LECTURE 26 ENERGY in COLLISION and POWER 10.7 Energy in Collisions Accident Investigation Is Done Using the Laws of Conservation of Momentum and Energy

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LECTURE 26 ENERGY IN COLLISION AND POWER 10.7 Energy in collisions Accident investigation is done using the laws of conservation of momentum and energy. Elastic collisions Forces in collisions 10.8 Power Learning objectives

! Use the concepts of momentum and energy conservation to solve elastic collision problems.

! Identify the transformation of energy during an inelastic collision.

! Describe power as the rate of energy transfer or transformation. 10.7 Energy in collisions

! Momentum is conserved in all collisions.

! In a perfectly inelastic collision, the colliding objects stick together and then move with a common final velocity.

! In a perfectly elastic collision collision, mechanical energy is conserved. Quiz: 10.7-1

! A box sliding on a frictionless surface collides and sticks to a second identical box which is initially at rest. Compare the

initial kinetic energy (Kinitial) and final kinetic energy (Kfinal) of the system of two boxes.

Initial

Final Quiz: 10.7-1

! !"#$%& < !#$#(#%& ! Since the boxes stick together after the collision, this is a perfectly inelastic collision.

! The kinetic energy usually decreases in an inelastic collision due to creation of thermal energy through sound and deformation. In every perfectly inelastic collision, total kinetic energy always decreases.

! The kinetic energy sometimes increases if collision sets off an explosion, releasing chemical energy etc.

! Assigning an arbitrary mass, ), and initial velocity, *#, we obtain an initial kinetic energy of the , . , . system: !# = -)*# + 0 = -)*#

! The system is isolated, so the initial momentum equals the final momentum: )*# = 2)*2 . , . 34 , . ! The final kinetic energy of the system is ! = 2) * = ) = )* 2 - 2 . 5 # 10.7 Elastic collisions

! Elastic collisions obey conservation of momentum and conservation of mechanical energy.

&" − &( !"# $ = !"# * &" + &(

2&" !(# $ = !"# * &" + &( Quiz: 10.7-2

! Two identical gliders are on a frictionless air track. The first glider with an initial velocity of +" collides perfectly elastically the second that is initially at rest. What is the final velocity of the first glider?

Before +" # # Quiz: 10.7-2 answer

Before +" . . Quiz: 10.7-3

Before +" # # Quiz: 10.7-3 answer / demo

Before +" - - Quiz: 10.7-4

Before +# ! 2! Quiz: 10.7-4 answer / demo

! Two gliders are on a frictionless air track. The first glider with a mass ! and initial velocity +# collides perfectly elastically the second glider with a mass of 2! that is initially at rest. What is the sign of the final velocity of the first glider? )*+), )+/) % ! #%& ' = #%& . = +# = − # < 0 )*-), )-/) 1 ! Negative. The velocity of the first glider reverses direction upon collision. Before +# ! 2! Quiz: 10.7-5

! In a Newton's cradle any collision between the balls in the device in the figure is perfectly elastic.

! If one end ball is pulled back and let go and two balls at the other end bounced up at half the first ball's speed, would it be a violation of conservation of momentum? Would the result be a violation of conservation of energy? A. It would be a violation of conservation of momentum. B. It would NOT be a violation of conservation of momentum. C. It would be a violation of conservation of energy. D. It would NOT be a violation of conservation of energy. Quiz: 10.7-5 answer / demo

! In a Newton’s cradle any collision between the balls in the device in the figure is perfectly elastic.

! If one end ball is pulled back and let go, as shown, and two balls at the other end bounced up at half the first ball's speed, would it be a violation of conservation of momentum? Would the result be a violation of conservation of energy?

! It would NOT be a violation of conservation of momentum. ! Twice the mass, but half the speed therefore ! = #$ stays the same.

! It would be a violation of conservation of energy. & ( ! Twice the mass, but half the speed therefore % = '#$ is halved. 10.8 Power

! Power (!) measured in W or horsepower (1 hp = 746 W) is the rate at which energy is transformed or transferred.

! If work (") is done, the power performed is " ! = ∆%

! If an object is moving at a constant speed &, the power exerted by the driving force ' can be written as

! = '&

! If energy (() is transformed, the power is ∆( ! = ∆% Quiz: 10.8-1 (Moving box at constant speed)

! You pull a box with a constant force of 250 N. It takes you 20 s to move the box 10 m along a rough surface at a constant speed. What power are you transferring to the system of the box and the rough surface?

! Enter your answer in W, but only enter the number. Quiz: 10.8-1 answer / demo

! Enter your answer in W, but only enter the number.

! ! = #$ ∆& ,- . ! ! = # = 250 N = 125 W ∆' /- 0

! The friction force between the wheel and the strap is 250 N. If you turn the wheel 20 times, the surface of the wheel will move 10 m relative to the strap.

Instructor 0.1 kW Tata Nano 28 kW Koenigsegg Regera 1100 kW Quiz: 10.8-2

! Alicia applied 10 N of force over 3 m in 10 seconds. Betty applied the same force over the same distance in 1 minute. Who did more work? Who produced more power? A. Alicia did more work. B. Betty did more work. C. They did the same work. D. Alicia produced more power. E. Betty produced more power. F. They produced the same power. Quiz: 10.8-2 answer

! They did the same work, and Alicia produced more power.

! Both exerted the same force (10 N) over the same displacement (3 m). Therefore, both did the same amount of work, 30 J. Time does not matter for determining the work done. # ! ! = Alicia produced 3 W, and Betty produced 0.5 W of power. ∆%