A crate of mass 10.6 kg is pulled up a rough incline with an initial speed of 1.
ID: 1359785 • Letter: A
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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