Question

A 4.5 kg box slides down a 5.2-m -high frictionless hill, starting from rest, across a 2.2-m -wide horizontal surface, then hits a horizontal spring with spring constant 550 N/m . The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 2.2-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.27.

Part A.

What is the speed of the box just before reaching the rough surface?

Express your answer to two significant figures and include the appropriate units.

Part B.

What is the speed of the box just before hitting the spring?

Express your answer to two significant figures and include the appropriate units.

Part C.

How far is the spring compressed?

Express your answer to two significant figures and include the appropriate units.

Part D.

Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

Answer 1

a) Using conservation of energy

P.E (top) + K.E (top) = P.E (bottom) + K.E (bottom)

mgh + 0 = 0 + 1/2mv²

v = sqrt (2gh)

v = sqrt ( 2*9.8*5.2)

v = 10.0955 m/s

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b) energy at bottom of hill = 1/2mv² = 0.5*4.5*10.0955² = 229.32

energy after rough surface = 26.1954

loss = 203.12 J

v = sqrt (2*203.12 / 4.5)

v = 9.5 m/s

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c) 1/2mv² = 1/kx²

x = sqrt (mv² / k) (here v is speed before spring)

x = 0.859 m

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d) it will make 8 complete trips