A box of mass m = 25kg is dragged across a horizontal surface with a rope that m
ID: 1837226 • Letter: A
Question
A box of mass m = 25kg is dragged across a horizontal surface with a rope that makes an angle of then = 31.44degree with the horizontal. The tension in the rope is T = 35N. The crate is also subject to a friction force of f = 92.41N. The box comes to rest after being dragged a distance of delta x = 5m. Calculate the work done by T (the tension in the rope) over the 5m displacement. Calculate the work done by friction over the 5m displacement. Apply the Work-Kinetic Energy Theorem to find the initial speed of the box.Explanation / Answer
1.
Work done by T
Work = Force*displacement
displacement = d = 5 m
Tx = T*cos A = 35*cos 31.44 deg = 29.86 N
W = Tx*d = 29.86*5 = 149.3 J
2.
Wf = Ff*d
Ff = -92.41 N
d = 5 m
W = -92.41*5 = -462.05 J
3.
Using work-energy theoram:
W = dKE
dKE = KEf - KEi = 0.5*m*vf^2 - 0.5*m*vi^2
vf = 0
m = 25 kg
dkE = 0 - 0.5*25*vi^2
Wt = 149.03 - 462.05 = -313.02 J
-313.02 J = 0 - 0.5*25*vi^2
vi = sqrt (313.02*2/25) = 5.004 m/sec
initial velocity = 5.004 m/sec
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