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.

a)In terms of vend, with what speed should an identical glass of beer be released if it is to stop at a customer sitting four-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

friction force remains the same in both cases.

let friction force magnitude be F.

distance to the end be d.

then for sending the glass to the end,

initial kinetic energy=work done against friction

==>0.5*mass*v_end^2=F*d...(1)

so if speed required in the second scenario is k*v_end,

then initial kinetic energy=work done against friction

==>0.5*mass*(k*v_end)^2=F*(4/5)*d...(2)

as F*d=0.5*mass*v_end^2,

equation 2 becomes,

0.5*mass*k^2*v_end^2=(4/5)*0.5*mass*v_end^2

==>k^2=4/5

==>k=0.8944

hence speed required is 0.8944*v_end.

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