local gravitational field. Unit of measurement is the kilogram (kg)  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 44 Mass vs. Weight One way to measure mass is to shake an object back and forth (this is how astronauts “weigh” themselves in space). It’s just as difficult to shake a stone in its weightless state in space as it is in its weighted state on Earth.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 45 Mass vs. Weight One kilogram of mass weighs 10 Newtons on Earth. If you prefer, a kilogram weighs 2.2 pounds on Earth The Imperial unit for mass is the stone, which weighs 14 pounds (I told you these units were stupid!) If we want to calculate the gravitational force at other locations, we use 𝑔𝑔𝐹𝐹𝑔𝑔 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚,where 𝑚𝑚 𝑚𝑚is the gravitational acceleration at that location. So weight and mass are proportional, but weight depends on the gravitational field strength!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 46 Quick Question Does a 2-kilogram bunch of bananas have twice as much inertia as a 1-kilogram loaf of bread? Twice as much mass? Twice as much volume? Twice as much weight, when weighed in the same location?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 47 Quick Question Does a 2-kilogram bunch of bananas have twice as much inertia as a 1-kilogram loaf of bread? Yes Twice as much mass? Yes Twice as much volume? No Twice as much weight, when weighed in the same location? Yes  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 48 Inertia = Mass  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 49 Quick Question When the string is pulled down slowly, the top string breaks, which best illustrates the A. weight of the ball. B. mass of the ball. C. volume of the ball. D. density of the ball.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 50 Quick Question When the string is pulled down slowly, the top string breaks, which best illustrates the A. weight of the ball. B. mass of the ball. C. volume of the ball. D. density of the ball The tension in the top string is the pulling tension in the bottom string plus the weight of the ball. So, the top string has greater tension and breaks first.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 51 Newton’s 2nd Law What if the net force is not zero (meaning the system is not in mechanical equilibrium)? Newton’s 2nd Law says ⃗𝐹𝐹 = 𝑚𝑚𝑎𝑎 Σ𝐹𝐹 ⃗ 𝑎𝑎 Here 𝑚𝑚 is the mass and 𝑎𝑎 ⃗ is the resulting acceleration. So this is the connection between kinematics and dynamics: forces cause accelerations Acceleration is inversely proportional to mass. 1 Acceleration ∼ mass  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 52 Newton’s 2nd Law This also means the acceleration is equal to the net force divided by the mass. If the net force acting on an object doubles, its acceleration is doubled. If the mass is doubled, then acceleration will be halved. If both the net force and the mass are doubled, the acceleration will be unchanged.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 53 Newton's second law of motion Newton's second law relates acceleration, force and mass: The acceleration produced by a net force on an object is directly proportional to the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object. In equation form: Acceleration = net force mass  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 54 Quick Question If a car can accelerate at 2 m/s2, what acceleration can it attain if it is towing another car of equal mass?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 55 Quick Question If a car can accelerate at 2 m/s2, what acceleration can it attain if it is towing another car of equal mass? 1 m/s2 Explanation F = ma a = F/m = 2 m/s2 But now m = 2m a = F/2m = 2 /2 = 1 m/s2  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 56 Quick Question How much force, or thrust, must a 30,000-kg jet plane develop to achieve an acceleration of 1.5 m/s2?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 57 Quick Question How much force, or thrust, must a 30,000-kg jet plane develop to achieve an acceleration of 1.5 m/s2? 45 kN F = ma F = (30,000)(1.5) = 45,000N F = 45 kN  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 58 Newton's second law of motion  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 59 Free Fall Now we can explain why (in the absence of air resistance) all masses fall at the same rate. Even though the force of gravity is larger for a larger mass, its mass is also larger by the same factor, so the acceleration (which is the ratio 𝐹𝐹𝐹𝐹/𝑚𝑚𝑚𝑚) is the same!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 60 Quick Question A cart is pushed and undergoes a certain acceleration. Consider how the acceleration would compare if it were pushed with twice the net force while its mass increased by four. Then its acceleration would be A. one quarter. B. half. C. twice. D. the same.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 61 Quick Question A cart is pushed and undergoes a certain acceleration. Consider how the acceleration would compare if it were pushed with twice the net force while its mass increased by four. Then its acceleration would be A. one quarter. B. half. C. twice. D. the same.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 62 Quick Question A 5-kg iron ball and a 10-kg iron ball are dropped from rest. For negligible air resistance, the acceleration of the heavier ball will be A. less. B. the same. C. more. D. undetermined.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 63 Quick Question A 5-kg iron ball and a 10-kg iron ball are dropped from rest. For negligible air resistance, the acceleration of the heavier ball will be A. less. B. the same. C. more. D. undetermined. Both are in "free fall." Hence their equal acceleration  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 64 Quick Question A 5-kg iron ball and a 10-kg iron ball are dropped from rest. When the free-falling 5-kg ball reaches a speed of 10 m/s, the speed of the free-falling 10-kg ball is A. less than 10 m/s. B. 10 m/s. C. more than 10 m/s. D. undetermined.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 65 Quick Question A 5-kg iron ball and a 10-kg iron ball are dropped from rest. When the free-falling 5-kg ball reaches a speed of 10 m/s, the speed of the free-falling 10-kg ball is A. less than 10 m/s. B. 10 m/s. C. more than 10 m/s. D. undetermined. Both are in "free fall." Hence their equal speeds.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 66 Nonfree Fall When an object falls downward through the air it experiences force of gravity pulling it downward. air drag force acting upward. The condition of nonfree fall occurs when air resistance is nonnegligible. depends on two things:  speed and  frontal surface area.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 67 Nonfree fall When the object is moving fast enough so that air resistance builds up to balance the force of gravity. Then no net force No acceleration Velocity does not change Terminal velocity when air resistance balances weight, net force is zero occurs when acceleration terminates refers to terminal speed along with the direction of motion, which is downward.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 68 Air Resistance If there is drag, the acceleration will not be a constant 𝑚𝑚𝑚𝑚. Drag is proportional to the speed of an object: the faster it goes, the greater the drag force. So the acceleration of a falling object would start at 𝑚𝑚 , but would drop off to 𝑚𝑚 zero as the object speeds up. When the acceleration finally reaches zero (so that the weight and the drag force have equal magnitude), the velocity the object has is called the terminal velocity.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 69 Skydiver in fall after jumping from a plane. Weight and air resistance act on the falling object. As falling speed increases, air resistance on diver builds up, net force is reduced, and acceleration is reduced. When air resistance equals the diver's weight, net force is zero and acceleration terminates. Diver reaches terminal velocity, then continues the fall at constant speed.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 70 Quick Question When a 20-N falling object encounters 5 N of air resistance, its acceleration of fall is A. less than g. B. more than g. C. g. D. terminated.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 71 Quick Question When a 20-N falling object encounters 5 N of air resistance, its acceleration of fall is A. less than g. B. more than g. C. g. D. terminated. Acceleration of a nonfree fall is always less than g. Acceleration will actually be (20N − 5 N)/2 kg = 7.5 m/s2.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 72 Quick Question Consider a heavy and a light person jumping together with same-size parachutes from the same altitude. Who will reach the ground first? A. The light person B. The heavy person C. Both will reach at the same time. D. Not enough information is provided.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 73 Quick Question Consider a heavy and a light person jumping together with same-size parachutes from the same altitude. Who will reach the ground first? A. The light person B. The heavy person C. Both will reach at the same time. D. Not enough information is provided. Both people feel a similar upward drag force at any given speed. The heavier person has a greater downward weight force than the lighter person. Thus, the heavier person must drop farther before the upward drag force balances the downward weight force, resulting in a greater terminal speed.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 74 Quick Question If the rock and the feather are dropped in a space where the air has been removed by a vacuum pump, A. the feather hits the bottom first, before the rock hits. B. the rock hits the bottom first, before the feather hits. C. the rock and the feather drop together side by side. D. more information is needed to determine whether the rock or the feather hits bottom first.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 75 Quick Question If the rock and the feather are dropped in a space where the air has been removed by a vacuum pump, A. the feather hits the bottom first, before the rock hits. B. the rock hits the bottom first, before the feather hits. C. the rock and the feather drop together side by side. D. more information is needed to determine whether the rock or the feather hits bottom first. There is no air, because it is vacuum. Hence no air resistance.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 80 Newton’s 3rd Law Newton’s 3rd Law states that To every action there is always an opposed equal reaction. It is important to note that these action-reaction pairs of forces always act on different objects!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 81 Newton’s 3rd Law The interaction that drives the nail is the same as the one that halts the hammer.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 82 Newton’s 3rd Law In every interaction, the forces always occur in pairs. You push against the floor, and the floor simultaneously pushes against you. The tires of a car interact with the road to produce the car’s motion. The tires push against the road, and the road simultaneously pushes back on the tires. When swimming, you push the water backward, and the water pushes you forward. When the girl jumps to shore, the boat moves backward.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 83 Action-Reaction Pairs When action is A exerts force on B, the reaction is simply B exerts force on A.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 84 Action-Reaction Pairs Earth is pulled up by the boulder with just as much force as the boulder is pulled down by Earth. So why doesn’t Earth “jump up” to meet the boulder?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 85 Action-Reaction Pairs Just because the forces are the same in magnitude, the accelerations are certainly not! Although the pair of forces between the boulder and Earth is the same, the masses are quite unequal. Acceleration is not only proportional to the net force, but it is also inversely proportional to the mass. Because Earth has a huge mass, we don’t sense its infinitesimally small acceleration.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 86 Action-Reaction Pairs The cannonball undergoes more acceleration than the cannon because its mass is much smaller.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 87 Action-Reaction Pairs F represents both the action and reaction forces; m (large), the mass of the cannon; and m (small), the mass of the cannonball. Do you see why the change in the velocity of the cannonball is greater compared with the change in velocity of the cannon?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 88 Action-Reaction Pairs The balloon recoils from the escaping air and climbs upward. If a balloon is released and allowed to move, it accelerates as the air comes out. A rocket accelerates in much the same way—it continually recoils from the exhaust gases ejected from its engine. Each molecule of exhaust gas acts like a tiny molecular cannonball shot downward from the rocket.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 89 Quick Question A tug of war occurs between boys and girls on a polished floor that’s somewhat slippery. If the boys are wearing socks and the girls are wearing rubber-soled shoes, who will surely win, and why?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 90 Quick Question A tug of war occurs between boys and girls on a polished floor that’s somewhat slippery. If the boys are wearing socks and the girls are wearing rubber-soled shoes, who will surely win, and why? Girls As no friction force on boys means net force is not zero  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 91 Action-Reaction Pairs So why don’t these pairs just cancel each other out and ⃗𝐹𝐹 = 0? produce Σ𝐹𝐹 We need to be careful about the system we are examining.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 92 Defining Systems A force acts on the orange, and the orange accelerates to the right. The dashed line surrounding the orange encloses and defines the system.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 93 Defining Systems The vector that pokes outside the dashed line represents an external force on the system. The system (that is, the orange) accelerates in accord with Newton’s second law. The force on the orange, provided by the apple, is not cancelled by the reaction force on the apple. The orange still accelerates.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 94 Defining Systems The force is provided by an apple, which doesn’t change our analysis. The apple is outside the system. The fact that the orange simultaneously exerts a force on the apple, which is external to the system, may affect the apple (another system), but not the orange. You can’t cancel a force on the orange with a force on the apple. So in this case the action and reaction forces don’t cancel.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 95 Defining Systems a) Action and reaction forces cancel. b) When the floor pushes on the apple (reaction to the apple’s push on the floor), the orange-apple system accelerates.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 96 Defining Systems When the force pair is internal to the orange-apple system, the forces do cancel each other. They play no role in accelerating the system. A force external to the system is needed for acceleration. When the apple pushes against the floor, the floor simultaneously pushes on the apple—an external force on the system. The system accelerates to the right. Inside a baseball, trillions of interatomic forces hold the ball together but play no role in accelerating the ball. They are part of action-reaction pairs within the ball, but they combine to zero. If the action-reaction forces are internal to the system, then they cancel and the system does not accelerate. A force external to the ball, such as a swinging bat provides, is needed to accelerate the ball.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 97 Horse-Cart Problem All the pairs of forces that act on the horse and cart are shown. The acceleration of the horse-cart system is due to the net force F – f.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 98 Horse-Cart Problem Will the horse’s pull on the cart be canceled by the opposite and equal pull by the cart on the horse, thus making acceleration impossible? From the farmer’s point of view, the only concern is with the force that is exerted on the cart system. The net force on the cart, divided by the mass of the cart, is the acceleration. The farmer doesn’t care about the reaction on the horse.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 99 Horse-Cart Problem Now look at the horse system. The opposite reaction force by the cart on the horse restrains the horse. Without this force, the horse could freely gallop to the market. The horse moves forward by interacting with the ground. When the horse pushes backward on the ground, the ground simultaneously pushes forward on the horse.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 100 Horse-Cart Problem Look at the horse-cart system as a whole. The pull of the horse on the cart and the reaction of the cart on the horse are internal forces within the system. They contribute nothing to the acceleration of the horse-cart system. They cancel and can be neglected. To move across the ground, there must be an interaction between the horse-cart system and the ground. It is the outside reaction by the ground that pushes the system.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 101 Quick Question What is the net force that acts on the cart? On the horse? On the ground?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 102 Quick Question What is the net force that acts on the cart? ∑ 𝑭𝑭 = 𝑷𝑷 − 𝒇𝒇 On the horse? ∑ 𝑭𝑭𝑯𝑯 = 𝑷𝑷 − 𝑭𝑭 On the ground? ∑ 𝑭𝑭𝑮𝑮 = 𝒇𝒇 − 𝑭𝑭  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 103 Action-Reaction Pairs If a sheet of paper is held in midair, the heavyweight champion of the world could not strike the paper with a force of 200 N (45 pounds). The paper is not capable of exerting a reaction force of 200 N, and you cannot have an action force without a reaction force. If the paper is against the wall, then the wall will easily assist the paper in providing 200 N of reaction force, and more if needed!  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 104 Vectors Vector components Vertical and horizontal components of a vector are perpendicular to each other. Determined by resolution. As the stone is released, its vertical component and its horizontal component are given as vertical and horizontal vectors. The velocity of the stone continues from the release point, going between the other components. A dashed line rises and falls below the velocity component of the stone.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 105 Quick Question Nellie Newton pulls on the sled as shown. Which component of her force F is greater? What two other forces (not shown) act on the sled?  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 106 Quick Question Nellie Newton pulls on the sled as shown. Which component of her force F is greater? The horizontal component Fx is greater. What two other forces (not shown) act on the sled? Weight mg and normal N also act on the sled.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 107 Summary So, our study of forces so far amounts to knowing Newton’s Three Laws: 1. (Law of Inertia) An object will remain in equilibrium unless the net force on that object is not zero. 2. If the net force is not zero, then it will accelerate according to Σ𝐹𝐹⃗𝐹𝐹 = 𝑚𝑚𝑎𝑎 ⃗. 𝑎𝑎 3. For every (action) force, there is a (reaction) force of equal magnitude but opposite direction.  Physics 110 - Lecture 2 - Summer 2024 - Sonia Katdare 108 Summary To solve any force problem, you can just follow these steps: 1. Draw a FBD for each system (mass) of interest. Clearly label all forces as vectors with their directions. 2. Add up the forces (possibly with components in each ⃗𝐹𝐹. direction) to get Σ𝐹𝐹 3. Use Newton’s 2nd Law Σ𝐹𝐹 ⃗𝐹𝐹 = 𝑚𝑚𝑎𝑎 (or, if in equilibrium, Newton’s 1st Law with 𝑎𝑎 ⃗ = 0).