A crate of mass 9.0 kg is pulled up a rough incline with an initial speed of 1.4

Question

A crate of mass 9.0 kg is pulled up a rough incline with an initial speed of 1.42 m/s. The pulling force is 98 N parallel to the incline, which makes an angle of 19.4degree with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.92 m. How much work is done by the gravitational force on the crate? J Determine the increase in internal energy of the crate-incline system owing to friction. J How much work is done by the 98-N force on the crate? J What is the change in kinetic energy of the crate? J What is the speed of the crate after being pulled 4.92 m? m/s

Explanation / Answer

a)

W = F.S
F --- force, S ---displacement

Since we have broken the gravitational force into two components, therefore~

W = w1 + w2
W = mgsin*(-4.92) + mgcos (0)

= (9)(9.8)sin(19.4)(-4.92) + 0

= - 226.98 J

b)

Ff = Normal reaction ( R ) x Coefficient of friction ( )

Ff = R

Ff = mgcos x 0.4

Ff = (9) (9.8) cos(19.4) (0.4)

Ff = 30.06 N

W(f) = (30.06) (-4.92)
= - 147.93 J

c)

W(F) = F.S
= (98 ) (4.92)
= 482.16 J

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