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 1.44 m/s. The pulling force is 94 N parallel to the incline, which makes an angle of 20.2° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled 4.98 m. (a) How much work is done by the gravitational force on the crate? (b) Detemine the increase in internal energy of the crate-incline system cwi g to friction () How much work is done by the 94-N force on the crate? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 4.98 m my's

Explanation / Answer

work done by gravity is negative because it is working in the opposite direction of motion

wg = -mgdsintheta

m = mass of crate = 10.6 kg

g = 9.8 m/s^2

d = 4.98 m

theta = 20.2 degree

wg = -178.6 J

part b )

internal energy owing to friction froce is equal to work done by fricntion force

wf = mu*m*g*d*costheta

mu = 0.4

wf = -194.2 J

part c )

W = F*d

W = 94 * 4.98 = 468.12 J

part d )

using work energy theorem for non conservative forces

dK = W - Wf - Wg

dK = 468.12 - 194.2 - 178.6

dK = 95.4 J

part e )

Kf-Ki = -Wf + Wotherforce

K = mv^2/2

mvf^2/2 - mvi^2/2 = Wotherforce - Wf

vf = sqrt(2/m [dK + mvi^2/2])

vi = 1.44 m/s

vf = 4.48 m/s

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