Suppose the block in the previous problem were launched with the same initial sp

Question

Suppose the block in the previous problem were launched with the same initial speed on the following ramps. In each case state whether the magnitude of the net work done on the block from the bottom to the top of the ramp is greater than, less than, or equal to the magnitude of the net work done one the block in problem 2. Explain your answer in each case. The ramp is steeper (alpha > 0). The ramp has two sections of different slope. The ramp has several sections of gradually increasing steepness. The ramp is curved. Use the work-energy theorem to rank the final speeds of the block on the ramps (a-d), assuming the block is launched with the same initial speed in each case. If the final speeds are the same in any of the cases, state that explicitly. Explain.

Explanation / Answer

Let the initial velocity of the object in all cases be Ve .

So Initally the Kinetic energy at inital point KE=(1/2)mVe2

Now in all cases the object goes on to the height H so the potential energy at that point is PE=mgH

so the kinetic energy after reaching at the top is

(1/2)mVe2-mgH = (1/2) m Vf2 (conservation of energy)

where Vf is the velocity of the object aafter reaching the top point .

Vf=sqrt(Ve2 -2gH) ANS

and in all cases the velocity will remain same .

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