A parcel of mass mp 2.2kg is thrown onto a stationary trolley of mass mT 8.3kg,

Question

A parcel of mass mp 2.2kg is thrown onto a stationary trolley of mass mT 8.3kg, that is free to move frictionlessly on a flat, horizontal surface The parcel is thrown so that when it hits the trolley it has a speed of v0 = 3.6m/s and direction given by = 39°below horizontal, as shown. The parcel has a plastic collision with the trolley surface (i.e. does not bounce) and proceeds to slide along the trolley's top surface. No kinetic friction exists between the trolley surface and the parcel The parcel slides into an undeformed linear spring of stiffness k-1,140N/m (a) What is the compression of the spring when the parcel comes to rest with respect to the trolley?

Explanation / Answer

The momentum must be conserved before and after the collision of parcel and trolley.

mv + 0 = (m + M)V

2.2(3.6)cos39 = (2.2 + 8.3)V

=> V = 0.5862 m/s

this is the velocity of the parcel and trolley system together.

so, their kinetic energy will be: T = (1/2)(M + m)V2 = (1/2)(2.2 + 8.3)(0.5862)2 = 1.804 J

by Conservation of energy, this energy will be entirely converted to elastic potential energy when the spring brings it to rest.

so, U = (1/2)kx2 = 1.804

=> (1/2)(1140)x2 = 1.804

=> x = 0.05626 m = 5.626 cm.

this is the compression in the spring.

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