An air-track glider of mass 0.100 kg is attached to the end of a horizontal air

Question

An air-track glider of mass 0.100 kg is attached to the end of a horizontal air track by a spring with force constant 20.0 N/m. Initially the spring is unstreched and the glider is moving at 1.50 m/s to the right. With the air track turned off, the coefficient of kinetic friction is ?k=0.47.

Part A

How large would the coefficient of static friction ?s have to be to keep the glider from springing back to the left when it stops instantaneously?

Express your answer giving two significant figures.

Part B

If the coefficient of static friction between the glider and the track is ?s = 0.65, what is the maximum initial speed v1 that the glider can be given and still remain at rest after it stops instantaneously?

Express your answer giving two significant figures.

Explanation / Answer

From Hookes law , F = k * x

sum of the vertical force on the block = 0

N = m*g

Definition of friction

friction = u * N = u * m* g

on equating

u * m*g = k*x

u = k* x / m* g

u = 20 * 1.50 / ( 0.100*9.81)= 30.58

b)Xf = u * m*g / k = 0.65 * 0.100 * 9.81 / 0.47 = 1.356 m

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