a. A hockey puck slides with an initial speed of 47 m/s on a large frozen lake.

Question

a. A hockey puck slides with an initial speed of 47 m/s on a large frozen lake. If the coefficient of kinetic friction between the puck and the ice is 0.030, what is the speed of the puck after15 s?
__________m/s

b. Two children are playing on a 147-m-tall bridge. One child drops a rock (initial velocity zero) at t = 0. The other waits 1.4 s and then throws a rock downward with an initial speed v0. If the two rocks hit the ground at the same time, what is v0?

________ m/s

c. Your friend is an environmentalist who is living in a tree for the summer. You are helping provide her with food, and you do so by throwing small packages up to her tree house. If her tree house is 20 m above the ground, what is the minimum (initial) speed you must use when throwing packages up to her?
_________m/s

d. A crate of mass 60 kg is attached to one end of a string, and the other end of the string runs over a pulley and is held by a person as in the figure below. If the person pulls with a force of 92 N, what is the crate's acceleration? (Assume that upward is the positive direction. Indicate the direction with the sign of your answer.)
________ m/s2

e. A car of mass 1,210 kg is lowered onto a junk pile at the end of the cable of a large crane. If the car is accelerating downward at 0.19 m/s2, what is the tension in the cable?
_________N

f. A mass with M = 110 kg is attached to the bottom of a block-and-tackle pulley system as depicted in in the figure below. How much tension force is needed to keep the mass at its current position?

________ N

Explanation / Answer

a) F = m a

u m g = m a

a = u g

v = v0 + a t = 47 - 0.03*9.81*15= 42.6 m/s

b) dropped stone

y = y0 + v0y t + 1/2 a t^2

0 = 147 - 0.5*9.81*t^2

t=5.47 s

thrown stone

0 = 147 - v*(5.47-1.4) - 0.5*9.81*(5.47-1.4)^2

v=16.15 m/s

c) v^2 = v0^2 + 2 a y

0 = v^2 -2*9.81*20

v=19.8 m/s

d)
T - mg = ma

92 - 60*9.81 = 60*a

a=-8.28 m/s^2

e) T - m g = ma

T - 1210*9.81 = 1210*-0.19

T=11640 N

f) 4 F = m g

F = 110*9.81/4= 270 N

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