The weight of an apple near the surface of Earth is 1 N. What is the weight of Earth in the gravitational field of the apple?

In April and May, 2011, tornadoes ripped through Tuscaloosa, Alabama, and Joplin, Missouri, killing hundreds and destroying thousands of homes and businesses. Perform a Web quest to report on rebuilding efforts in these two towns. Use software to report om how the cities allocated resources, what improvements were made to the new structures in the area, and how the people of Joplin and Tuscaloosa have responded psychologically to these efforts.

How would the gravitational field at Earth’s surface be affected if Earth shrank in size without any change in mass? What would be its relative strength at the new surface if Earth shrank to half size? To one-tenth size?

If the radius of Earth somehow shrank by half without any change in Earth’s mass, what would be the value of g at the new surface? What would be the value of g above the new surface at a distance equal to the present radius?

How much energy is required to ionize a hydrogen atom initially in the n=2 state?

The gravitational field strength at Earth’s surface is 9.8 N/kg. What is the field strength at the center of Earth? At a distance one Earth radius beyond the surface?

The mass of Saturn is 95 times that of Earth and its radius is 9 times that of Earth. Calculate the acceleration due to gravity at the surface of Saturn. Express your answer in g’s

As part of their training before going into orbit, astronauts ride in an airliner that is flown along the same parabolic trajectory as a freely falling projectile. Explain why this gives the same experience of apparent weightlessness as being in orbit.

A satellite can orbit at 5 km above the Moon’s surface but not at 5 km above Earth’s surface. Why?

A kilogram of water on the side of Earth nearest the moon is gravitationally attracted to the moon with a greater force is gravitationally attracted to the moon with a greater force than a kilogram of water on the side of Earth farthest from the moon. The difference in force per mass, the tidal force, is approximated by

$$F _ { T } = \frac { 4 G M R } { d ^ { 3 } }$$

where G is the gravitational constant, M is the mass of the moon, R is the radius of Earth, and d is the distance between the centers of the moon and Earth. Even a 1-kg melon held above your head exerts a tidal force on you. The above equation, however, is a good approximation only when d is much larger than R. The distance d between the center of the melon and your center is only about twice R. So the general tidal force equation (the source of the above equation) must be used, which is

$$F _ { \mathrm { T } } = ( 4 G M d R ) / \left( d ^ { 2 } - R ^ { 2 } \right) ^ { 2 }$$

Use this to calculate the melon‘s

$$F_T$$

on you. Here M = 1 kg, and if you’re 2 m tall, R = 1 m, and d = 2 m. How does this compare with the tidal force of the moon on you?

Ignoring air resistance, could a satellite be put into orbit in a circular tunnel beneath Earth's surface?

Determine whether the following series converge. $\sum _ { k = 1 } ^ { \infty } ( - 1 ) ^ { k + 1 } \frac { k ^ { 2 } } { k ^ { 3 } + 1 }$

How are sex pili different from fimbriae and what is their significance?

A kilogram of water on the side of Earth nearest the moon is gravitationally attracted to the moon with a greater force than a kilogram of water on the side of Earth farthest from the moon. The difference in force per mass, the tidal force, is approximated by

$$F _ { \mathrm { T } } = \frac { 4 G M R } { d ^ { 3 } }$$

where G is the gravitational constant, M is the mass of the moon, R is the radius of Earth, and d is the distance between the centers of the moon and Earth. Calculate

$$F_T$$

of the moon on Earth in units

$$\mathrm { N } / \mathrm { kg } . ( M = 7.35 \times 10 ^ { 22 } \mathrm { kg } , R = 6.4 \times 10 ^ { 6 } \mathrm { m }, \text {and} d = 3.85 \times 10 ^ { 8 } \mathrm { m } )$$