A ball of mass 4 kg slides down a circular slope of heigh 2 m as shown in the diagram. Assume no air resistance.
(a) State the type of energy the ball possesses prior to release from the top of the slope.
(b) Calculate the speed of the ball when it reaches point Q. Assume the slope is frictionless.
(c) If the track is not frictionless and the ball reaches point Q at 6 m/s. What is the work done against friction?
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Answer:
(a) Gravitational Potential Energy
(b) Using conservation of energy,
loss in GPE = gain in KE
mgh = ½ m v2
v2 = 2gh
v2 = 2 (10) (2) = 40
v = 6.32 m/s
(c) Using conservation of energy,
loss in GPE = gain in KE + work done against friction
mgh = ½ m v2 + work done against friction
(4)(10)(2) = ½ (4) (6)2 + work done against friction
work done against friction = 80 -72
work done against friction = 8 J
