A crate of mass 10.6 kg is pulled up a rough incline with an initial speed of 1.
ID: 1339087 • 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?
m/s
Explanation / Answer
(a)
component of weight along the plane = W*sintheta
Wg = m*g*sintheta
Wg = 10.6*9.8*sin19 = 33.82 J
(b)
increase in internal energy = U = Wf = uk*m*g*costheta*L
Wf = 0.4*10.6*9.8*cos19*5.08 = 199.58 J
(c)
WF = F*L = 108*5.08 = 584.64
(d)
dKE = WF - Wf - Wg = 584.64-199.58-33.82 = 351.4 J
(e)
0.5*m*(v2^2 - v1^2) = 351.4 J
0.5*10.6*(v2^2-1.42^2) = 351.4
v2 = 8.26 m/s <<-----answer
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