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. Conservation of Energy Slide KE i + PE gi +Pe si + W ext = KE f + PE gf + Pe sf +  E th

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example: Speed of a Pendulum Slide 10-23

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example: Spring Launch A 200 g block on a frictionless surface is pushed against a spring with spring constant 500 N/m, compressing the spring by 2.0 cm. When the block is released, at what speed does it shoot away from the spring? Slide 10-23

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. A 2.0 g desert locust can achieve a takeoff speed of 3.6 m/s (comparable to the best human jumpers) by using energy stored in an internal “spring” near the knee joint. A.When the locust jumps, what energy transformation takes place? B.What is the minimum amount of energy stored in the internal spring? C.If the locust were to make a vertical leap, how high could it jump? Ignore air resistance and use conservation of energy concepts to solve this problem. D.If 50% of the initial kinetic energy is transformed to thermal energy because of air resistance, how high will the locust jump? Slide Spring Launch 2

Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example: Spring Launch 3 A 50 g wooden cube on a 30 degree (to the horizontal) wooden slope is held against a spring, of spring constant 25 N/m. The spring is compressed 10 cm. Consider the coefficient of friction for ice on wood to be When the cube is released and launched up the ramp, what total distance will it travel up the slope before reversing direction? Slide 10-23

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. Hooke’s Law Slide F s = k  l = k (l - l 0 ) Hooke’s Law region Elastic but not linear Elastic Limit

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?