In: Physics

# A cart for hauling ore out of a gold mine has a mass of 423 kg,...

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

## Solutions

##### Expert Solution

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

?Fy = N - mg cos?2 = 0
N = mg cos?2
= 4132.56 N
?Fx = 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

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