1D Motion: Review Packet Problem 1: Consider the following eight velocity vs. time graphs. Positive velocity is forward velocity.

Transcription

1 Name: 1D Motion: Review Packet Problem 1: Consider the following eight velocity vs. time graphs. Positive velocity is forward velocity. Graph A Graph B Graph C Graph D Graph E Graph F Graph G Graph H (a) Rank the objects based on their acceleration from most forward to most backward. (If any two graphs show the same acceleration, put an equal sign between those letters.) Most forward acceleration Most backward acceleration (b) Rank the objects based on their displacement over the 4-second interval. Most forward displacement Most backward displacement (c) Rank the objects based on their distance traveled over the 4-second interval. Remember that distance is a scalar that can never be less than zero. Longest distance Shortest distance (d) Positive net work is done on an object if it gains kinetic energy. Negative net work is done on an object if it loses kinetic energy. (i) For which two objects was positive net work done during the 4-second interval? (ii) For which two objects was negative net work done during the 4-second interval? (iii)for which four objects was zero net work done during the interval? (e) Which three graphs could represent a cart with frictionless bearings on this incline? Explain your reasoning.

2 2D Motion: Review Packet Problem 1: An object of mass m is projected horizontally from the top of a building. The object s initial velocity is v, its initial height is H, and it travels a horizontal distance D before striking the ground. Let t represent the time that the object is a projectile. (a) Write two equations that relate the quantities v, H, D, t, and fundamental constants. (b) Write a single equation that expresses D in terms of v, H, fundamental constants, and NOT time. (c) Suppose the ball is launched a second time with greater initial velocity. What must the velocity be multiplied by in order to double the horizontal landing distance D? Explain your reasoning. (d) Suppose the ball is launched a third time with the initial velocity v, but from a greater initial height. What must H be multiplied by in order to double the horizontal landing distance D? Explain your reasoning. (e) In terms of the given quantities and fundamental constants, write an expression for the net force acting on the object while it is a projectile. Explain your reasoning. (f) In terms of the given quantities and fundamental constants, write an expression for the object s kinetic energy just before striking the ground. Explain your reasoning.

3 Forces: Review Packet Problem 1: For each case, draw and label the forces (not components) acting on the object. Each arrow must start on the white dot and be straight. Then write one or more equations relating the forces on the object. ly, rank the three forces in the blanks. Acceptable labels are F W (or F g or mg), F N, F f, F T, and F applied. (a) Car slows down (3 (b) Child has a constant speed (3 Rank the forces: = > Rank the forces: > > (c) Box moves with constant speed (4 Rank the forces: > > > (d) Block held at rest against wall (4 Rank the forces: = > = (e) A man and bicycle go over a hill at constant speed (2 (f) The satellite orbits the Earth (1 force)

4 Problem 2: Provide written answers and explanations to the following questions. (a) A loaded barrel is attached to a rope that passes around an overhead pulley and is tied to a ring on the floor. Linda, a construction worker, plans to untie the rope from the ring, pull on the barrel to lift it one meter higher, than retie the rope. Linda s mass is 80 kg, she is capable of lifting twice her weight, and the loaded barrel has a mass of 120 kg. Explain what is wrong with Linda s plan. (b) A person using a rope pulls a heavy slab across a rough horizontal surface at constant speed. The person s applied tension force is T, the object s weight is W, the normal force is N, and the frictional force is f. A student observes this situation and states, I think that T = f and that W = N. Because f = N and < 1, the correct ranking of forces must be W=N > T=f. Explain what is wrong and what is right about the student s observation. Then write a completely correct sentence relating all of the forces. (c) Graphs are shown of the velocity vs. time of two identical train engines on a straight track. A positive velocity represents eastward travel. Both graphs have the same scales. On each graph, time t = 2 s is indicated with a dot. A student makes the following observation: I think that B has the greater net force acting on the engine at time t = 2 sec because the net force on A is zero at that time. What is wrong with the student s statement? What would the correct statement be? Train A Train B

5 Work-Energy-Power: Review Packet Problem 1: Each part shows a set of energy bar graphs that are in sequence. Explain a situation where the energy of a system could be represented by that sequence of bar graphs. Draw a diagram to help your explanation. As you explain the energy transformations, reference the diagrams using (1), (2), etc. If the total energy of the system changes, explain what external force does work to change the energy of the system. Note that K T represents translational kinetic energy, U g represents gravitational potential energy, and U S represents the potential energy of a spring. (a) Diagram (1) (2) (3) (b) Diagram (1) (2) (3) (c) Diagram (1) (2) (Repeat 1 and 2 over and over)

6 Momentum: Review Packet Problem 1: Five objects of various masses m all start at rest on a frictionless surface. At time time = 0, a constant forward force F is applied to each object for a time t. At the end of the time t, the force is removed. Let d represent the distance that each object travels during the time t while the force is applied. The table shows the values of m, F, t, and d for each of the five objects. Mass Force Time t m F Object A 2 kg 4 N 3 sec 9 m Object B 4 kg 2 N 6 sec 9 m Object C 4 kg 3 N 8 sec 24 m Object D 8 kg 9 N 2.7 sec 4 m Object E 3 kg 6 N 5 sec 25 m Distance d (a) Which object has the same acceleration as Object A while the force is applied? Explain your reasoning. (b) Which object has the same momentum as Object A after the force is applied? Explain your reasoning. (c) Which object has the same kinetic energy as Object A after the force is applied? Explain your reasoning. (d) Which object has the same speed as Object A after the force is applied? Explain your reasoning. Problem 2: In all four of the cases below, a 0.25 kg bullet strikes a 6 kg block on frictionless wheels. Rank the cases based on the block s final velocity after the collision. You may use conservation of momentum to find the final speed in each case. Case A Case B Case C Case D Initial Initial Initial Initial (Bullet sticks to block.) (Bullet passes through block.) (Bullet bounces off of block.) (Bullet stops and drops.) > > > Greatest final speed of the block Least final speed of the block Justify your answer without using any numbers. Your justification must be entirely conceptual and discuss the relationships between changes in momentum in these situations.