A crate of mass 10.6 kg is pulled up a rough incline with an initial speed of 1.

Question

A crate of mass 10.6 kg is pulled up a rough incline with an initial speed of 1.52 m/s. The pulling force is 90 N parallel to the incline, which makes an angle of 19.6 with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 5.08 m

(a) How much work is done by the gravitational force on the crate?

(b) Determine the increase in internal energy of the crate%u2013incline system owing to friction.

(c) How much work is done by the 90-N force on the crate?

(d) What is the change in kinetic energy of the crate?

(e) What is the speed of the crate after being pulled 5.08 m?

Explanation / Answer

change in height=5.08*sin 19.6 degree=1.7m

a)work done by gravity =-mgh=-10.6*9.8*1.7=-176.6 J

b)work done by friction = umgdcos19.6=0.4*10.6*9.8*5.04*cos 19.6 degree=-197.3J

increase=197.3J

c)it is 90*5.08=457.2J

d)change in KE=work=457.2-197.3-176.6=83.3J

e)final ke=83.3+0.5*10.6*1.52=91.36J

0.5*10.6*v^2=91.36

v=4.15m/s

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