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1. If an 82.5kg father gets on a 5.0 meter see-saw with his 21.0kg son at one end, at what distance should the father sit in order to balance the torques? Assume the fulcrum is in the center.
2. Consider a ring and a coin that both have a mass of 6.0 grams rolling down an inclined plane, which would get to the bottom first? Explain.
3. The planet Jupiter is about 300 times as massive as Earth, but an object on its surface would weigh only 2.5times as much as it would on Earth. Can you come up with an explanation?

2007-03-13 14:54:53 · 1 answers · asked by Rose 3 in Education & Reference Homework Help

1 answers

1.) For a lever, F1d1 = F2d2
F1 = dad = m1g = 82.5 kg * 9.8 m/s^2 = 808.5
d1 = x
F2 = son = m2g = 21.0 * 9.8 = 205.8
d2 = 2.5 m (half length of the see saw)

808.5x = 205.8 * 2.5
x = 0.713 m

2.) The acceleration due to gravity is the same for both, and they are both circles, so unless they have significantly different rolling friction, they would arrive at the same time. Being hollow doesn't make a difference.

3.) Newton's law of universal gravitation:
F = G * m1m2/r^2

If you compare gravitational forces for 2 objects, you can cancel certain things:
G is a constant, and the same for both, so it can be cancelled.
m2 is insignificant compared to a planet, and is ignored. Thus:
2.5 (the ratio between weights) * mE/rE^2 = mJ/rJ^2

Substitute the 300 masses of Earth for the mass of Jupiter:
2.5 * mE/rE^2 = 300mE/rJ^2

Solve:
rJ^2/rE^2 = 120
rJ/rE = √120 = 10.95: thus Jupiter has about 11 times the radius (and diameter) of Earth, explaining the weight difference.

2007-03-15 02:46:11 · answer #1 · answered by ³√carthagebrujah 6 · 0 0

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