A block of ice slides down a frictionless ramp at angle θ=50° ⃗ while an ice worker pulls on the block (via a rope) with a force that has a magnitude of 50 n and is directed up the ramp. as the block slides through distance d=0.50 m along the ramp, its kinetic energy increases by 80 j. how much greater would its kinetic energy have been if the rope had not been attached to the block?
Answers
Given:
A block of ice slides down a frictionless ramp at angle θ=50° ⃗ while an ice worker pulls on the block (via a rope) with a force that has a magnitude of 50 n and is directed up the ramp.
As the block slides through distance d=0.50 m along the ramp, its kinetic energy increases by 80 j.
To find:
How much greater would its kinetic energy have been if the rope had not been attached to the block?
Solution:
From given, we have,
Force = F = 50 N
Distance = d = 0.5 m
Angle = θ = 50°
When the block slides a distance d = 0.5 m along the ramp, then it's vertical distance is given by, d sin 50
Hence its K.E. should have increased by the same amount as its P.E. has decreased as mgd sin 50. but given it's increased by 80 J.
This is because of the work done by the force F, that is W
W = Fd = 50 × 0.5 = 25 J .
Thus,
mgd sin θ - 25 = 80
M × 9.8 × 0.5 × sin 50 - 25 = 80
M = 27.97 kg.
Hence its K.E. should have increased by,
mgd sin θ
27.97 × 9.8 × 0.5 × sin 90 = 105 .
Thus, its K.E. would have been greater by 105 - 80 = 25 J
If the rope had not been attached to the block, the kinetic energy would have been greater by 25 J.