A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficie

Rivka Thorpe 2021-03-22 Answered
A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant but starts at .100 at P and increases linerly with distance past P, reaching a value of .600 at 12.5 m past point P. (a) Use the work energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid iff the friciton coefficient didn't increase, but instead had the constant value of .1?
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Expert Answer

Neelam Wainwright
Answered 2021-03-24 Author has 102 answers
Let x be the distance past P.
μb=0.100+Ax
When x=12.5mμb=0.600
A=0.50012.5m=0.0400m
a)
W=KE:Wf=KEfKEi
μbmgdx=012mvi2
g0xf(0.100+Ax)dx=12vi2
g[(0.100)xf+Axf22]=12vi2
(9.80ms2)[(0.100)xf+(0.0400m)xf22]=12(4.50ms)2
Now solve for xf, We get the answer as xf=5.11m
b)
μk=0.100+(.40m)(5.11m)=0.304
c)
Wf=KEfKEi
μbmgx=012mv12
x=v122μbg=(4.50ms)22(0.100)(9.8ms2)=10.3m
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