Question

A cart for hauling ore out of a gold mine has a mass of 423 kg, including its load. The cart runs along a straight stretch of track that is sloped 4.51° 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 535-N force for a distance of 159 m by means of a rope that is parallel to the ground and makes an angle of 13.1° with the track. The coefficient of friction for the cart\'s wheels on the track is 0.0127. Take g = 9.81 m/s2.

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

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

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

Answer 1

givent aht

mass m = 423 kg

coeffiecient of friction ? = 0.0127

accleration due to gravity g = 9.8 m/s²

inclied angel ?₂ = 4.51

inclined angel ?₁ = 13.1

distance travelled d = 159 m

applied fore F = 535 N

the component of the force from the donkey in the direction of motion is

   F₂ = F₁ cos?₁

        =521.08 N

from the free body diagram

  

?F_y = N - mg cos?₂ = 0

    N = mg cos?₂

       = 4132.56 N

?F_x = F₂ - mg sin?₂ - f = ma

  here   f = ? N

              = 52.48

F₂ - mg sin?₂ - f = ma

a = F₂ - mg sin?₂ - f/ m

    = 0.337 m/s^2

work done by donkey

    W = F₂ d

       =82851.72 J

work done by gravity

    W = - mg sin?₂ d

        = -51828.53 J

work done by friction W = - fd

                                          = - 8344.32 J