1. An object is released from rest from a great height and reaches its terminal velocity. Which of the following statements is true of the object while it is falling with terminal velocity?
(A) There is no longer a gravitational force on it.
(B) There is no longer a drag (air resistance) force on it.
(C) Its acceleration is upward.
(D) The magnitudes of the gravitational and drag forces on it are equal.
(E) The gravitational and drag forces on it act in the same direction.
2. A student with a mass of 50 kg is standing on a bathroom scale while riding in an elevator. If the reading on the scale is 400 N, which of the following is a correct description of the elevator’s motion?
(A) Moving upward with increasing speed
(B) Moving upward with constant speed
(C) Moving downward with constant speed
(D) Moving downward with increasing speed
(E) Moving downward with decreasing speed
3. The system represented above consists of two objects of unequal masses, M1 and M2 ,with M1 > M2 . The objects hang from the ends of a cord of negligible mass that passes over a pulley with negligible mass and friction. Which of the following is true about the changes in the gravitational potential energy, △U , and kinetic energy, △K, of the system soon after the objects are released from rest?
(A) △U < 0 and △K > 0
(B) △U = 0 and △K > 0
(C) △U < 0 and △K = 0
(D) △U = 0 and △K = 0
(E) △U > 0 and △K < 0
A tape attached to a moving object was pulled by the object through a marker that put dots on the tape at a constant rate of 10 dots per second for a period of 2.5 s. The figure below shows the marked tape next to a centimeter ruler.
4. The average speed of the object for the total time recorded on the tape is most nearly
(A) 2.0 cm/s
(B) 3.3 cm/s
(C) 4.5 cm/s
(D) 5.5 cm/s
(E) 7.0 cm/s
5. Which of the following best represents the graph of the velocity of the object versus time?
6. Which of the following best represents the graph of the acceleration of the object versus time?
Experiment 1: A block of mass 1.5 kg is placed on a long board. You are to design an experiment to determine the coefficient of static friction between the block and the board.
i. From the following list of available equipment, check those additional items you would use for the purpose of determining the coefficient of static friction.
____ Ruler ____ Spring scale ____ String
____ Meterstick ____ Pulley ____ Protractor
____ Photogate ____ Stopwatch ____ Mass hanger
____ Clamps and supports ____ Objects of various known masses
ii. Sketch a diagram of your experimental setup and label the pieces of equipment that would be used.
iii. Outline the experimental procedure you would use, including a list of quantities you would measure.For each quantity, identify the equipment you would use to make the measurement.
(b) Explain how to use the measurements described in part (a) to calculate the coefficient of static friction.Include a free-body diagram in your explanation that shows all forces (not components) acting on the block while the measurements are being made.
Experiment 2: In a second experiment, the coefficient of kinetic friction between the block and the board is determined to be 0.10. The board is now inclined at an angle of 25° above the horizontal. The block is released from rest at the top of the incline and slides 2.0 m down the incline.
(c) Calculate the work done by kinetic friction as the block slides down the incline.
(d) The mass of the block is now increased without changing the coefficient of kinetic friction, and experiment 2 is repeated. How does each of the following change?
i. The magnitude of the frictional force
____Increases ___Decreases ___Remains the same
ii. The magnitude of the velocity of the block as it reaches the bottom of the incline
___Increases ___Decreases ___Remains the same
iii. The kinetic energy of the block at the bottom of the incline
___Increases ___Decreases ___Remains the same
A satellite of mass m is in a stable circular orbit around Earth at a distance R1 from the center of Earth.The mass of Earth is Me .
(a) Derive an expression for the following in terms of m, R1 , Me , and fundamental constants, as appropriate.
i. The orbital speed v1 of the satellite
ii. The total energy of the satellite in this orbit, assuming gravitational potential energy to be zero at an infinite distance from the center of Earth
The satellite’s booster rockets fire and lift the satellite to a higher circular orbit of radius 12R1 . The satellite follows the path shown in the diagram below, moving a total distance S during the orbital change. The component of the rockets’ force parallel to the path is given by the equation F=F0(1-x/S ) , where x is the variable distance traveled along the path at any moment.
(b) Derive an expression for the total work done on the satellite by the force F in terms of F0 and S.
(c) If the total distance S is equal to 3R1 , derive an expression for F0 in terms of Me , R1 , m, and fundamental constants, as appropriate.