40.  The drawing shows two boxes resting on frictionless ramps. One box is relatively light and sits on a steep ramp. The other box is heavier and rests on a ramp that is less steep. The boxes are released from rest at A and allowed to slide down the ramps. The two boxes have masses of 11 and 44 kg. If A and B are 4.5 and 1.5 m, respectively, above the ground, determine the speed of (a) the lighter box and (b) the heavier box when each reaches B. (c) What is the ratio of the kinetic energy of the heavier box to that of the lighter box at B?

 

No Friction implies no non-conservative forces, so mechanical energy is conserved.  We also know that the boxes are released from rest so that initial kinetic energy is zero.

 

For both boxes

 

 

 

 

Turns out the mass cancels out, so for either heavier or lighter mass, the speed at B is

 

 

 

 

This is true for both the lighter and heavier boxes.

Ratio of kinetic energies of Heavier to lighter box is

 

 

 

 

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This page last updated on January 11, 2020