For Problems II and III show ALL your work. We want to give you partial credit, but this can be done only if your work is shown.
Correct answers with unsubstantiated work on Problems II and III will receive ZERO CREDIT.
Here are some useful equations
S F = ma w = mg You can take g = 10 m/s2
ar = v2/r ar = r(2p /T)2 ar = r(2p f)2
v = vo + at x - xo = vot +½ at2
2a(x - xo) = v2 - vo2 x - xo = ½(v + vo)t
vx = vocosq o vy = vosinq o - gt
x = vocosq ot y = vosinq ot - ½ gt2
Impulse = FavgD t, momentum = mv, Impulse = S (mv)f - S (mv)i
Kinetic energy = ½ mv2

1.
Two carts on a frictionless air track are forced together with a compressed spring between them. After the carts, initially at rest, are released, cart B (m_B = 2kg) moves right at a speed of 3.0 m/s, as shown in the figure. The speed in of cart A (m_A = 4 kg) is closest to

A) 0.5 m/s       B)  1.25 m/s    C) 1.5 m/s    D) 2.0 m/s      E) 2.12 m/s

2. A 0.040-kg bullet traveling at 400 m/s hits and embeds itself in a 0.20-kg wooden block resting on a horizontal frictionless surface. The speed of the bullet-block system immediately after the collision is closest to

A) 67 m/s      B) 80 m/s       C) 163 m/s          D ) 178 m/s         E) 400 m/s

3.
The mass of body B is twice the mass of body A. Bodies A and B are on a collision course with equal speeds, as shown. After the collision, body A moves along the +y direction. From the "after" picture, choose the letter corresponding to the quadrant in which the body B is moving after the collision.

4. A 4-kg and 2-kg object are approaching each other with equal speeds of 5 m/s. They collide and stick together. The magnitude of the change of kinetic energy of the two-object system is closest to

A) 0      B) 40 J        C) 60 J           D) 80 J          E) 100 J

5. A 2-kg object is moving at 3 m/s toward the right. A 4-N force is suddenly applied pointing opposite the direction of motion (toward the left). The force acts for a time interval of 4 s, and then is removed. The final velocity of the object is closest to

A) 0      B) 5 m/s pointing left     C) 5 m/s pointing right        D) 11 m/s pointing left       E) 11 m/s pointing right

The following statement applies to problems 6 and 7, and the figure shown. A hammer starikes the 0.3-kg block A, which is initially at rest. The hammer’s contact time with block A is 0.05 s. As a result, block A obtains a velocity of 5 m/s. Block A slides along a frictionless surface until it collides with block B, which is initially at rest. After the collision, block A sticks to block B, and they slide together along another frictionless surface with a velocity of 0.8 m/s.

6. The average force acting on block A during the time interval it is in contact with the hammer is closest to

A) 5 N      B) 12 N      C) 20 N      D) 30 N      E) 300 N

7. The mass of block B is closest to

A) 1.4 kg     B) 1.6 kg       C) 1.8 kg       D) 2.0 kg        E) 2.2 kg

8. A 0.2-kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30 m/s and rebounds up at 20 m/s. The magnitude of the impulse due to the collision with the sidewalk is closest to

A) 2.0 N-s        B) 6.0 N-s        C) 9.8 N-s          D) 10 N-s E)         19.6 N-s

9. A 500-kg sack of coal is dropped vertically onto a 2,000-kg railroad flatcar which was initially moving at 3 m/s toward the right, as shown. Just after the sack comes to rest on the flatcar, the speed of the flatcar is closest to

A) 0.6 m/s       B) 1.2 m/s          C) 1.8 m/s        D) 2.4 m/s        E) 3.6 m/s

10.
A ball of mass M is dropped from a height H, strikes the ground, and rebounds to a smaller height h. The speed of the ball just before striking the ground is v₁, and just after rebound from the ground the ball’s speed is v₂. Which of the following statements is correct for the motion of the ball?

A) Kinetic energy is conserved.       B) Momentum is conserved.          C) Momentum is not conserved.
D) The collision is perfectly elastic.        E) The change of momentum is Mv₂ - Mv₁.

II.

A 4,000-kg truck is on a collision course with a 2,000-kg car, moving as shown in the figure. After the collision, the car and truck stick together, and move directly north. Neglect any friction effects of the road on the car-truck system.

a) Draw a CLEAR picture of the final situation after the collision in the space provided.

b) What is the initial speed v of the truck? Answ___________

c) What is the final speed V of the coupled car-truck combination after the collision? Answ______________

d) What is the change of kinetic energy in the collision? Answ_________________________

III.

An elevator cab in the New York Marquis Marriot has a total nonstop upward run of 100 m from start (at rest) to the end (at rest). When the elevator reaches its maximum speed, it moves at this constant speed until it begins to decelerate Its maximum speed is 6 m/s. Its acceleration is 1 m/s², and its deceleration is 2 m/s².

a) In the space at the right, draw a CLEAR pictorial representation of the elevator cab as it is making its upward trip. Show the values of all relevant quantities in the trip.

b) How far does the cab move while accelerating to full speed from rest? Answ________________

c) How far does the cab move while decelerating from full speed to rest? Answ________________

d) How long does it take the cab to make its nonstop 100-m run, starting and ending at rest? Answ______________

Correct  Answers
I     1C, 2A, 3C, 4C, 5B,  6D, 7B,  8D,  9D,  10C
II    b)  8.19 m/s    c)  3.82 m/s    d)  - 490,000 J
III   b) 18 m     c) 9 m       d) 21.25