1. 1 Honors Physics 1 Class 08 Fall 2013 Review of quiz 3 Integrating equation of motion Work-Energy Theorem Potential Energy Intro

2. 2 Integrating the equation of motion If we know the force as a function of time, then it is in principle straightforward to solve the motion of a particle. Frequently though, we only know the force as a function of position (spring force, gravitational force...) We will now develop some tools for addressing such situations.

3. 3 Integrating the equation of motion

4. 4

5. 5 Example 1 A mass m is thrown vertically upward with initial speed v 0. How high does it rise? (Assume g is constant and neglect friction.)

6. 6 Example A mass m is shot vertically upward from the surface of the earth at initial speed v 0. Assuming that the only force is gravity (GmM/r 2 ), a)Find the height to which the mass rises. b)Find the escape velocity.

7. 7 Example 2

8. 8 Equation of motion in three dimensions

9. 9 Escape velocity: General case What if the projectile is not shot straight up?

10. 10 The Work-Energy Theorem (in one dimension)

11. 11 So what?