A cart for hauling ore out of a gold mine has a mass of 431 kg, including its lo

Question

A cart for hauling ore out of a gold mine has a mass of 431 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.87° from the horizontal. A donkey, trudging along and to the side of the track, has the unenviable job of pulling the cart up the slope with a 451-N force for a distance of 159 m by means of a rope that is parallel to the ground and makes an angle of 15.1° with the track. The coefficient of friction for the cart's wheels on the track is 0.0181. Use g = 9.81 m/s2.

Find the work that the donkey performs on the cart during this process.

Find the work that the force of gravity performs on the cart during the process.

Calculate the work done on the cart during the process by friction.

Explanation / Answer

here,

mass of crate , m = 431 kg

theta = 4.87 degree

force exerted by donkey , f = 451 N

distance , d = 159 m

phi = 15.1 degree

uk = 0.0181

the work that the donkey performs on the cart during this process, Wd = f * d * cos(phi)

Wd = 451 * 159 * cos(15.1)

Wd = 69233.1 J

the work that the donkey performs on the cart during this process is 69233.1 J

the work that the force of gravity performs on the cart during the process, Wg = m * g * d * sin(theta)

Wg = 431 * 9.8 * 159 * sin(4.87)

Wg = 57014.29 J

the work done on the cart during the process by friction , Wf = uk*m*g*d*cos(theta)

Wf = 0.0181 * 431*9.8*159*cos(4.87)

Wf = 12111.79 J

the work done on the cart during the process by friction is 12111.79 J

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