Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 10. Energy This pole vaulter can lift herself nearly 6 m (20 ft) off the ground by transforming the kinetic energy of her run into gravitational potential energy. Chapter Goal: To introduce the ideas of kinetic and potential energy and to learn a new problem-solving strategy based on conservation of energy.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Topics: A “Natural Money” Called Energy Kinetic Energy and Gravitational Potential Energy A Closer Look at Gravitational Potential Energy Restoring Forces and Hooke’s Law Elastic Potential Energy Elastic Collisions Energy Diagrams Chapter 10. Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Kinetic and Potential Energy There are two basic forms of energy. Kinetic energy is an energy of motion Gravitational potential energy is an energy of position The sum K + U g is not changed when an object is in freefall. Its initial and final values are equal

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Kinetic and Potential Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Zero of Potential Energy You can place the origin of your coordinate system, and thus the “zero of potential energy,” wherever you choose and be assured of getting the correct answer to a problem. The reason is that only ΔU has physical significance, not U g itself.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Zero of Potential Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Zero of Potential Energy

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Quick Quiz 1 A block slides down a frictionless ramp of height h. It reaches velocity v at the bottom. To reach a velocity of 2v, the block would need to slide down a ramp of height A. 1.41h B. 2h C. 3h D. 4h E. 6h

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Quick Quiz 2 A block is shot up a frictionless 40° slope with initial velocity v. It reaches height h before sliding back down. The same block is shot with the same velocity up a frictionless 20° slope. On this slope, the block reaches height 2h h ½ h > h, but I can’t predict an exact value < h, but I can’t predict an exact value

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Quick Quiz 3 Two balls, one twice as heavy as the other, are dropped from the roof of a building. Just before hitting the ground, the heavier ball has one half the same amount as twice four times the kinetic energy of the lighter ball.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Conservation of Mechanical Energy The sum of the kinetic energy and the potential energy of a system is called the mechanical energy. Here, K is the total kinetic energy of all the particles in the system and U is the potential energy stored in the system. The kinetic energy and the potential energy can change, as they are transformed back and forth into each other, but their sum remains constant.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Hooke’s Law If you stretch a rubber band, a force appears that tries to pull the rubber band back to its equilibrium, or unstretched, length. A force that restores a system to an equilibrium position is called a restoring force. If s is the position of the end of a spring, and s e is the equilibrium position, we define Δs = s – s e. If (F sp ) s is the s-component of the restoring force, and k is the spring constant of the spring, then Hooke’s Law states that The minus sign is the mathematical indication of a restoring force.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Hooke’s Law

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Elastic Potential Energy Consider a before-and-after situation in which a spring launches a ball. The compressed spring has “stored energy,” which is then transferred to the kinetic energy of the ball. We define the elastic potential energy U s of a spring to be

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Quick Quiz 4 A block sliding along a frictionless horizontal surface with velocity v collides with and compresses a spring. The maximum compression is 1.4 cm. If the block then collides with the spring while having velocity 2v, the spring’s maximum compression will be 0.35 cm2.0 cm 0.70 cm2.8 cm 1.0 cm5.6 cm 1.4 cm

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Quick Quiz 5 A block sliding along a frictionless horizontal surface with velocity v collides with and compresses a spring. The maximum compression is 1.4 cm. If this spring in is replaced by a spring whose spring constant is twice as large, a block with velocity v will compress the new spring a maximum distance 0.35 cm2.0 cm 0.70 cm2.8 cm 1.0 cm5.6 cm 1.4 cm

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 10.6 A spring-launched plastic ball QUESTION:

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 10.6 A spring-launched plastic ball

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 10.6 A spring-launched plastic ball

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 10.6 A spring-launched plastic ball

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Elastic Collisions

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Elastic Collisions Consider a head-on, perfectly elastic collision of a ball of mass m 1 having initial velocity (v ix ) 1, with a ball of mass m 2 that is initially at rest. The balls’ velocities after the collision are (v fx ) 1 and (v fx ) 2.These are velocities, not speeds, and have signs. Ball 1, in particular, might bounce backward and have a negative value for (v fx ) 1.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Elastic Collisions Consider a head-on, perfectly elastic collision of a ball of mass m 1 having initial velocity (v ix ) 1, with a ball of mass m 2 that is initially at rest. The solution, worked out in the text, is

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Energy Diagrams A graph showing a system’s potential energy and total energy as a function of position is called an energy diagram.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Energy Diagrams

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting an energy diagram

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Interpreting an energy diagram