Two gliders move toward each other on a linear air track (Figure 1) , which we a

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Question

Two gliders move toward each other on a linear air track (Figure 1) , which we assume is frictionless. Glider A has a mass of 0.50 kg, and glider B has a mass of 0.30 kg; both gliders move with an initial speed of 2.0 m/s. After they collide (Figure 2) , glider B moves away with a final velocity whose x component is +2.0 m/s (Figure 3) . What is the final velocity of A?

SET UP We take the x axis as lying along the air track, with the positive direction to the right. All the velocities and momenta have only x components. Our system consists of the two gliders. There are no external horizontal forces, so the x component of total momentum is the same before and after the collision.

SOLVE Let the final x component of velocity of A be vA,f,x. Then we write an expression for the total x component of momentum before the collision (subscript i) and one for after the collision (subscript f):

Pi,xPf,x==(0.50kg)(2.0m/s)+(0.30kg)(2.0m/s)(0.50kg)vA,f,x+(0.30kg)(+2.0m/s)

From conservation of the x component of momentum, these two quantities must be equal. When we solve the resulting equation for vA,f,x, we get

vA,f,x=0.40m/s (final x velocity of glider A)

REFLECT The two initial velocities are equal in magnitude, but the two final velocities are not. Although the total momentum is the same before and after the collision, it is distributed differently after the collision than before.

Part A - Practice Problem:

Suppose glider B is initially moving to the left at 3.1 m/s when it runs into glider A, which is initially at rest. At what speed does glider A move away from the collision if glider B bounces back with a speed of 0.65 m/s ?

Express your answer to two significant figures, and include appropriate units.

Explanation / Answer

we will use conservation of momentum,

0.3 (3.1) +0.5 (0) = 0.3 (0.65) + 0.5 ( v)

0.93 - 0.195 = 0.5 (v)

0.735 = 0.5v

v ( speed of glider A after collision) = 1.47 m/s apprx

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