Changes in Energy and Momentum.Show your work and explain your reasoning. Two ca

Question

Changes in Energy and Momentum.Show your work and explain your reasoning. Two carts of unequal mass (mA>mB) move on frictionless tracks.Both starts from rest and have the same constant force exerted on them until they reach the finish line.The force begins to be exerted on cart A first.The force starts acting on cart B only as cart A passes it>Both carts reach the finish line at the same time.At the finish,cart B is moving faster than cart A At an instant when both carts have the force exerted on them,is the acceleration of cart A greater than,less than or equal to the acceleration of cart B? Explain. Is the magnitude of the final momentum of cart A greater than,less than or equal to the magnitude of the final momentum of cart B? Explain. Is the final kinetic energy of cart A greater than,less than,or equal to energy of cart B? Explain.

Explanation / Answer

a) Cart B will always have greater acceleration....

For A and B as the forces are constant...and Ma > Mb

Also, F = M * a

So, accn of b must be larger.

b) Force = rate of change of momentum, Here Force = same...

So, rate of change must be same...Here initial momentum of both A and B are zero...

And Since time taken for B is less...So its final momentum of B must be larger

c) KE = momentum ^ 2 / 2*m

here momemtum of B is larger...and mass smaller....

So, KE of B is greater than KE of A

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