A 550g air-track glider collides with a spring at one end of the track. Glider’s

Question

A 550g air-track glider collides with a spring at one end of the track. Glider’s velocity-time graph and the force (only the magnitude)-time graphs for the exerted force on the glider by the spring is shown below.

A) What is the maximum force exerted on the glider by the spring? (provide the proper sign for the force)

B) If the spring is replaced with another, which can double the maximum force within the same time limit, what will be the glider’s recoil velocity?

If you could explain the answers that would be great, thanks!

Explanation / Answer

given that

m = 550 g = 0.55 kg

delta t = 8-0 = 8*10^(-3) s

we know that

impulse = change in momentum

from the graph

impulse = area under the curve

1/2*Fmax*delta t = m*(v2-v1)

Fmax = 2*0.55*(-3-(3)) / 8*10^(-3)

Fmax = -825 N

(b)

according to the condition

Fmax = -1650 N

1/2 * (-1650)*.008 = 0.55*(v2-3)

v2 = -9 m/s

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