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 190 kg and is traveling east with a velocity of magnitude 5.10 m/s . Find the final velocity of the car in each case, assuming that the handcar does not leave the tracks.

Part A

An object with a mass of 28.0 kg is thrown sideways out of the car with a speed of 2.30 m/s relative to the car's initial velocity.

Part B

An object with a mass of 28.0 kg is thrown backward out of the car with a velocity of 5.10 m/s relative to the initial motion of the car.

Part C

An object with a mass of 28.0 kg is thrown into the car with a velocity of 6.50 m/s relative to the ground and opposite in direction to the initial velocity of the car.

Explanation / Answer

Using Momentum Conservation =

(a)
Since a rock is thrown sideways out of the car, no change in momentum occurs in the direction of travel of the car. This means the center of mass of the two objects must maintain momentum in the direction of travel of the car. The car's velocity is unchanged = 5.10m/s

(b)
m_1*v_1=m_2*vf + m_3*v_3
190*5.1 = (190-28)* vf + 28*0
vf = 5.98 m/s
Final Velocity of the car, Vfinal = 5.98 m/s

(c)
190*5.1 - 28*6.5 = (180+28)*Vfinal
Vfinal = 3.78 m/s

Final Velocity of the car, Vfinal = 3.78 m/s

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