Introduction to Mechanical Energy Energy Conservation Collisions conservation

Introduction to Mechanical Energy • Energy Conservation • Collisions • (conservation of momentum and energy in collisions)

Kinetic Energy: The energy of Motion � What are the SI units for KE? › kg • m 2/s 2 or N • m or J

Potential Energy associated with an object’s potential to move due to an interaction with its environment › A book held above the desk › An arrow ready to be released from the bow � Some types of PE are listed below: › Gravitational › Elastic › Electromagnetic �

Gravitational Potential Energy � What are the SI units? › kg • m 2/s 2 or N • m or J � The height (h) depends on the “zero level” chosen where PEg = 0.

What do you think? � What is meant when scientists say a quantity is conserved? � Describe examples of quantities that are conserved. › Are they always conserved? If not, why?

Mechanical Energy (ME) � ME = KE + PEg + PEelastic › Does not include the many other types of energy, such as thermal energy, chemical potential energy, and others � ME is not a new form of energy. › Just a combination of KE and PE

Conservation of Mechanical Energy The sum of KE and PE remains constant. � One type of energy changes into another type. � › For a falling book, the PE of the book changed into KE as it fell. › As a ball rolls up a hill, KE is changed into PE.

Collisions � To analyze collisions we consider two thing: › Conservation of Momentum › Conservation of Energy

What do you think? • Two skaters have equal mass and are at rest. They are pushing away from each other as shown. • Compare the forces on the two girls. • Compare their velocities after the push. • How would your answers change if the girl on the right had a greater mass than her friend? • How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?

Momentum During Collisions � When the bumper cars collide, F 1 = -F 2 so F 1 t = -F 2 t, and therefore p 1 = - p 2. The change in momentum for one object is equal and opposite to the change in momentum for the other object. � Total momentum is neither gained not lost during collisions.

Conservation of Momentum � Total momentum remains constant during collisions � The momentum lost by one object equals the momentum gained by the other object � Conservation of momentum simplifies problem solving.

Practice Problem �A 62. 0 kg astronaut on a spacewalk tosses a 0. 145 kg baseball at 26. 0 m/s out into space. With what speed does the astronaut recoil? �Answer: -0. 0608 m/s or -6. 08 cm/s � Does a pitcher recoil backward like the astronaut when throwing the ball? Explain.

Practice Problem � Zach is a quarterback and Jake is a defensive lineman. Zach’s mass is 75. 0 kg and he is at rest. Jake has a mass of 112 kg, and he is moving at 8. 25 m/s when he tackles Jake by holding on while they fly through the air. With what speed will the two players move together after the collision? � Answer: 4. 94 m/s

What do you think? • Collisions are sometimes described as elastic or inelastic. To the right is a list of colliding objects. 1. 2. 3. 4. • • Rank them from most elastic to most inelastic. What factors did you consider when ranking these collisions? 5. 6. 7. A baseball and a bat A baseball and a glove Two football players Two billiard balls Two balls of modeling clay Two hard rubber toy balls An automobile collision

Perfectly Inelastic Collisions � Two objects collide and stick together. › Two football players › A meteorite striking the earth Momentum is conserved. � Masses combine. �

Inelastic Collisions � Momentum is Conserved: � m 1 iv 1 i +m 2 iv 2 i = m 1 fv 1 f +m 2 fv 2 f � Kinetic energy is less after the collision. › It is converted into other forms of energy. �Internal energy - the temperature is increased. �Sound energy - the air is forced to vibrate. � Some kinetic energy may remain after the collision, or it may all be lost.

Practice Problems � An 2. 0 x 105 kg train car moving east at 21 m/s collides with a 4. 0 x 105 kg fully-loaded train car initially at rest. The two cars stick together. Find the velocity of the two cars after the collision. › Answer: 7. 0 m/s to the east � Now calculate the kinetic energy of the two cars before and after the collision. Was kinetic energy conserved? › Answer: KEbefore= 4. 4 x 107 J, KEafter= 1. 5 x 107 J �KE is not conserved. It is less after the collision.

Elastic Collisions Objects collide and return to their original shape. � Kinetic energy remains the same after the collision. � Perfectly elastic collisions satisfy both conservation laws shown below. �

Elastic Collisions � Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of momentum? › vf, A = 2. 0 m/s, vf, B = 2. 0 m/s › vf, A = 0 m/s, vf, B = 4. 0 m/s › vf, A = 1. 5 m/s, vf, B = 2. 5 m/s � Answer: all three m = 0. 35 kg v = 4. 0 m/s v = 0 m/s

Elastic Collisions � Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of kinetic energy? › vf, A = 2. 0 m/s, vf, B = 2. 0 m/s › vf, A = 0 m/s, vf, B = 4. 0 m/s › vf, A = 1. 5 m/s, vf, B = 2. 5 m/s � Answer: only vf, A = 0 m/s, vf, B = 4. 0 m/s m = 0. 35 kg v = 4. 0 m/s v = 0 m/s

Types of Collisions