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)iKinetic energy = ½ mv2
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1) A 1500-kg car is traveling at 30 m/s along a horizontal road when the brakes are applied. The car skids to a stop in 4.0 s. How much kinetic energy (in J) does the car lose in this time?

A) 3.75x10⁴    B) 6.00x10⁴   C) 1.50x10⁵      D) 6.75x10⁵   E) can’t determine because friction force is not given

2) Block X, of mass 2 kg, is moving to the right at 10 m/s. Block Y, of mass 4 kg, is moving to the left at 10 m/s. The two blocks collide head-on. The ratio of the magnitude of the impulse exerted by X on Y to that exerted by Y on X is:
A) 1/4      B) 1/2       C)      D) 1        E) need to know whether the collision is elastic or inelastic

3)
A 2-kg object initially at rest is acted upon by a single force in the x direction in a manner described by the graph shown. The momentum acquired by the object is
A) 30 kg m/s    B) 50 kg m/s     C) 100 kg m/s     D) 120 kg m/s       E) 180 kg m/s
 
 
 

4)
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
A) 0.6 m/s       B) 1.2 m/s      C) 1.8 m/s       D) 2.4 m/s         E) 3.0 m/s

5)   A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The club is in contact with the ball for time T. The average force on the club on the ball during the time T is
A) mvT      B) mv/T       C) (1/2)mv²T      D) mv²/(2T)         E) mT²/(2v)

6)
A 4-kg body moving with speed v breaks up into a two 1-kg and 3-kg pieces. The 1-kg body moves off at a right angle to the original 4-kg body with an unknown speed, as shown. The 3-kg body moves off at and angle of 48⁰ below the x - axis, as shown. The final speed of the 3-kg body is
A) 0        B) 1 v        C) 2 v        D) 3 v         E) 4 v
 
 
 
 

7)
An 8-kg body is at rest. At a certain instant an internal explosion occurs splitting the body into two chunks of 2-kg and 6-kg mass. The explosion gives the chunks a total kinetic energy of 108 J. The speed the 2-kg chunk after the explosion is
A) 4 m/s      B) 6 m/s      C) 9 m/s        D) 16 m/s        E) 48 m/s

8) A 3.0-kg gun mounted on frictionless wheels shoots a 8.0-g bullet in the horizontal direction at a speed of 360 m/s relative to the ground. The recoil speed of the gun is
A) 0.12 m/s      B) 0.96 m/s      C) 1.20 m/s     D) 2.40 m/s       E) 3.60 m/s

9)
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) The change of momentum is Mv₂ - Mv₁    C) The collision is perfectly elastic
D) Momentum is conserved.      E) Momentum is not conserved

10) Two carts on a frictionless air track are forced together with a compressed spring between them. After the carts, initially at rest, are released, they move apart, as shown. Which of the following statements is correct for the motion of the ball?

A) Kinetic energy is conserved.      B) The change of momentum is M_Av_A - M_Bv_B      C) Momentum is not conserved
D) Momentum is conserved.       E)   The explosion is perfectly elastic

II.

A 3,000-kg truck is on a collision course with a 1,300-kg car, as shown in the figure. After the collision, the car and truck stick together, and move directly north with velocity of 20 m/s. 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_t of the truck? Ans. _______________

c) What is the initial speed v_c of the car? Ans. ______________

d) What is the change of kinetic energy in the collision? Ans. __________________

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III.

A hammer strikes the 0.5 kg block A, which is initially at rest. The average force exerted by the hammer is 75 N. As a result block A obtains a velocity of 7 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.

a)   Find the time interval that the hammer is in contact with the block A. Ans._____________
b)   Find the mass of block B. Ans. _________________
c)   Find the impulse given to block B by block A. Ans. __________________
d)   The direction of this impulse is (circle one) left right vertical up vertical down

Correct Answers

I       1D,     2D,      3D,     4D,     5B,     6C,     7C,     8B,     9E,     10D
II     b)  40.9 m/s          c)  115 m/s          d)  -10,300,000 J
III    a)  0.04675           b)  3.88 kg          c)  3.10 kgm/s               d)  right