A railroad handcar is moving along straight, frictionless tracks with negligible

Question

A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of 160 kg and is traveling east with a velocity of magnitude 5.30 m/s. Find the final velocity of the car in each case, assuming that the handcar does not leave the tracks. An object with a mass of 29.0 kg is thrown sideways out of the car with a speed of 1.90 m/s relative to the car's initial velocity. An object with a mass of 29.0 kg is thrown backward out of the car with a velocity of 5.30 m/s relative to the initial motion of the car. An object with a mass of 29.0 kg is thrown into the car with a velocity of 6.00 m/s relative to the ground and opposite in direction to the initial velocity of the car.

Explanation / Answer

part a )

momentum in x direction is conserved

after the mass is thrown sideways relative to the car it still has the same eastward component of velocity

(m1+m2)v1 = m1v1x + m2v2x

v2x = [160 * 5.3 - 29 *5.3) / 131

v2x = 5.3 m/s

part b )

Px = constant

final velocity of A relative to the ground

v_1/E = v_1/2 + v_2/E

v_2/E = 5.3 m/s

v_1/2 = -5.3 m/s ( minus since the mass is moving west relative to the car)

v_1/E = 0

the mass is at rest relative to the earth after it is thrown backwards from the car

(m1+m2)v1 = m1v1x + m2v2x

v2x = (m1+m2)*v1/m2 = 160 * 5.3 / 131 = 6.47 m/s

part c )

(m1 + m2) v2f = -m1v1i + m2v2i

v2f = 160 * 5.3 - 29*6 / ( 160 +29)

v2f = 3.57 m/s

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