11. Consider 3 situations. 1.) An object, with mass m is held over a vertical dr

Question

11. Consider 3 situations. 1.) An object, with mass m is held over a vertical drop of height, h. It is then dropped. 2.) An object, with mass m is at the top of a ramp with ramp length, 2h and vertical height, h. It is then allowed to slide down the slope. 3.) An object, with mass 2m is at the top of a ramp with ramp length, 2h and vertical height, h. It is then allowed to slide down the slope. In each case, there is no air resistance or friction. In 100 words or less, rank each situation according to which is traveling the with the fastest speed when each hits bottom of their fall/ramp. Explain your reasoning. (Worth 2 points on correctness.)

Explanation / Answer

Using energy balance equation which will be applicable on all the 3 given cases:

Considering potential of the ground level to be Zero for our refrence,

Initial Potential Energy at height = Final Kinetic Energy at the ground level

(Mass)*g*(Height) = (1/2)*(mass)*(v)^2

=>   v = sqrt [2*g*(Height)]

As mentioned in the question, the Height for each case is same and it will be "h",

  =>   v = sqrt [2*g*h]

   So, v1 = v2 = v3 = sqrt [2*g*h] (Independent of mass)

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