A crate of mass 9.20 kg is pulled up a rough incline with an initial speed of 1.

Question

A crate of mass 9.20 kg is pulled up a rough incline with an initial speed of 1.40 m/s. The pulling force is 99.0 N parallel to the incline, which makes an angle of 20.7° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.95 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 due to friction. J (c) How much work is done by the 99.0 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 4.95 m? m/s

Explanation / Answer

a) Work done by the gravitational force is Wg = -m*g*sin(theta)*S = -9.2*9.81*sin(20.7)*4.95 =-157.91 J

b) work done by friction = change in internal energy = -mu_k*m*g*cos(theta)*S = -0.4*9.2*9.81*cos(20.7)*4.95 = -167.16 J

C) work done by 99 N is W = 99*4.95 = 490.5 J

d) Work done by the net force = change in KE

-157.91-167.16+490.5 = chnage in KE

change in KE = 165.43 J

e) 0.5*m*(v^2-u^2) = 165.43

v^2-1.4^2 = 2*165.43/9.2

v = 6.15 m/s

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