1. Monday, October 19, 1998 Chapter 7: Newton’s Law of Gravity Gravitational Potential Energy Kepler’s Laws

2. Hint: Be able to do the homework (both the problems to turn in AND the recommended ones) you’ll do fine on the exam! Friday, October 23, 1998 in class Chapters 5 - 7 inclusive You may bring one 3”X5” index card (hand-written on both sides), a pencil or pen, and a scientific calculator with you. I will put any constants, math, and Ch. 1 - 4 formulas which you might need on a single page attached to the back of the exam.

4. When an object experiences a centripetal acceleration, there must be a force acting which results in such an acceleration. F c = m a c For objects moving in a circle, Newton’s 2nd Law takes the form

5. What kind of forces might result in a centripetal force? Force of Tension What makes this car turn to the right? Frictional Force of Tires on Road

6. Component of Normal Force of Road on Car What if the car now goes around an inclined bend? Frictional Force of Tires on Road Could point up or down the road. On what will the direction of the frictional force depend? Angle of the incline Speed of the car

7. And for a given velocity, there exists one angle at which the frictional force exerted by the road on the tires is 0. Component of Normal Force of Road on Car FNFN FgFg 

8. Component of Normal Force of Road on Car FNFN FgFg  Notice that in this case, the Normal Force exerted by the road on the car is greater in magnitude than the weight of the car! WHY? Think about the direction of the tangential velocity and the shape of the road in front of the car...

10. Every massive particle in the Universe attracts every other massive particle in the Universe with a force that is directly proportional to the product of their gravitational masses and inversely proportional to the square of their separation distance.

11. To make this proportional relationship an equality, we simply multiply by a constant of proportionality... The proportionality constant, G, is called the constant of universal gravitation, and has been experimentally determined to be The vector points in the direction from one mass to the other.

12. To make our life simpler in applying the universal law of gravitation, we are aided by the fact that the gravitational force exerted by spherical objects acts as if all the mass were concentrated at the center of the object! So the gravitational force these astronauts feel high above the Earth’s surface depends upon how far away from the CENTER of the Earth they are!

13. And the force they feel hovering above the Earth would be exactly the same as the force exerted by a point mass equal to the mass of the Earth and located at the very center of the Earth!

14. The planets in our solar system move around the Sun in roughly circular orbits. This means that some centripetal force must be acting on the planets. What force is responsible?

15. Given that the Earth (m = 6 X 10 24 kg) orbits the Sun (m = 2 X 10 30 kg) in roughly a circular orbit (r = 1.5 X 10 11 m) once per year, calculated the mean orbital speed of the Earth.

16. Given that the Earth (m = 6 X 10 24 kg) orbits the Sun (m = 2 X 10 30 kg) in roughly a circular orbit (r = 1.5 X 10 11 m) once per year, calculated the mean orbital speed of the Earth. Spaceship Earth travels through the Cosmos at a surprisingly high speed!