AP1 X4 - DTFizzix

AP1 EXAM #4 2014 : Ch 2-10 Free Response Section
1. (10pts: MV) A nerf dart shot toward Paul’s general direction is diverted by futuristically evolved telekinetic powers.
The dart, of mass 25-g and speed of 400 m/s (Yes, it is a fast one…), strikes and passes through the first of two wooden
blocks of mass 2-kg each. Each wooden block is initially at rest. After passing through the 1st block, the dart is now
moving with a speed less than 400 m/s and the 1st block is noticed to be moving at a speed of 1 m/s. The dart then
strikes and embeds in the 2nd wooden block. Ignore friction and monsters.
1st
Block
2nd
Block
(A) What is the speed of the dart after passing through the 1st block?
(B) What is the speed of the 2nd block immediately after the dart embeds in it?
Now, this situation is repeated, because it was so cool, to include both inelastic collisions; the dart embeds in the 1st
block which in turn sticks to the 2nd block.
(C) What is the final speed of the combination dart-1st Block-2nd Block after all is said and done?
2. (10pts: Energy) The diagram below shows a 5-kg block sliding on a frictionless chute toward a set of two springs; one
nestled inside the other. The initial speed of the mass is vo. The block makes contact with the first (inner) spring at point
A, moves 10 cm where it makes contact with the 2nd (outer) spring at point B. The block then moves an additional 5 cm
before coming to rest at point C. The accompanying graph shows the magnitude of the force exerted on the object by
the springs as a function of the block distance from point A.
(A) Calculate the spring constant for the 1st spring.
(B) Calculate the loss of kinetic energy of the block as it moves from point A to point B.
(C) Calculate the additional loss of kinetic energy as the block slides from point B to point C.
(D) Calculate the initial speed of the block, vo.
(E) Calculate the spring constant of the outer spring.
3. (10pts: MV & E) During target practice for the upcoming Hunger Games, Doc T shoots a bullet at a block of wood
sitting stationary at the bottom of a frictionless vertical loop as shown below. The block has mass 2m and the loop has a
radius of r. The bullet has a mass of m and initial speed of vo. The ensuing collision is totally inelastic; the bullet embeds
in the block. Determine each of the following in terms of the given quantities of m, vo, r, and g.
(A) The speed of the bullet-block combination immediately after impact.
(B) The kinetic energy of the bullet-block combination when it is at point P.
(C) The speed of the bullet-block combination when it is at the top of the loop.
(D) The minimum speed, vmin, needed for the bullet-block combination at the top of the loop to remain in contact with the
loop.
(E) The newly required velocity of the bullet if your answer in Part (C) is to be followed.
4. (10pts: ) Our Sun has a mass of 2x1030 kg, a diameter of 14x108m, and takes 25 Earth days to complete one rotation
around its axis. In about another 5 billion years, the Sun will exhaust its hydrogen fuel and bloat into a red giant and just
“go quietly into that night.” However, the core will be left behind. It will be what is called a white dwarf; a burned out
hot cinder of a once powerful mid-sized star.
The size of this white dwarf is predicted to be about the same size as the Earth and contain 75% of the original mass of
the Sun.
Find the rotational velocity of this white dwarf we used to call our Sun.
5. (10pts: L) A solid bowling ball of uniform density is at rest at the top of an inclined plane. The inclined plane makes an
angle of  above the horizontal, the radius of the ball is R, and the bottom of the ball starts at a height of h above the
base of the plane. The ball is then released and it rolls without slipping down the incline. Express all these answers in
terms of, M, R, h, g, and .
(A) Determine the following two thingers when the ball is at the bottom of the incline.
i) Its translational kinetic energy.
ii) Its rotational kinetic energy.
(B) Determine the following two thingers when the ball is on the incline anywhere between the top and the bottom.
i) Its linear acceleration
ii) The magnitude of the friction
(C) The solid bowling ball is then replaced with a hollow bowling ball of the same R and M; yeah, like that’s going to
happen in this Universe… What is the total kinetic energy of the hollow bowling ball when it reaches the bottom of the
same incline?
(D) State whether the final linear speed of the hollow bowling ball is the same, greater then, or less than the speed of
the solid bowling ball used in parts A & B. Justify your answer.

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