24. Ideal and Non-Ideal Air Tracks A glider is timed as it accelerates from rest

Question

24. Ideal and Non-Ideal Air Tracks A glider is timed as it accelerates from rest on an air track. The distance traveled along the track is 1.0 m. The air track is inclined by 2" relative to the horizontal. The glider has a mass of 400 g. In (a) - (c), we will consider an air track which is ideal and has zero friction. (a) Find the net force which acts on the glider. (b) Find the acceleration of the glider (c) Find the time which it takes the glider to travel 1.0 m along the track. In (d) and (e), we will consider the case where the air track is less than ideal and friction is present. (d) Suppose we measure the time which it takes for the glider to travel 1.0 m and we obtain a time which is twice as large as the ideal time (from part (c)). Find the acceleration in this case. (e) Find the coefficient of kinetic friction.

Explanation / Answer

Given,

d = 1 m ; theta = 2 deg ; m = 400 g

a)The net force is:

Fnet = mg sin(theta)

b)Fnet = ma = mg sin(theta)

a = g sin(theta)

a = 9.81 x sin2 = 0.342 m/s^2

Hence, a = 0.342 m/s^2

c)we know that,

S = ut + 1/2 at^2

1 = 0 + 1/2 x 0.342 t^2

t = sqrt (2/.342) = 2.42 s

Hence, t = 2.42 s

d)t' = 2t = 2 x 2.42 = 4.84 s

S = ut + 1/2 at^2

a = 2S/t^2 = 2 x 1/4.84^2 = 0.085 m/s^2

Hence, a = 0.085 m/s^2

e)We know that with friction the net force is:

Fnet = mg sin(theta) - uk mg cos(theta) = ma

a = g sin(theta) - uk g cos(theta)

0.085 = 9.8 x sin2 - uk x 9.8 x cos2

uk = 0.026

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