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 1.42 m/s. The pulling force is 108 N parallel to the incline, which makes an angle of 19.0° 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?

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 108-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 5.08 m?

Explanation / Answer

here,

mass of the crate ,m = 10.6 kg

initial speed , v0 = 1.42 m/s

pulling force , f = 108 N

theta = 19 degree

uk = 0.4

distance pulled , d = 5.08 m

(a)

the work done by the gravitational force , Wg = m*g*sin(theta) * d

Wg = 10.6 * 9.8 * sin(19) * 5.08

Wg = 171.81 J

the work done by the gravitational force is 171.81 J

(b)

the increase in internal energy of the crate–incline system owing to friction , Wf = uk * m * g * cos(theta) * d

Wf = 0.4 * 10.6 * 9.8 * cos(19) * 5.08

Wf = 199.58 J

the increase in internal energy of the crate–incline system owing to friction is 199.58 J

(c)

work done by the 108-N force on the crate , Wf = F * d

Wf = 108 * 5.08

Wf = 548.64 J

work done by the 108-N force on the crate is 548.64 J

(d)

the change in the kinetic energy of the crate be KE

KE = Wnet

KE = Wf - Wf - Wg

KE = 548.64 - 199.58 - 171.81

KE = 177.71 J

the change in kinetic energy is 177.71 J

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