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A uniform rod of length L and mass M has been placed on a rough horizontal surface. The force F applied on the rod is such that the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation μ=KX, where K is a positive constant. Suppose friction is present only from X=0 to X=L. If the rod moves in the direction of application of force then the total heat generated in the time in which the rod crosses this region, is equal to
Asked by fekishfaker | 18 Nov, 2023, 01:39: PM
answered-by-expert Expert Answer
When the rod is moved from X=0 to X=L , It is assumed that energy due to workdone against the friction force is
dissipated in the rod in the form of heat .
 
Wokdone dW against friction force to move the rod through a distance dx is
 
dW = f dx = ( μ m g ) dx
 
where μ is kinetic friction coefficient , m is mass of rod , g is accelertion due to gravity .
 
If friction coefficient varies with distance x as begin mathsize 14px style mu space equals space K space x end style , then workdone dw against friction force is
begin mathsize 14px style d W space equals space left parenthesis space K space m space g space right parenthesis space x space d x end style
 
Workdone W against friction force from x=0 to x=L is
 
begin mathsize 14px style W space equals left parenthesis space K space m space g space right parenthesis space integral subscript 0 superscript L x space d x space equals space 1 half space left parenthesis space K space m space g space right parenthesis space L squared end style
Heat generated in the rod = (1/2) K m g L2
 
 
Answered by Thiyagarajan K | 18 Nov, 2023, 03:36: PM
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A uniform rod of length L and mass M has been placed on a rough horizontal surface. The force F applied on the rod is such that the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation μ=KX, where K is a positive constant. Suppose friction is present only from X=0 to X=L. If the rod moves in the direction of application of force then the total heat generated in the time in which the rod crosses this region, is equal to
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