3. Glider A, of mass m, moves to the right with constant speed v, on a frictionl

Question

3. Glider A, of mass m, moves to the right with constant speed v, on a frictionless track toward glider B. Glider B has mass 2m and is initially at rest. nt Glider A Glider B System S consists of gliders A and B a. In the spaces provided, draw momentum vectors for glider A, glider B, and systems. Label each vector with its magnitude (express magnitudes in terms of the given quantities m and v,). Momentum vectors GliderA Glider B System S Glider X, of mass 5m, (not shown in the diagram) moves to the right with speed v, (ie., the same speed as glider A) on a second frictionless track parallel to the original track. b. Apply the Galilean transformation of velocities to Velocity vectors in the frame of glider X determine the velocity vectors of gliders A and B in the reference frame of glider X. Draw the vectors in the space at right. Label each vector with its magnitude. (Express the magnitudes in terms of the given quantities.) Glider A Glider B Momentum vectors in the frame of glider X Glider A Glider B Draw momentum vectors of gliders A and B in the reference frame of glider X. Label each vector with its magnitude. Explain your reasoning. c. d. Consider the following incorrect statement "Glider X has momentum 5mv, to the right, so in the reference frame of glider X, the momentum of glider A is mn,-5mt, 4mt_ or 4nt, to the left. Explain the error(s) in the reasoning Suppose glider X had a different mass (ie., something other than 5m). Would the magnitude of the momentum of glider A in the reference frame of glider X be the same as or different than the value you determined in part c? Explain.

Explanation / Answer

b)
For glider A, the reference frame the glider X is traveling with the same velocity.
For glider A, velocity vector is 5vo - 5vo = 0
For glider B, velocity = 0 - 5vo = -5vo towards left

c)
For glider A, momentum is zero since velocity is zero in the reference frame of glider X
For glider B, velocity = -5vo, mass = 2m
Momentum = -10mvo, which is towards left.

d)
Momentum of glider X measured in its own reference frame is zero since every particle is moving with zero relative velocity with each other. This is same with any other mass moving with the same velocity as that of glider X.
Momentum of glider A relative to glider X = 0.

The momentum of glider A will be same irrespective of the mass of glider X. This is because Galilean transformation of velocities is mass independent.

e)
Velocity of glider A in the reference frame of glider X = 0
Velocity of glider B in the reference frame of glider X = -5vo
Momentum of the system = m x 0 + 2m x (-5vo) = -10mvo towards left

f)
Momentum in the reference frame of the tracks = mvo + 2m x 0 = mvo towards right
From the previous part, momentum in the reference frame of glider X = -10mvo towards left

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