Constants: Acceleration due to gravity = 9.81 m/s 2 PROBLEMS: 1. In an experiment, it is found that the time t required for an object to travel a distance x is given by the equation = where is the acceleration due to gravity. What value of the power makes this equation dimensionally consistent? (A) 1/2 (B) 1 (C) 3/2 (D) -1/2 (E) -1 2. A point-like object travels in one dimension. Its velocity is recorded at three different times. At t = 0.500 s, 1.50 s and 3.00 s, the velocities are +3.40 m/s, +4.20 m/s and -1.10 m/s, respectively. The object s average acceleration during the time interval between 0.500 s and 3.00 s is (A) -1.37 m/s 2 (B) -1.10 m/s 2 (C) +2.80 m/s 2 (D) -0.31 m/s 2 (E) -1.80 m/s 2
3. The figure below shows the time dependence of the position x of two cars, C and D, that are moving on the same straight road. According to this figure, which statement about these cars must be true? (A) Both cars have the same magnitude of acceleration. (B) At time t = 10 s, the speed of car D is larger than the speed of car C. (C) The magnitude of the acceleration of car C is greater than the magnitude of the acceleration of car D. (D) The magnitude of the acceleration of car C is less than the magnitude of the acceleration of car D. (E) At time t = 10 s, both cars have the same velocity. 4. Car A is moving at a constant velocity of 5.00 m/s and is initially 50.0 m ahead of car B. At that instant, car B is moving with an initial velocity of 2.00 m/s (in the same direction as Car A) with a constant acceleration. The two cars pass each other 10.0 s later. What is the acceleration of car B? (A) +0.574 m/s 2 (B) +1.23 m/s 2 (C) +1.60 m/s 2 (D) +2.05 m/s 2 (E) +3.80 m/s 2
5. To determine the height of a flagpole, Anastasia throws a ball straight up and times it. She sees that the ball goes by the top of the flagpole after 0.500 s and then on the way down, it passes the top of the flagpole again after a total elapsed time of 4.10 s. How high is the pole above the point where the ball was launched? (Neglect air resistance.) (A) 26.3 m (B) 18.2 m (C) 16.7 m (D) 13.4 m (E) 10.1 m 6. A particle leaves the origin with an initial velocity = (2.40 m/s) + (-4.00 m/s), and moves with constant acceleration = ( 1.50 m/s 2 ) + (3.50 m/s 2 ). What is the particle s distance from the origin when the vertical component of the velocity vanishes? (A) 1.76 m (B) 3.64 m (C) 4.73 m (D) 2.29 m (E) 2.89 m 7. A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will (A) depend on the speed of the plane when the package was released. (B) depend on the height of the plane when the package was released. (C) be behind the package. (D) be directly over the package. (E) be in front of the package.
8. Jerry and Debra stand on a roof. They both throw snowballs from the same height with the same initial speed, but in different directions. Jerry throws his snowball downward, at 30 below the horizontal. Debra throws her snowball upward, at 30 above the horizontal. Which of the following statements are true about the snowballs as they reach the ground below? (Neglect air resistance.) (A) Both snowballs hit the ground at the same time. (B) Jerry's snowball reaches the ground after Debra's snowball. (C) Debra's snowball will have a higher speed than Jerry's snowball. (D) Jerry's snowball will have a higher speed than Debra's snowball. (E) Both snowballs will hit the ground with the same speed. 9. A particle is launched with an initial speed of 100 m/s at an angle θ above the horizontal. At the highest point, the speed of the particle is 20.0 m/s. What is the value of θ? (Neglect air resistance.) (A) 78.5 0 (B) 63.8 0 (C) 47.7 0 (D) 27.4 0 (E) 11.5 0 10. An airplane flying at an altitude of 1500 m launches a package horizontally with a speed of 250 m/s. In what direction will the package be traveling when it hits the ground? (Neglect air resistance.) (A) 22.8 0 below horizontal (B) 72.3 0 below horizontal (C) 34.5 0 below horizontal (D) 42.3 0 below horizontal (E) 53.1 0 below horizontal
11. A ball is launched at a speed of 15.0 m/s, at an angle of 40.0 0 above the horizontal, towards a wall that is 4.00 m away. How high is the ball when it hits the wall? (Neglect air resistance.) (A) 0.532 m (B) 1.85 m (C) 2.76 m (D) 1.23 m (E) 3.18 m 12. Consider the following four situations where a block is on a smooth (frictionless) surface that is inclined at an angle of θ above the horizontal: (Only the force of gravity and the normal force are acting on the block.) Block A with mass M ; surface s inclination angle θ = 0 0 (horizontal surface). Block B with mass 1.5M ; surface s inclination angle θ = 30 0. Block C with mass 2M ; surface s inclination angle θ = 45 0. Block D with mass 2M ; surface s inclination angle θ = 60 0. Rank the magnitudes of the normal forces N j (where the subscript j labels the block) exerted on the blocks: (A) N B < N A < N C = N D (B) N A = N B < N C = N D (C) N A = N D < N B < N C (D) N A < N B < N C = N D (E) N C = N D < N B < N A
13. Three forces act on an object of mass 1.00 kg, causing it to accelerate along the +x-axis with a magnitude of 15.0 m/s 2. One force is 75.0 N along the +y-axis. A second force is 60.0 N along a direction making a counterclockwise angle of 235 0 with the +x-axis. What is the direction of the third force, measured counterclockwise from the +x-axis? (A) 332 0 (B) 302 0 (C) 217 0 (D) 127 0 (E) 53.6 0 14. Two boxes, one of mass m 1 = 5.00 kg and the other of mass m 2 = 10.0 kg, rest on the floor in contact with one another. A person pushes on the box of mass m 1 in the +x direction with a force of magnitude 15.0 N. Another person pushes on the box of mass m 2 in the opposite direction with a force of magnitude 6.00 N. Assuming that the two boxes move together, what is the magnitude of the contact force between the two boxes? (A) 12.0 N (B) 14.0 N (C) 3.00 N (D) 4.00 N (E) 10.0 N
15. Refer to the figure below. A 10.0 kg block is placed on a smooth (frictionless) ramp that is inclined at 30.0 0 above the horizontal. A force of magnitude 40.0 N is applied to the block at an angle of 60.0 0 above the surface of the ramp. What is the magnitude of the acceleration of the block? (A) 4.90 m/s 2 (B) 6.49 m/s 2 (C) 2.91 m/s 2 (D) 1.43 m/s 2 (E) 2.00 m/s 2 16. While in an elevator, Jane stands on a scale and sees that it displays a value three times of what the same scale should show outside the elevator. She concludes that the acceleration of the elevator is: (A) 3g upwards (B) 2g upwards (C) g upwards (D) 2g downwards (E) g downwards ================= END OF THE EXAM ===============