An air-track glider of mass 0.103 kg is attached to the end of a horizontal air

Question

An air-track glider of mass 0.103 kg is attached to the end of a horizontal air track by a spring with force constant 21.0 N/m

a) With the air track turned off, the glider travels 8.8 cm before it stops instantaneously. How large would the coefficient of static friction s have to be to keep the glider from springing back to the left?

(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 remain at rest after it stops instantaneously? With the air track turned off, the coefficient of kinetic friction is k= 0.50.

Explanation / Answer

a) Sum of the horizontal forces on the block (opposite friction is positive) = 0 <---- no movement
0 = F - friction
F = friction

From Hooke's Law
F = k*x

Sum of the vertical force on the block (up is positive) = 0
0 = N - m*g
N = m*g

Definition of friction
friction = u*N
friction = u*m*g

Plug back in and solve for u
u*m*g = k*x

u = kx/mg = 21*0.088/0.103*9.8 = 1.83

b) umg = kx

x = umg/k = 0.65*0.103*9.8/21 = 0.031 m

from the energy conservation

1/2mv^2 = 1/2kx^2+µk*m*g*x

1/2mv^2 = 0.01009+0.0156

v = 0.706 m/s

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