Applying Newton s Second Law

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Bridget Andrews
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1 Applying Newton s Second Law Problem-Solving Strategy for Dynamics Problems Sketch and Translate: Sketch the situation described in the problem; include all known information. Choose a system object and make a list of objects that interact with the system. Indicate the direction of acceleration, if you know it. Simplify and Diagram: Consider the system as a particle. Decide if you can ignore any interactions of the environment with the system object. Draw a force diagram for the system. Label the forces with two subscripts. Make sure the diagram is consistent with the acceleration of the system object (if known). Include perpendicular x- and y-coordinate axes. Represent Mathematically: Apply Newton s Second Law in component form to the situation you represented in the force diagram. Add kinematics equations if necessary. Solve and Evaluate: Solve the equations for an unknown quantity and evaluate the results to see if they are reasonable (the magnitude of the answer, its units, how the solution changes in limiting cases, and so forth). Need Some Help? Here is an example that applies the strategy shown above: A 5-kg object (the Earth exerts a 50 N force on it) is lifted by a cable that exerts a 70 N force on it. Calculate the acceleration of the object. Translate: The object is our system; the Earth and the cable interact with the object. The acceleration is up. y F C on O F E on O Simplify and Diagram: In this case there are two forces exerted on the object one exerted by the cable and one exerted by the Earth. We choose the positive axis to be down. Represent Mathematically: Newton s second law in component form: a O y F C on O y F E on O y m O Solve and Evaluate: The component of the force exerted by the cable is negative as the force points in the negative direction, the component of the force exerted by the Earth is positive. Thus ( 70 N) 50 N a O y ( 4 N/kg) = (-4 m/s 2 ). The negative sign of acceleration means that it is pointed 5 kg upward the elevator is accelerating in the upward direct (not necessarily moving in the upward direction, it can be slowing down). Lesson Activity adapted from PUM and Active Learning Guide, Etkina and Van Heuvelen,

2 1. George is participating in a rock lifting contest. The 68 kg rock starts at rest on the ground. If George exerts a 720N force on the rock, what is the acceleration of the rock as he lifts it off the ground? Draw a Force Diagram for the rock as George lifts it. Are there any balanced forces? Explain. Draw a Motion Diagram for the rock. Is your motion diagram consistent with your force diagram? Explain. What physical quantities do you know? What physical quantities can you solve for? Use Newton s 2 nd Law to find the rock s acceleration. Lesson Activity adapted from PUM and Active Learning Guide, Etkina and Van Heuvelen,

2. Buster (mass = 72 kg) drives his new SUV into a wall at 50 mph. The seat belt exerts a force of 5256 N on Buster. What is Buster s acceleration? How many G s is this?

3 2. Buster (mass = 72 kg) drives his new SUV into a wall at 50 mph. The seat belt exerts a force of 5256 N on Buster. What is Buster s acceleration? How many G s is this? (G is a common notation for acceleration - 1 G = 9.8m/s 2, 2G s = 19.6m/s 2, etc.) Draw a Force Diagram for Buster. Are there any balanced forces? Explain. Draw a motion diagram for Buster. Is your motion diagram consistent with your force diagram? What physical quantities do you know? What can you solve for? Use Newton s 2 nd Law to solve for Buster s acceleration. Lesson Activity adapted from PUM and Active Learning Guide, Etkina and Van Heuvelen,

3. The Twilight Zone Tower of Terror at Disney World is not really a free fall ride; the ride vehicle actually pulls riders downwards with an acceleration greater than 9.8m/s 2.

4 3. The Twilight Zone Tower of Terror at Disney World is not really a free fall ride; the ride vehicle actually pulls riders downwards with an acceleration greater than 9.8m/s 2. If the acceleration of the elevator is 13m/s 2, what is the force that the cables must exert on the ride vehicle? You estimate that the ride vehicle has a mass of 2500kg when fully loaded with passengers. Draw a Force Diagram for the elevator. Are there any balanced forces? Draw a motion diagram for the elevator. Is your motion diagram consistent with your force diagram? What physical quantities do you know? What can you solve for? Use Newton s 2 nd Law to solve for the force of the cables on the elevator. Lesson Activity adapted from PUM and Active Learning Guide, Etkina and Van Heuvelen,

5 4. Regular Problem Homework A 72 kg crate on a freight elevator accelerates upwards at a rate of 0.2 m/s 2 while moving down. Represent the object with a sketch, motion diagram, force diagram, equation and solve for anything you do not know. 5. Regular Problem In a grocery store, you push a 14.5 kg shopping cart. It is initially rolling at a constant speed of 2 m/s. You push on it in the direction opposite to its motion exerting a force of 12 N. a) Draw a force diagram and a motion diagram for the cart when you start pushing in the direction opposite to its motion. b) Assuming you push the cart exerting constant force for a while, how far will it travel in 3 seconds? (Ignore friction for all parts of this problem.) Use the problem-solving strategy steps illustrated above. Lesson Activity adapted from PUM and Active Learning Guide, Etkina and Van Heuvelen,

EQUATIONS OF MOTION: RECTANGULAR COORDINATES

EQUATIONS OF MOTION: RECTANGULAR COORDINATES Today s Objectives: Students will be able to: 1. Apply Newton s second law to determine forces and accelerations for particles in rectilinear motion. In-Class