TEST 3 AU ‘12

1. (40 POINTS)

At the instant shown, a 2.000-kg block has been pressed against a spring to a compression distance D. The block is released from rest from that position and moves right. The spring has force constant k = 10.00 N/m and is attached to a wall. The diagram below shows time sequence shots of the block and compressed spring at rest initially (i) and finally (f) after the block has moved to the right to where the spring is un-deformed (not compressed or stretched). In the final position shown below the block has speed 2.000 m/s as it moves right. The coefficient of kinetic friction between the horizontal ground and bottom of the block is µ = 0.200.

(a) (24 points) What is D (in m)?.

(b) (10 points) What is the work done by friction (in Joules) during
this motion? Is this work positive or negative? Explain.

(c) (6 points) The block loses contact with the un-deformed
spring at the final (f) position shown below. Thus, the block
continues motion to the right without being connected to the spring.
How far from this position will the block travel to the right before
finally coming to rest ?

2. (40 POINTS) A block of mass m = 1.000 kg slides counter-clockwise along the inside of a 3-quarter circular track of radius R = 20.0 m. The block starts out moving vertically downward at point A at the end of a horizontal diameter with initial speed V ₁ = 40.0 m/s and exits at point C at the top. No friction.

(a) (6) What is the magnitude N of the normal force of the track on the block when it reaches point B at the other end of the horizontal diameter ? What is the direction of the normal force at this point?
(b) (4) At point B what is the magnitude | a_t | and direction of the tangential acceleration ?
(c) (23 points) What is the magnitude N of the normal force of the track on the block just before it reaches point C at the top ? What is the direction of the normal force at this point?
(d) (7 points) At point C, the mass exits the track and undergoes projectile motion (with no air resistance) until it hits the ground at the same vertical level as the bottom of track. Use conservation of energy to compute the speed of the mass just before it hits the ground.

3. (38) In a simulated experiment, a subcompact car with a mass 950.00 kg traveling to the right with speed 15.00 m/s collides with a truck of mass 1900.00 kg traveling to the left with speed 10.00 m/s. See schematic below of the situation before the collision; no person is hurt in the simulation. The two cars stick together as a result of the collision and just after colliding they move together with a common speed | V_f |.

(a) (18) What is the speed | V_f | ?

(b) (10) What is the direction of motion of the stuck cars immediately after the collision, left or right? (circle one)

(c) (10) Assume the kinetic energy of the system is lost to heat. How much heat energy is created during the collision?

4. (12 points) A wheel is rotating about an axis that is in the z-direction. The angular velocity is ω_o = --6.00 rad/s at t = 0 and increases linearly with time at constant angular acceleration α.
At t = 7.00 seconds, the angular velocity is ω₇ = +8.00 rad/s. We have taken counter-clockwise rotation to have positive angular velocity.

(a) (2 points) Is the angular acceleration α positive or negative?

(b) (4 points) Through what angle (in rads) does the wheel rotate in the time interval between 0 and 7.00 seconds?

(c) (4 points) At what time t does the wheel momentarily come to rest?

(d) (2 points) During what time interval is the speed of the wheel increasing? Decreasing?

5. EXTRA CREDIT. (11 POINTS) A 1.000-kg block hangs vertically at the end of a string wrapped around a pulley of radius R = 0.250 m and mass M = 2.000-kg shaped in the form of a solid cylinder. Thus, the pulley has I = ½MR² about the axis of rotation through the center. The vertically hanging block and pulley are shown at the start of the motion when they are released from rest. The block is released from a height h = 1.000 m above the ground.

What is the linear speed v of the block just before it hits the ground?

1. Kinetic energy may be positive or negative. True or False. (a) True (b) False

2. The quantity ½kx² is (a) the kinetic energy of an object (b) the potential energy of a spring (c) the gravitational potential energy of an object (d) the power supplied to an object by a force.

3. The quantity mgy is (a) the kinetic energy of an object (b) the potential energy of a spring (c) the gravitational potential energy of an object (d) the power supplied to an object by a force.

4. The dot product of the force and the velocity is (a) the kinetic energy of an object (b) the potential energy of a spring (c) the gravitational potential energy of an object (d) the instantaneous power supplied to an object by the force

5. What we have learned so far is that the work done W_fk by a friction force is negative. True or False. (a) True (b) False

6. What we have learned so far is that the heat is the negative of the work of frictions i.e.
heat = - W_fk . True or False. (a) True (b) False

7. An apple falls from a tree. Let KE represent its kinetic energy and PE represent its potential energy. As the apple falls: (a) KE increases and PE decreases
(b) KE decreases and PE decreases (c) KE decreases and PE increases

8. A ball drops some distance and loses 30 J of gravitational potential energy. Do not ignore air resistance (air friction). How much kinetic energy did the ball gain ?
(a) more than 30 J (b) exactly 30 J (c) less than 30 J

9. A ball drops some distance and loses 30 J of gravitational potential energy. Ignore air resistance(air friction) . How much kinetic energy did the ball gain ?
(a) more than 30 J (b) exactly 30 J (c) less than 30 J

10. A ball is thrown straight up with initial speed Vo. If air resistance cannot be ignored, when the ball returns to its initial location its speed is (a) less than Vo (b) more than Vo (c) the same as Vo.

11. Friction is a conservative force. True or False. (a) True (b) False

12. A potential energy function is shown below. It is only a function of x.

Point B is a position of (a) stable equilibrium (b) unstable equilibrium

13. Linear momentum has magnitude and direction. True or False. (a) True (b) False

14. A single particle that has zero momentum must also have zero kinetic energy. True or False. (a) True (b) False

15. A system of two particles that has zero total momentum must also have zero total kinetic energy. True or False. (a) True (b) False

16. A Ping-Pong ball moving East at 4 m/s collides with a bowling ball that is stationary (at rest) . After the collision, the Ping-Pong Ball bounces back toward the West, and the bowling ball moves very slowly to the East. Which object experiences the larger magnitude of force during the collision? (a) the Ping-Pong ball (b) the bowling ball (c) Neither; both experienced the same magnitude of force.

17. In an elastic collision, (a) kinetic energy is conserved during the collision (b) kinetic energy is lost during the collision after being transformed into Heat and other forms of energy

18. True or False. A flywheel rotates with constant angular velocity. A point on the rim (edge) of the wheel has zero tangential acceleration.
(a) True (b) False

19. True or False. In the previous problem, a point on the rim of the wheel has zero radial (centripetal) acceleration. (a) True (b) False