2. WEIGHT The weight of a body is the Weight (a quantity) is different from mass (a quantity). The weight of a body varies with its location near the Earth (or other astronomical body), whereas its mass is the same everywhere in the universe. The weight of a body is the force

3. THE NORMAL FORCE A normal force is a force Note: The gravitational force and the normal force are not an action-reaction pair.

4. FREE BODY DIAGRAMS In all but the simplest problems that involve forces, it is helpful to draw a free body diagram (FBD) of the situation. This is a vector diagram that shows all the forces that act on the body whose motion is being studied. Forces that the body exerts on anything else should not be included, since such forces do not affect the body's motion.

5. FTFT FNFN FfFf FgFg FaFa FsFs Complete the free body diagram showing all of the forces acting on the mass M. Be sure to show the direction of each force as an arrow and label each force clearly! Example Forces:

6. Example:

7. The secret to these problems is to treat each body as a separate object.

11. Newton’s Law of Universal Gravitation

12. NEWTON’S LAW OF UNIVERSAL GRAVITATION Any two objects in the Universe exert an attractive force on each other -called the gravitational force- whose strength is proportional to the product of the objects’ masses and inversely proportional to the square of the distance between them. If we let G be the universal gravitational constant, then the strength of the gravitational force is given by the equation: Units: Newtons (N)

13. The equation for Universal Gravitation is an inverse square law

14. Henry Cavendish determined the first reasonably accurate numerical value for G more than one hundred years after Newton’s Laws were published. To three decimal places, the currently accepted value is:

15. Example What is the force of gravity acting on a 2000 kg spacecraft when it orbits two Earth radii from the center of Earth?

16. Example a. Derive the expression for g from the Law of Universal Gravitation.

17. b. Estimate the value of g on top of Mt. Everest (8848 m) above the Earth’s surface.