1. Ch. 6 Work and Kinetic Energy AP Physics C

2. What is work? Write your thoughts on the whiteboard, Share with your table partner, Share with the whole class

3. Weightlifter If the weightlifter squats through a vertical distance of 80 cm and has 163.6 kg on the bar, how work does he do on the bar to push the weight back up at a constant speed?

4. Why is this considered work?

5. Is there work done? The woman carries the groceries –at a level position over a level floor? –Up a flight of stairs?

6. Definition for work done on an object when the forces are constant: By definition, the dot product is: Where  is the angle between the net force vector and the displacement vector.

7. Dot Product The dot product or scalar product is defined as Using a geometric interpretation allows us to find the angle between two vectors.

8. What does this mean? Recall that: – A = A x i + A y j + A k k and – B = B x i + B y j + B k k A· B = (A x i + A y j + A k k )· (B x i + B y j + B k k ) or

9. Sample Problem #1 Given: F = 2 i + 3 j – 5 k s = -3 i – 4 j + 6 k Find: The total work done The angle between the force and displacement vectors

10. How is work and energy related to each other? W = Fd (The force and the displacement are parallel to each other.) W = mad W = m(½v f 2 - ½v i 2 ) W = ½m v f 2 - ½m v i 2 W = K f – K i W = ∆K This is known as the Work- Kinetic Energy Theorem

11. Sample Problem #2 If the initial speed is 10 m/s and the mass of the object is 50 kg, what is the final speed? Note: The work done was determined by finding the area under the F-d graph.

12. Work done by varying forces: To calculate the work done, you determine the area under the force- displacement graph. This graph is for the work done when stretching a linear spring.

13. Work done by varying forces: Which means in some cases, you will need to divide the area into an infinite number of infinitesimal pieces.

14. Work done by varying forces: That means that you will be determining the integral (i.e. anti- derivative):

15. Sample Problem 3 A block of mass 1.5 kg is pushed against a spring with a force constant of 50 N/m. If the spring is compressed 0.10 m, at what speed does the block leave the spring? Neglect any frictional effects.

16. Sample Problem 2 If the net force is given by the force- position function, How much work is done to move the object from x = 1.0 m to x = 3.0 m?

17. Power Rate of doing work 1 horsepower (hp) = 746 watts The power rating for an object is 2.2 hp. If the object can move with an average speed of 15 m/s, what is the net force that acts on it?

18. Any Questions?