An experienced bartender knows just the right initial speed of a glass of beer t

Question

An experienced bartender knows just the right initial speed of a glass of beer to get it to come to a stop in front any customer sitting along the bar. Say the initial speed needed to move a glass all the way to the end of the bar is vend.

In terms of vend, with what speed should an identical glass of beer be released if it is to stop at a customer sitting three-fifths of the way down the bar? (The kinetic energy converted to thermal energy because of friction is proportional to the distance the glass skids.) .

Explanation / Answer

According to Work-energy theorem,

External work done, Wext = Change in mechanical energy

=> fd = mvend2/2 - 0

=> vend = (2fd/m)1/2

Let the required speed be v. Then,

v = [2f * (3d/5) / m]1/2 = (3/5)1/2 * vend = 0.775 vend

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