User:Inconspicuum/Physics (A Level)/Gravity Questions

Gravitational Forces

1. Jupiter orbits the Sun at a radius of around 7.8 x 10¹¹m. The mass of Jupiter is 1.9 x 10²⁷kg, and the mass of the Sun is 2.0 x 10³⁰kg. What is the gravitational force acting on Jupiter? What is the gravitational force acting on the Sun?
2. The force exerted by the Sun on an object at a certain distance is 10⁶N. The object travels half the distance to the Sun. What is the force exerted by the Sun on the object now?
3. What is the magnitude of the gravitational force that two 1kg weights exert on each other when they are 5cm apart?
4. The radius of the Earth is 6360km, and its mass is 5.97 x 10²⁴kg. What is the difference between the gravitational force on 1kg at the top of your body, and on 1kg at your head, and 1kg at your feet? (Assume that you are 2m tall.)

Gravitational Fields

G = 6.67 x 10^-11 m³kg^-1s^-2

1. A 15kg object has a weight of 8000N. What is the gravitational field strength at this point?
2. Draw a graph of gravitational field strength against distance.
3. What is the gravitational field strength of the Sun (mass 2 x 10³⁰kg) on the Earth (mass 6 x 10²⁴kg, mean orbital radius 15 x 10¹⁰m)?
4. What is the difference in the acceleration due to gravity over a vertical distance d?
5. How far would one have to travel upwards from the Earth's surface to notice a 1Nkg^-1 difference in gravitational field? (The Earth has a radius of 6400 km.)

Gravitational Potential Energy

1. A ball rolls down a 3m-high smooth ramp. What speed does it have at the bottom?
2. In an otherwise empty universe, two planets of mass 10²⁵ kg are 10¹² m apart. Both the planets have a radius of 10⁶ m. What are their speeds when they collide?
3. What is the least work a 2000kg car must do to drive up a 100m hill?
4. How does the speed of a planet in an elliptical orbit change as it nears its star?

Gravitational Potential

G = 6.67 x 10^-11 m³kg^-1s^-2

g = 9.81 ms^-2

1. What is the gravitational potential at the Earth's surface? (mass of Earth = 5.97 x 10²⁴ kg,radius of Earth = 6371 km)
2. Taking the Earth's surface as V_grav = 0, what is the gravitational potential 2m above the ground?
3. A 0.2kg firework reaches a gravitational potential relative to the ground of 500Jkg^-1. If the firework is 30% efficient, how much energy was expended to get there?
4. Express gravitational potential in terms of gravitational force.
5. Draw the equipotentials and field lines surrounding the Earth.