Physics 100: Homework Problems
Chapters 8 and 9: due Mar 1
1) Why must you bend forward when carrying a heavy load on your back? (hint: consider stability)
You bend forward when carrying a heavy load on your back to shift the center of gravity of you and your load above the area bounded by your feet—otherwise you topple backward. The condition for stability is that a vertical line dropped down from the center of gravity meets a point in the base of the object.
2) If the polar ice caps of the Earth were to melt, the oceans would be deeper by about 30 m. What effect would this have on the Earth’s rotation?
The mass contained in the ice would spread more evenly around the world instead of being localized near the poles. In accord with the conservation of angular momentum, since mass is moving farther from the axis of rotation (this goes through the poles), the rotational speed decreases. So Earth would slow in its daily rotation and the day would become longer.
3) A friend says that since Earth’s gravity is so much stronger than moon’s gravity, rocks on the moon could be dropped to the Earth. What goes wrong with his conclusion?
The force of gravity on Moon rocks at the Moon’s surface is considerably stronger than the force of gravity of the distant Earth. The force of gravity of a planet or moon on the rock depends not only on the masses of the planet or moon and rock but also on how far the rock is from the planet. Rocks dropped on the Moon fall onto the Moon surface since the gravitational force from the Moon is so much stronger than from the Earth when the rock is near the moon’s surface because the moon is so much closer to the rock. (The force of the Moon’s gravity is about 1⁄6 of the weight the rock would have on Earth; the force of the Earth’s gravity at that distance is however only about 1⁄3600 of the rock’s Earth-weight.)
4) Most people today know that the ocean tides are caused principally by the gravitational pull of the moon. And most people therefore think that the gravitational pull of the moon on the Earth is greater than that of the sun on the Earth. What do you think?
The gravitational pull of the Sun on the Earth is greater than the gravitational pull of the Moon, about 180 times as large. The tides, however, are caused by the differences in gravitational forces by the Moon on opposite sides of the Earth. The difference in gravitational forces by the Moon on opposite sides of the Earth is greater than the corresponding difference in forces by the stronger pulling but much more distant Sun.