C12 Power, Collisions, and Impacts. General Physics 1

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1 C12 Power, Collisions, and Impacts General Physics 1

2 Power The magnitude of the rate at which energy flows into or out of a given form P! dk dt or dv dt or du dt We select the formula based on the which energy we re discussing dk, dv, and du are all small changes in kinetic, potential or thermal energies, respectively. The unit of power is the watt, 1 W 1 J/s General Physics 2

3 Power Benchmarks General Physics 3

4 Two Minute Problems C12T.1 A trained bicyclist in excellent shape might be able to convert food energy to mechanical energy at a rate of 0.25 hp for a reasonable length of time. Imagine such a person pedaling a stationary bike connected to a perfectly efficient electrical generator. Could such a person generate enough electrical power to run a toaster (T=yes, F=no)? How about a single ordinary lightbulb toaster (T=yes, F=no)? General Physics 4

5 Power and Force If an interaction exerts a force on a moving object, we can calculate the rate P P = [ dk] dt = r r F! dr dt r r F! v [dk]/dt is the rate at which the interaction contributes k-work = r F r dr! dt = General Physics 5

6 Two Minute Problems C12T.3 An object moving with a velocity whose components are [4 m/s, -1 m/s, 3 m/s] is acted on by a force whose components are [-5N, 0, +5N]. What is the power of the energy transfer involved in this interaction? A. -35 W B. -5 W C. 0 D. -5 W E. +35 W General Physics 6

7 Elastic Collisions A collision that conserves the colliding objects total kinetic energy Examples Gentle collisions between rubber, steel or billiard balls Collisions between objects that interact strongly gravitationally or electromagnetically as they pass without touching General Physics 7

8 Two Minute Problems C12T.6 An object moving with speed v 0 collides headon with an object at rest that is very much more massive. If the collision is elastic, how does the lighter object s speed v after the collision compare with its original speed v 0? A. v is about equal to v 0 B. v is noticeably less than v 0 C. v is one-half of v 0 D. v is very small E. v is exactly zero F. v - v 0 General Physics 8

9 Solving Elastic Collision Problems Both momentum AND kinetic energy are conserved When solving elastic collision problems, you ll usually use both equations General Physics 9

10 A Two-Dimensional Collision A pool ball moving at speed v0 strikes an identical ball at rest a glancing blow. The collision deflects the first ball by an angle θ. If the collision is elastic, what are the balls speeds immediately afterward? In what direction is the second ball traveling? General Physics 10

11 General Physics 11

12 The Slingshot Effect A close encounter with a planet can dramatically increase a spacecraft s speed Elastic Collision Momentum is conserved Kinetic energy is conserved General Physics 12

13 General Physics m A v 0 0 " # % & + +m B v p " # % & = m A v 0 0 " # % & + m B v px m B v py 0 " # % & 1 2 m A v m B v P 0 2 = 1 2 m A v m B v P 2

14 Inelastic Collisions A collision that converts some kinetic energy to internal energy Does not conserve the colliding objects total kinetic energy Completely inelastic The objects remain stuck together after the collision Converts as much kinetic energy to internal energy as the COM allows Most collisions are elastic or inelastic General Physics 14

15 Solving Inelastic Collision Problems Momentum is conserved Kinetic energy is NOT conserved We can use conservation of energy if we know how much kinetic energy is transferred to internal energy General Physics 15

16 Another 2-D Collision A 0.45-kg wooden ball moving at a speed of 1.0 m/s in the +x direction collides with a wooden ball with the same mass at rest. Just after the collision, the velocities of both balls make a 30 angle with the +x direction. What fraction of the system s original kinetic energy has been converted to internal energy of this collision? General Physics 16

17 "U = #"K = # 1 2 mv mv 2 2 # 1 2 mv 2 & 0) = m 1 % ( 2 v 2 2 & 0 # v % 1 ) ( General Physics 17

18 Asteroid Impacts Scientists believe the dinosaurs that an asteroid that hit the earth wiped out the dinosaurs. They estimate Mass kg Speed, v 0 = 20 km/s The asteroid s kinetic energy is 1 2 mv 2 0 = kg ( ) 2 " 2 #10 23 J ( ) 20,000m /s ~ 500 million atomic bombs! General Physics 18

19 Asteroid Consequences Since the kinetic energy of the earthasteroid system after impact is still a negligible fraction of this energy, all of this energy will go into various consequences. General Physics 19

20 General Physics 20

21 Group Problems C12S.5 C12R.1 General Physics 21