Gravitation

1)             If someone were so unfortunate as to step into a hole bored from one side of the earth to the other, what would be their motion through the tunnel? Neglect air resistance.

2)             If air resistance were a factor in Question 1, how would the person’s motion change?

3)             The weight of an apple near the surface of the earth is about 1 N. What is the weight of the earth in the gravitational field of the apple? Which of Newton’s Laws is helpful here?

4)             Suppose that for some odd reason you have sealed yourself inside a windowless box. After a while you notice that objects no longer fall to the floor when released from your hand. Without reference to anything outside the box, how can you tell whether you and the box are in free fall or gravity has been mysteriously turned off?

5)             The mass of the earth is 5.97 ´ 1024 kg, and its radius is 6370 km. A TV satellite with a 200 kg mass is in a circular orbit of radius 40,000 km around the center of the earth. Find the gravitational force on the satellite. Next, calculate the weight of the satellite if it were on Earth instead of in orbit, and find the percentage decrease when it’s in space.

6)             In the late 1700’s, a clever person by the name of Henry Cavendish calculated the mass of the Earth. To do so, he first had to measure the gravitational constant, G. He found that a sphere of mass 0.8 kg attracted another sphere of mass 0.004 kg with a force of 1.3 ´ 10-10 N when the distance between the centers of the spheres was 0.04 m. The acceleration due to gravity was already known to be 9.8 m/s2 and the radius of the planet had been measured as 6400 km. First, calculate G. Second, find the mass of Earth. Use only this data.

7)             Imagine three masses at the angles of an isosceles triangle. The base of the triangle is 0.16 m long, and each of the upright legs is 0.10 m. The masses at the two angles on the base are each 6.4 kg, and the mass at the peak of the triangle is 0.01 kg. If the only forces acting on the 0.01 kg mass are the attractions from the 6.4 kg masses, find the initial direction and magnitude of the acceleration of the 0.01 kg mass at the instant it is released.