TJ AP Physics C Unit 2 Dynamics PDF

9/11/2023 Unit 2 Topics Newton’s Laws of Motion Types of Forces: Weight, Normal For...

9/11/2023 Unit 2 Topics Newton’s Laws of Motion Types of Forces: Weight, Normal Force, Tension Solving Problems with Newton’s Laws: The Method Inclines Unit 2: Dynamics Friction AP Physics C Uniform Circular Motion Mrs. Kelly Air Drag Lab Skill: Linearizing Data 1 2 Why Dynamics? Defining Force Study of forces Force: A push or pull that Kinematics: Describe motion changes an object’s velocity Dynamics: Why is motion? 3 4 Newton’s Laws of Motion Newton’s First Law of Motion Often called the law of inertia: 1. Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. 5 6 1  9/11/2023 7 8 Newton’s Second Law of Motion Newton’s Third Law of Motion Acceleration is proportional to Whenever one object exerts a force on a second net force and inversely object, the second exerts an equal force in the proportional to mass. opposite direction on the first. (Units of Force?) Newton’s Second Law: 𝐹 = 𝑚𝑎⃗ 𝐹 = 𝑚𝑎⃗ 9 10 11 12 2  9/11/2023 Types of Forces: Weight Types of Forces: Normal Force 𝑭𝒂𝒑𝒑 Weight is the force exerted on an Normal force: Contact force that is object by gravity. exerted perpendicular to the Close to the surface of the Earth, common surface of contact weight is: 𝐹 = 𝑚𝑔⃗ Question: What is the magnitude of the normal force in the picture? (Greater, less than, or equal to mg?) 13 14 Types of Force: Tension Types of Force: Friction Contact force pulling from a string, rope or wire Resists motion Always in direction of string or rope Contact force If rope is massless (usually assumed), tension is constant in the rope Parallel to surfaces More on this later 15 16 Identifying Forces: Practice Homework You are pulling a box along a frictionless Webassign problems surface. The magnitude of the force exerted is 𝐹 = 40.0 N, and it is exerted at a 30.0°angle as shown. Identify all the forces acting on the box in the picture to the right. Be sure to label the forces. If possible, draw vectors indicating the direction of these forces. 17 18 3  9/11/2023 Do-Now: Day 2 Unit 2 Topics You are pulling a box along a frictionless Newton’s Laws of Motion surface. The magnitude of the force Types of Forces: Weight, Normal Force exerted is 𝐹 = 40.0 N, and it is exerted at a 30.0°angle as shown. Solving Problems with Newton’s Laws: The Method Inclines Identify all the forces acting on the box in Friction the picture to the right. Be sure to label Uniform Circular Motion the forces. If possible, draw vectors indicating the direction of these forces. Air Drag Lab Skill: Linearizing Data 19 20 Do-Now: Discussion Dynamics Problems: The Method You are pulling a box along a frictionless 1. Draw a sketch with coordinate system. surface. The magnitude of the force exerted is 𝐹 = 40.0 N, and it is exerted at 2. Draw a free-body diagram. a 30.0°angle as shown. 3. Draw a component diagram: Resolve vectors into components. Identify all the forces acting on the box in the picture to the right. Be sure to label 4. Write Newton’s 2nd Law in vector form. the forces. If possible, draw vectors 5. Write Newton’s 2nd Law in component form. indicating the direction of these forces. 6. Solve. 21 22 Class Problem Force Stations: Using The Method You are pulling a box along a frictionless surface. Use your knowledge of The Method to solve for the missing items at each station. Follow the The magnitude of the force exerted is 𝐹 = directions at each station. 40.0 N, and it is exerted at a 30.0°angle as shown. If the stations are busy, try this problem (Difficulty 2/3): a) Draw the Raw FBD and the component FBD. Two boxes are connected by a lightweight cord and are resting on a table. The boxes have masses of 𝑚 and 𝑚. A variable horizontal force of 𝐹 𝑡 = 𝐶𝑡 is applied by a person to the box with mass Write Newton’s 2nd Law equations (vector 𝑚. Find: and component forms). a) If the boxes start from rest, what are the boxes’ velocities as a function of t? b) Find the acceleration of the box b) The middle string will break when its tension exceeds some tension 𝐹. Find the time will this occur in terms of the given variables. c) The magnitude of the normal force on the box Answers: A) 𝑣 𝑡 = , B) 𝑡 = ( ) 23 24 4  9/11/2023 Worked Example: Try This Group Problem: Try This Draw a free body diagram for the Draw a free body diagram for the two blocks in this diagram. What two blocks in this diagram. What are the possible directions Block are the possible directions Block A can move? A can move? 𝑚 𝑚 Problem: Block A has vertical 𝑚 AND horizontal components of 𝑚 acceleration! (Doable, but messy). 25 26 Dynamics Problems: The Method Group Problem: Variable Force 1. Draw a sketch with coordinate system. Two boxes are connected by a lightweight cord and are resting on a table. The boxes have masses of 12.0 kg and 10.0 kg. A variable horizontal force of 2. Draw a free-body diagram. 𝐹 𝑡 = 𝐵𝑡 is applied by a person to the 10.0 kg box, where B = 5.00 N/s. Find: A. Include + label all forces on object. a) If the boxes start from rest, what are the boxes’ velocities when t = 4 s? B. Magnitudes and directions accurate as possible. C. Multiple objects  separate FBDs. b) The middle string will break when its tension exceeds 100 N. What time will this occur? 3. Resolve vectors into components. 4. Apply Newton’s 2nd law to each component. 5. Solve. 27 28 Homework Do Now: Day 3 Webassign problems We want to develop a model of how the friction force works. Predict which of the following factors will affect the friction force: Object Object Object Surface Object Mass Surface Area Material Material With a partner, design mini-experiments that will test whether the friction force depends on the above variables. For each experiment, design a procedure Surface and discuss your expected results. 29 30 5  9/11/2023 Unit 2 Topics Newton’s Laws of Motion Types of Forces: Weight, Normal Force Solving Problems with Newton’s Laws: The Method Inclines Homework Discussion Friction Uniform Circular Motion Air Drag Lab Skill: Linearizing Data 31 32 Defining Friction 𝑭𝑷 Modeling Friction Force that resists relative motion of surfaces Object Question: Suppose the block to the right is traveling at a constant velocity under Object Object Object Surface an applied force 𝐹. What is the Surface Mass Material Material direction of the friction force? Area What is the magnitude of the friction Surface force? 33 34 4-8 Applications Involving Friction, Inclines Modeling Sliding Friction Kinetic Friction 𝐹 =𝜇 𝐹 𝐹 = Normal Force 𝜇 = Coefficient of kinetic friction (depends on object/surface material) Friction opposes direction of motion 35 36 6  9/11/2023 Modeling Static Friction Static Friction 𝐹 ≤𝜇 𝐹 𝐹 = Normal Force 𝜇 = Coefficient of kinetic friction (object/surface material) External forces must overcome static friction to make object to move 37 38 39 40 Class Problem A box rests on a rough 30.0° incline. a) Draw a free-body diagram, showing all the forces acting on the box. b) How would the diagram change if the box were sliding down the plane? c) How would it change if the box were sliding up the plane after an initial shove? d) Suppose the coefficient of static friction between the block and ramp is 𝜇. At what angle does the block start to slide? 41 42 7  9/11/2023 Mini-Lab Now: Demonstrations Find 𝜇 and 𝜇 for the block-track system. Sit and Spin Test your prediction! At what angle does the block start to slide? Cup of water on a string 43 44 Uniform Circular Motion Uniform circular motion: motion in a circle of constant radius at constant speed 45 46 Acceleration in UCM Summary: Centripetal Acceleration Centripetal Acceleration 𝑣 𝑎 = − 𝑟̂ 𝑟 Objects in UCM have centripetal acceleration Acceleration points toward center of circle (−𝑟̂ direction) 𝑟̂ 47 48 8  9/11/2023 More UCM Quantities Class Problem v Quantity Variable/Formula Description A 150-g ball at the end of a string is revolving uniformly in a vertical on the end Frequency 𝑓 Revolutions per second of a 1.10-m cord. The ball is moving at a speed of 6.56 m/s. a) What is the tension of the cord at the R 1 bottom of the arc? Period 𝑇= Time to complete 1 revolution 𝑓 b) What is the tension of the cord in the top of the arc? 2𝜋𝑟 Speed 𝑣= 1 circumference per period 𝑇 49 50 Do-Now: Day 5 A 1000-kg car rounds on a curve on a flat road of radius 50 m at a speed of 14 m/s. a) What is the minimum possible coefficient of static friction for the car to make this turn? b) What is the maximum speed possible Homework Discussion on this curve if the pavement is icy and 𝜇 =0.25? 51 52 Unit 2 Topics Do-Now: Discussion Newton’s Laws of Motion A 1000-kg car rounds on a curve on a flat Types of Forces: Weight, Normal Force road of radius 50 m at a speed of 14 m/s. Solving Problems with Newton’s Laws: The Method a) What is the minimum possible coefficient of static friction for the car to Inclines make this turn? Friction b) What is the maximum speed possible on this curve if the pavement is icy and Uniform Circular Motion 𝜇 =0.25? Air Drag Lab Skill: Linearizing Data 53 54 9  9/11/2023 UCM Application: Banked Turns 𝐹 𝐹 𝐹 𝐹 𝐹 𝑚𝑔 𝑚𝑔 𝑚𝑔 A B C 55 56 y y 𝐹 x x A B y x x 𝑚𝑔 y C D 57 58 59 60 10  9/11/2023 Class Problem Class Problem A curve with a radius of 100 m is banked at 15°. The road is icy, so A curve with a radius of 100 m is banked at 15°. The road is icy, so there is no frictional force on the tires. there is no frictional force on the tires. a. What is the appropriate speed to traverse this curve? a. What is the appropriate speed to traverse this curve? b. The ice melts, and the car can navigate the curve at 25 m/s. Draw and label the forces on the car. c. What is the minimum coefficient of static friction needed for the car to round the curve at 25 m/s? 61 62 Do-Now: Day 6 A cart is released from rest at the top of a ramp. An experimental system measures the cart’s speed at different points along the ramp. a. Download the data on the class website. Create a graph of the independent variable vs. the dependent variable. What type of graph is this? (Linear, quadratic, exponential, etc.?) b. Discuss: Is it possible to find the acceleration solely from these data? If so, explain how. If not, explain what information you need. Homework Discussion Photogates (measure speed) 63 64 Unit 2 Topics Do-Now: Discussion Newton’s Laws of Motion A cart is released from rest at the top of a ramp. An experimental system measures the cart’s speed at different displacements along the ramp. Types of Forces: Weight, Normal Force a. Download the data on the class website. Create a graph of the independent Solving Problems with Newton’s Laws: The Method variable vs. the dependent variable. What type of graph is this? (Linear, quadratic, exponential, etc.?) Inclines b. Discuss: Is it possible to find the acceleration solely from these data? If so, Friction explain how. If not, explain what information you need. Uniform Circular Motion Photogates (measure speed) Lab Skill: Linearizing Data Air Drag 65 66 11  9/11/2023 Skill: Data Linearization Now: Air Resistance Linearizing Data = Adjusting the variables so that you can graph a What do we know about air straight line. resistance? Use slope and/or intercepts to calculate physical quantities. How does motion with air Why? resistance differ from motion Linear graphs are easy. without air resistance? Accounts for variation across trials What factors might affect air This is on the AP resistance? For our Do-Now: What equation relates ∆𝑥 and 𝑣? (Assume constant acceleration). 67 68 Lab: Developing a Model of Air Resistance Goal: develop an equation to for the drag force on a set of coffee filters. 69 12