Billy Bob Bubba Hickman wants to move some heavy boxes up to the loft in his bar
ID: 1553266 • Letter: B
Question
Billy Bob Bubba Hickman wants to move some heavy boxes up to the loft in his barn. He uses a 2.25 horsepower motor to pull the boxes a distance of 9.35 meters up a ramp inclined at an angle of 36.2° with respect to horizontal. The boxes have a coefficient of kinetic friction of 0.381 as they slide along the ramp.
a) What is the heaviest box that Bubba can pull up the incline with this motor at a constant speed of 76.5 cm/s?
b) What is the work done by the motor as it pulls the box up the incline?
c) What is the change in potential energy of the box?
d) Explain why answers b and c do not match?
Explanation / Answer
(A) P = F.v
(2.25 x 745.7) W = F (0.765 m/s)
F = 2193.23 N
Along the incline,
F = mg sin(theta) + fk
fk = uk N = uk m g cos(theta)
F = m g (sin(theta) + uk cos(theta))
2193.23 = m x 9.8 ( sin36.2 + 0.381 cos36.2)
m = 249.2 kg
(B) Work done = F.d
2193.23 x 9.35
= 20506.7 J
(C) change in PE = m g deltaH
= 249.2 x 9.8 x 9.35 sin36.2
= 13486 J
(D) work done will be more than change in Potential energy.
because some energy will lost due to friction
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