## Astr 2100 Descriptive Astronomy Fall 2017 - Assignment 6 - Answers

1. True or false?
1. If you drive down a straight road at constant speed then the net force on you is zero This is true. Since you are travelling in a stright line at constant speed your velocity is not changing. That means the acceleration is zero, and so in turn the net force on you is zero. See also Newton's fist Law of Motion.
2. A comet coming into the Solar System from the far reaches (beyond Pluto) speeds up towards the Sun because it is falling without any force acting on it. Since the planet's speed is changing its acceleration is not zero, and so in turn the net force on it is not zero. The force acting on it is the force og gravity
2. When a force F is applied to a mass M then the acceleration is 2 m/s². If a force 3F is applied to a mass 3M what is the acceleration?
1. The increase in force by a factor of 3 increases the acceleration by a factor of 3
2. The increase in mass by a factor of 3 decreases the acceleration by a factor of 3
3. The two factors give no overall change in the acceleration
4. The acceleration is still 2 m/s².
3. When a force F is applied to a mass M then the acceleration is 2 m/s². If a force 3F is applied to a mass ½M what is the acceleration?
1. The increase in force by a factor of 3 increases the acceleration by a factor of 3
2. The decrease in mass by a factor of ½ increases the acceleration by a factor of 2
3. The two factors give an overall change in the acceleration of 3 * 2 = 6 times
4. The acceleration is still 6 * 2 =12 m/s².
4. On the Earth (4000 miles from the center) your weight is 120 lbs. What would it be inside a rocket at a distance of 24,000 miles from the center (that is 20,000 miles above the surface)?
1. You are now 6 times the radius of the Earth away from its center
2. Your new wieght is therefore 120 / 6² = 3.33 lbs
5. On the Earth (4000 miles from the center) your weight is 120 lbs. How far (measured from the center of the Earth) would you have to go to have a weight of only 25 lbs?
1. Let your new position be x times the radius of the Earth away from its center
2. Your new weight is therefore 120 / x² = 25 lbs
3. Solving for x² and from that solving for x we get x = 2.19 Earth radii
4. In absolute terms this is 2.19 * 4000 = 8760 miles from the centre (4760 miles above the surface)
6. On the Earth your weight is 120 lbs. What would it be on the surface of a planet which has 12 times the mass and twice the radius?
1. The increase in mass of the plaet by a factor of 12 increases your weight by a factor of 12
2. The increase in radius of the plaet by a factor of 2 decreases your weight by a factor of 2² = 4
3. The two factors give an overall change in the weight of 12 / 4 = 3 times
4. Your new weight is therefore 3 * 120 = 360 lbs.