# Physics 2111 Unit 7. Today s Concepts: Work & Kinetic Energy Power. Mechanics Lecture 7, Slide 1

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1 Physics 2111 Unit 7 Today s Concepts: Work & Kinetic Energy Power Mechanics Lecture 7, Slide 1

2 Work-Kinetic Energy Theorem The work done by force F as it acts on an object that moves between positions r 1 and r 2 is equal to the change in the object s kinetic energy: W K W r r 2 1 F dl 1 K 2 Units for both are Joules: 1 Newton X 1 meter mv 2 Mechanics Lecture 7, Slide 3

3 r 2 W F dl r 1 OR How How much much of the of the distance force is the in object the moves direction is in the the direction object of moves. the force. Mechanics Lecture 7, Slide 4

4 Example 7.1 (Work on cart) A 2kg frictionless lab cart is pushed with a force of 5N for a distance of 1m. The force is horizontal. What is the kinetic energy of the cart after the push? What is the cart s velocity after the push? Mechanics Lecture 7, Slide 5

5 Example 7.2 (Work on cart) A 2kg frictionless lab cart is pushed with a force of 5N for a distance of 1m. The force has an angle of 30 o to the horizontal. What is the kinetic energy of the cart after the push? What is the cart s velocity after the push? Mechanics Lecture 7, Slide 6

6 the whole pre-lecture was confusing. the apple has zero kinetic energy and thus 0 work because it started and stopped at rest; however a ball that is dropped does have work, when it too starts and stops at rest??? makes no sense The fact that work can be zero after something moves can be confusing. Mechanics Lecture 5, Slide 7

7 Checkpoint A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives forward. a S The work done on the box by the static frictional force as the truck moves a distance D to the left is: A) Positive B) Zero C) Negative Mechanics Lecture 7, Slide 8

8 r 2 Derivation not so important F dl K Concept very important r 1 A force pushing over some distance will change the kinetic energy. r 2 r 1 F dl K q W r r 2 1 F dl Mechanics Lecture 7, Slide 9

9 Example 7.3 (Block on Ramp) A 5kg block is pulled up a distance of 2m along a frictionless ramp by a 20N force. How much work did force do on the block? How much work did gravity do? If it starts from rest, what is the velocity of the box after the 2m? 20 o Mechanics Lecture 7, Slide 10

10 Can break any path into tiny pieces (calculus!) W W W... W TOT 1 2 mg dl1 mg dl2... mg dln mgdy... 1 mgdy 2 mgdy N mg y N dl 1 dl N y mg dl 2 Wg mg y Mechanics Lecture 7, Slide 11

11 Work-Kinetic Energy Theorem If there are several forces acting then W is the work done by the net (total) force: WNET K W W You can just add up the work done by each force W NET W TOT Mechanics Lecture 7, Slide 12

12 Checkpoint H Three objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. Free Fall Frictionless incline String A) Free Fall B) Incline C) String D) All the same In which case does the object have the biggest net work done on it by all forces during its motion? Mechanics Lecture 7, Slide 13

13 Checkpoint A car drives up a hill with constant speed. Which statement best describes the total work W TOT done on the car by all forces as it moves up the hill? A) W TOT > 0 B) W TOT = 0 C) W TOT < 0 Let s ask this in a different way Mechanics Lecture 7, Slide 14

14 Work done by a Spring Physics 211 Lecture 7, Slide 15

15 Example 7.4 (Box on Spring) 10cm 40cm A 20kg box is placed gently on a vertical spring which compresses it 10cm. I then compress the spring an additional 40cm with my hand. When I release the box and spring, how high will the box fly? Mechanics Lecture 7, Slide 17

16 Example 7.5 (Speeding Proton) A proton with a mass of 1.67X10-27 kg is heading directly towards a fixed nucleus. It starts 4meters away at a speed of 8X10 4 m/sec. The nucleus repulses the proton with a force equal to a/r 2, where a is a constant with a value of 1.82X10-26 Nm 2. What is the speed of the proton when its 8X10-9 meters from the nucleus? Mechanics Lecture 7, Slide 18

17 Power Power = Energy/Time Example: Note: 1 Joule/ 1 sec = 1 Watt 60 Watt light bulb uses 60 Joules of electrical energy every second. kilowatt is power kilowatt hour is energy 1HP = Watts Mechanics Lecture 7, Slide 19

18 Example 7.6 (Motorcycle Power) A motorcycle and rider are going down the road at a constant velocity of 15m/sec. At this velocity, the wind drag is 160N. Their combined mass is 260kg. What is the power produced by the engine? How much power would be needed for him to go up a 15 o incline at this same speed? Mechanics Lecture 7, Slide 20

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