Question

A 283 g air track glider moving at 0.69 m/s on a 2.4 m long air track collides elastically with a 467 g glider at rest in the middle of the horizontal track. The end of the track over which the struck glider moves is not frictionless, and the glider moves with a coefficient of kinetic friciton = 0.02 with respect to the track. Will the glider reach the end of the track? Neglect the length of the gliders.

Answer 1

Let:
m1 be the mass (0.283kg) of the air track glider,
m2 be the mass (0.467kg) of the glider at rest,
u1 be the initial velocity (0.69m/s) of the air track glider,
v1 be the velocity after collision of the air track glider,
v2 be the velocity after collision of the glider initially at rest,
g be the acceleration due to gravity,
u be the coefficient of friction,
s be the distance travelled by the glider initially at rest.

Equating momentum before and after collision:
m1u1 = m1v1 + m2v2 ...(1)

As the collision is elastic, velocity of separation equals velocity of approach:
v2 - v1 = u1 ...(2)

Substituting for v1 from (2) in (1) gives:
m1u1 = m1(v2 - u1) + m2v2
v2 = 2m1u1 / (m1 + m2) ...(3)
v2 = 2 * 0.283 * 0.69 / (0.283 + 0.467)
= 0.52072 m/s.

The retarding friction force on glider is (- um2 g), and its acceleration after collision is therefore ( - ug.)
0 = v2^2 - 2ugs
s = v2^2 / 2ug ...(4)
s = 0.52072^2 / 2 * 0.02 * 9.81
= 0.69 m

The distance to be covered by glider is 1.2 m.
Thus the glider will not reach the end of the 2.4 m. track.

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