2. Physics 221 Chapter 7

3. Problem 1... Work for slackers! WORK = Force x Distance W = F. D Units: Nm = J Newton meters = Joules Problem 1 : You push a car with a force of 200 N over a distance of 3 m. How much work did you do?

4. Solution 1... Work W = F.d W = 200x3 W = 600 J 200 N

5. Problem 2... Energy Energy is the capacity to do work Units : Joules (J) Kinetic Energy: Energy due to motion Problem 2 : What is the kinetic energy of the car in Problem 1?

6. Solution 2... Kinetic Energy Kinetic Energy = Work done (if no friction) K.E. = 600 J Problem 3 : Given that m = 1000 kg, what is the speed of the car?

7. Solution 3... Speed and K.E. F = ma 200 = 1000 a a = 0.2 m/s 2 V f 2 = V i 2 + 2ad V f 2 = 0 + 2(0.2)(3) V f 2 = 1.2 V f = 1.1 m/s

8. Kinetic Energy : Formula K.E. = 1/2 m v 2 Problem 4 : The K.E. of a car is 600 J and its mass is 1000 kg. What is its speed?

9. Solution 4... more K.E. K.E. = 1/2 m v 2 600 = 1/2(1000)(v 2 ) v = 1.1 m/s Does this look familiar? Moral of the story: We can find the speed either by using Newton’s Laws or Energy Principles.

10. Problem 5... Lugging the Luggage What is the speed when the distance is 3 m? 60 0 40 N Hawaii or Bust! 10 kg

11. Solution 5... Lugging the Luggage What is the speed when the distance is 3 m? F.d = 1/2 m v 2 (40 cos 60 0 )(3) = (1/2)(10)(v 2 ) v = 3.5 m/s Moral of the story W = (F)(d)(cos  ) 60 0 40 N Hawaii or Bust! 10 kg

12. Scalar Product (Dot Product) A. B = |A| |B| cos  i. i = 1 i. j = 0 W = F. d

13. Problem 6... work is a scalar ! F = 3 i + 2 j acts on an object and causes a displacement of 7 i (a) How much work was done? (b) What is the angle between F and d? Salisbury University

14. Solution 6... work is a scalar ! (a) W = F.d W = (3 i + 2 j). 7 i W = 21 + 0 W = 21 (b) | F| = 5 and |d| = 7 and F.d = 21 F.d = |F| |d| cos  21 = (5)(7) cos  cos  = 3/5  = 53 0 Salisbury University

15. Stretching Springs Hooke’s Law: The amount of stretch is directly proportional to the force applied. F = k x F x Slope = “k” Lab Experiment

16. Example 6.6... Springy Spring The spring constant (k) of a spring is 20 N/m. If you hang a 50 g mass, how much will it stretch?

17. Solution 6.6... Springy Spring F = k x mg = kx (50 /1000)(9.8) = (20)(x) x = 2.5 cm Lab Experiment

18. Problem 8... Body building How much work would you have to do to stretch a stiff spring 30 cm (k= 120 N/m)?

19. “Solution” 8... Body building W = F. d W = (kx)(x) W = kx 2 W = (120)(0.3) 2 W = 10.8 J  

20. Correct Solution 8... Body building F is a variable force so integration must be performed. W =  F. dx W =  kx. dx W =1/2 kx 2 W = (1/2)(120)(0.3) 2 W = 5.4 J 

21. Problem 1... Potential Energy You lift a 2 kg book and put it on a shelf 3 meters high. A. How much work did you do? B. Was the work “lost”?

22. Solution 1... Hidden Energy (P.E.) A. W = F.d W = mgh W = 2x10x3 W = 60 J B. Work is stored as Potential Energy (hidden).

23. Problem 2... In other words In other words, if the 2 kg book fell down from the top of the bookshelf (3m), what would its K.E. be?

24. Solution 2... In other words The K.E. would be equal to the P.E. K.E. = 600 J. In other words, energy was converted (transformed) from one form (P.E.) to another (K.E.)

25. Conservative Forces If the work done against a force does not depend on the path taken then that force is called a conservative force. Examples are gravity and spring force. The total mechanical energy (P.E. + K.E.) will remain constant in this case. If the work done against a force depends on the path taken then that force is called a non- conservative force. Example is friction. The total mechanical energy (P.E. + K.E.) will not remain constant in this case. Vote Democrat... Just kidding!