A crate of mass 9.0 kg is pulled up a rough incline with an initial speed of 1.5
ID: 1795444 • Letter: A
Question
A crate of mass 9.0 kg is pulled up a rough incline with an initial speed of 1.54 m/s. The pulling force is 110 N parallel to the incline, which makes an angle of 20.2° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.98 m.
(a) How much work is done by the gravitational force on the crate?
J
(b) Determine the increase in internal energy of the crate–incline system owing to friction.
J
(c) How much work is done by the 110-N force on the crate?
J
(d) What is the change in kinetic energy of the crate?
J
(e) What is the speed of the crate after being pulled 4.98 m?
m/s
Explanation / Answer
a) Workdone by gravity = m*g*sin(theta)*d*cos(180)
= 9*9.8*sin(20.2)*4.98*(-1)
= -151.7 J
b) increase in internal energy = -workdone by friction
= -fk*d*cos(180)
= mue_k*m*g*cos(theta)*d
= 0.4*9*9.8*cos(20.2)*4.98
= 164.9 J
c) W_applied force = F*d*cos(0)
= 110*4.98
= 547.8 J
d) change in kinetic energy = net workdone
= -151.7 - 164.9 + 547.8
= 231.2 J
e) delta_KE = (1/2)*m*v^2
==> v = sqrt(2*delta_KE/m)
= sqrt(2*231.2/9)
= 7.17 m/s
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