Physics 1120 In-Class Problems: Gravitation

1. Ted and Alice are mutually attracted to one another in the gravitational sense. If Ted's mass is 80.0 kg and Alice's is 55.0 kg and they are 0.150 m apart, what is the magnitude of the attraction on each? Treat them as point masses. What does this tell you about the gravitational effects of ordinary sized objects?

2. The distance between the centres of the earth and the moon is 3.85 × 10⁸ m. The moon has a mass which is only 1.29% that of earth. Where would a satellite have to be placed to feel no net gravitational pull from the earth and the moon?

3. Given that the mass of the moon is 7.35 × 10²² kg, that the distance between the centres of the earth and the moon is 3.85 × 10⁸ m, and that the radius of the earth is 6378 km, find the gravitational pull of the moon on a 75-kg person when the moon is directly overhead. Compare this to the person's weight (i.e. look at the ratio of the two).

4. The moon circles the earth once every 27.3 days. We have already determined that the mass of the earth is 5.98 × 10²⁴ kg. What is the distance from the centre of the earth to the centre of the moon?

5. The earth is a satellite of the Sun. The distance from the sun to the earth is 1.50 × 10¹¹ m. What is the mass of the Sun?

6. The brightest four moons of Jupiter were discovered by Galileo with one of his earliest telescopes. These moons, Io, Europa, Ganymede, and Callisto, are called the Galilean moons in his honour. Some of the available data about these moons are given below.
   

   MOON	r (km)	v	T (earthyears)
   Io	4.219 × 105	-	0.004837
   Europa	6.712 × 105	-	-
   Ganymede	-	-	0.0195884
   Callisto	1.853 × 106	-	-

   The radii are from the centre of Jupiter to the centre of the moon in question. One earth year has 365 days. From the above data, determine (a) the mass of Jupiter, (b) the period of Europa, (c) the distance between Jupiter and Ganymede, and (d) the speed of Callisto.

7. The mass of the planet Mercury is 3.30 × 10²³ kg and its radius is 2.439 × 10⁶ m. What would a 65.0-kg person weigh on Mercury?

8. You wish to send a rocket from the surface of the earth to a point halfway between the centres of the earth and the moon. At that point it should have zero velocity. What initial speed must the rocket have to accomplish this feat? You must consider the potential energy of the rock with respect to both the earth and the moon. The centre to centre earth-moon distance is 3.84 × 10⁸ m. The radius of the earth is 6378 km. The mass of the earth is 5.98 × 10²⁴ kg and the moon has a mass of 7.36 × 10²² kg.

9. A large star after is novas can collapse back into a superdense object call a neutron star. A large enough star can theoretically collapse back into a black hole. In the case of a neutron star light cannot escape from its surface because the pull of gravity is so great. For black holes, one talks of an event horizon below which light cannot escape. If the neutron star (black hole) has a mass of 100 of our suns, what is the radius of the neutron star (event horizon)? Calculate the density of such a neutron star. The mass of our sun is 1.99 × 10³⁰ kg and the speed of light is 3.0 × 10⁸ m/s.

10. At perigee, the point of closest approach, a satellite moves with 3 times the speed that it has at apogee, the point of greatest separation. At perigee it is 1000 km above the surface of the earth. The mass of the earth is 5.98 × 10²⁴ kg and it's radius is 6378 km. (a) How far away is it at apogee? Hint: consider the angular momentum at apogee and perigee. (b) What is the speed of the satellite at perigee and apogee?
    

Problems : Chapter 10 - #9,10,20,21,31,32,37,41,55,61

Questions? mike.coombes@kwantlen.ca