Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Important forms of energy How energy can be transformed and transferred Definition of work Concepts of kinetic, potential, and thermal energy The law of conservation of energy Elastic collisions Chapter 10 Energy Topics: Sample question: When flexible poles became available for pole vaulting, athletes were able to clear much higher bars. How can we explain this using energy concepts? Slide 10-1

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Work Energy Theorem Slide W net =  ma*Delta x * cos(  )= 1/2 mv f 2 - 1/2 mv i 2 2 * ma*Delta x = 2 * (1/2 mv f 2 - 1/2 mv i 2 ) v f 2 - v i 2 = 2a*Delta x v f 2 = v i 2 + 2a*Delta x Look familiar

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Work Energy Theorem Slide Answer these questions: Does KE increase or decrease? A) increase B) decrease C) can’t tell What is the sign of  KE? (A) positive, (B) negative, or (C) zero What forces act on the object in question? For each of these forces, is the work (A) positive, (B) negative, (C) zero? Is Wnet (A) positive, (B) negative, or (C) zero?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Work Energy Problem 1 Slide Solve this problem two ways, with Newton's 2nd Law and with the Work-Energy Theorem 1. A 200 g Ball is lifted upward on a string. It goes from rest to a speed of 2 m/s in a distance of 1 m. What is the tension (assumed to stay constant) in the string?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Work Energy Problem 2 Slide A 1000 kg car is rolling slowly across a level surface at 1 m/s, heading towards a group of small children. The doors are locked so you can't get inside and use the brake. Instead, you run in front of the car and push on the hood at an angle 30 degrees below the horizontal. How hard must you push to stop the car in a distance of 1 m?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Work Energy Problem 1 Slide A 1 kg block moves along the x-axis. It passes x = 0 with a velocity v = 2 m/s. It is then subjected to the force shown in the graph below. a.Which of the following is true: The block gets to x = 5 m with a speed greater than, less than, or equal to 2 m/s. State explicitly if the block never reaches x = 5 m. b.Calculate the block speed at x = 5 m.

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Spring Force The magnitude of the spring force is proportional to the stretch of the spring: Slide 8-14 F sp = k ∆L = k (L - L 0 )

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The spring force is directed oppositely to the stretch of the spring. In this case, we can then write Hooke’s law as Hooke’s Law Slide 8-15 (F sp ) x = –k ∆x

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Beyond the Elastic Limit Slide 8-25

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding Which spring has the largest spring constant? Slide 8-16

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Which spring has the largest spring constant? Slide 8-17 Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Checking Understanding The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude? Slide 8-18

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The same spring is stretched or compressed as shown below. In which case does the force exerted by the spring have the largest magnitude? Slide 8-19 Answer

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Spring Problem 1 Slide A 20-cm long spring is attached to the wall. When pulled horizontally with a force of 100 N, the spring stretches to a length of 22 cm. What is the value of the spring constant?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Spring Problem 2 Slide The same spring is used in a tug-of-war. Two people pull on the ends, each with a force of 100 N. How long is the spring while it is being pulled?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Spring Problem 3 Slide The same spring is now placed vertically on the ground and a 10.2 kg block is balanced on it. How high is the compressed spring?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Spring Problem 4 Slide The same spring is placed vertically on the ground and a 10.2 kg block is held 15 cm above the spring. The block is dropped, hits the spring, and compresses it. What is the height of the spring at the point of maximum compression?

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Spring Problem 5 A spring with spring constant k = 125 N/m is used to pull a 25 N wooden block horizontally across a tabletop. The coefficient of friction between the block and the table is µ k = By how much does this spring stretch from its equilibrium length? Slide 8-22