Posted by admin | Posted in Uncategorized | Posted on 29-04-2008
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Kelli weighs 415 N, and she is sitting on a playground swing seat that hangs 0.37 m above the ground. Tom pull?
(entire question)
Kelli weighs 415 N, and she is sitting on a playground swing seat that hangs 0.37 m above the ground. Tom pulls the swing back and releases it when the seat is 1.00 m above the ground. Assume that air resistance is negligible.
a. How fast is Kelli moving when the swing passes through its lowest position?
b. If Kelli moves through the lowest point at 2.0 m/s, how much work was done on the swing by friction?
Let:
h be the descent of the swing from its original position to the lowest point,
m be Kelli's mass,
v be Kelli's speed at the lowest point,
g be the acceleration due to gravity.
(a)
Equating potential energy initially to kinetic energy at the lowest point:
mgh = mv^2 / 2
v^2 = 2gh
v = sqrt(2 * 9.81 * [ 1.00 - 0.37 ])
= 3.52 m/s to 3 sig. fig.
(b)
Let W be the work lost through friction.
W = mgh - mv^2 / 2
= m(gh - v^2 / 2)
= 415(9.81 * [ 1.00 - 0.37 ] - 2.0^2 / 2)
= 1730 J to 3 sig. fig.
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