In: Physics

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

givent aht

mass m = 423 kg

coeffiecient of friction ? = 0.0127

accleration due to gravity g = 9.8 m/s^{2}

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

F_{2} = F_{1} 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} = F_{2} - mg sin?_{2} - f =
ma

here f = ? N

=
52.48

F_{2} - mg sin?_{2} - f = ma

a = F_{2} - mg sin?_{2} - f/ m

= 0.337 m/s^2

work done by donkey

W = F_{2} 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

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