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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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