Answer to Question #156724 in Physics for Garyson McDoodle

Question #156724

An object of mass 3.0 kg travels with a speed of - 3.5 m/s on a frictionless

surface. The object collides with a 4.0 kg object at rest that exerts an average

net force over an interval of time 2.0 ​m​s such that the 3.0 kg object comes to

rest.

A. What is the average force on the 4.0 kg object?

B. What is the final velocity of the 4.0 kg object?


1
Expert's answer
2021-01-19T20:05:35-0500

A) We can find the average force on the 4.0 kg object from the impulse-momentum change equation:


"F_{avg}\\Delta t=m\\Delta v,""F_{avg}\\Delta t=m(v_f-v_i),""F_{avg}=\\dfrac{m(v_f-v_i)}{\\Delta t},""F_{avg}=\\dfrac{3.0\\ kg\\cdot(0-(-3.5\\ \\dfrac{m}{s}))}{2.0\\cdot10^{-3}\\ s}=5250\\ N."

B) We can find the final velocity of the 4.0 kg object from the law of conservation of momentum:


"-m_1v_1=m_2v_2,""v_2=-\\dfrac{m1v_1}{m_2}=-\\dfrac{3.0\\ kg\\cdot 3.5\\ \\dfrac{m}{s}}{4.0\\ kg}=-2.625\\ \\dfrac{m}{s}."

The sign minus means that 4.0 kg object is moving to the left after the collision.

Answer:

A) "F_{avg}=5250\\ N."

B) "v_2=2.625\\ \\dfrac{m}{s}," to the left.


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