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Potential energy diagrams Given a potential energy diagram one can get the behavior of systems affected by the potential. Systems with E>V h are unbound;

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Presentation on theme: "Potential energy diagrams Given a potential energy diagram one can get the behavior of systems affected by the potential. Systems with E>V h are unbound;"— Presentation transcript:

1 Potential energy diagrams Given a potential energy diagram one can get the behavior of systems affected by the potential. Systems with E>V h are unbound; Systems with E

2 Latent heat is energy spent in transforming the state of the substance: it doesn’t change its temperature. (Example: boiling water) Microscopically: energy is spent into separating atoms against their attractions. Notice that constant heating results in no T variation during phase transitions

3 Power Unit = J/s = Watt Electricity company likes to use kiloWatt-hour == 3.6 MJ for units of energy. Internal versus external interactions. No external interactions  p tot conserved Momentum

4 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 (1 hp=746 Watts) for a reasonable length of time. Imagine such a person pedaling a stationary bike connected to a perfectly efficient electrical generator. Such a person could generate enough electrical power to: i. run a toaster ii. run an ordinary light bulb iii. heat a home in winter (just for 1/2 hour or so). A. Only i. is true. B. Only ii. is true. C. i. ii. and iii are true. D. i. ii. are true; iii is false. E. i. is true; ii. and iii are false.

5 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 (1 hp=746 Watts) for a reasonable length of time. Imagine such a person pedaling a stationary bike connected to a perfectly efficient electrical generator. Such a person could generate enough electrical power to: i. run a toaster ii. run an ordinary light bulb iii. heat a home in winter (just for 1/2 hour or so). A. Only i. is true. B. Only ii. is true. C. i. ii. and iii are true. D. i. ii. are true; iii is false. E. i. is true; ii. and iii are false.

6 Elastic collisions: p and K conserved Inelastic collisions: p conserved, K not conserved

7 Problem: a bullet of mass m b at speed v b, imbeds and stops within a sand bag of mass M. What is the maximum height of the sand bag?

8 Right after collision bag+bullet moving at speed V Using conservation of energy after collision tells us how high the bag goes:

9 Problem: a bullet of mass m b at speed v b, imbeds and stops within a sand bag of mass M. What is the maximum height of the sand bag? Energy conserved in collision? No Energy conserved after the collision? Yes Momentum in x,y conserved in collision? Yes in x, Yes in y Momentum in x,y conserved after collision? No in x, No in y.

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

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

12 A motor is attached to the axle of a pulley, which can be considered as a uniform disk with mass M and radius R and rotates it counter-clockwise so that the block of mass m is pulled vertically upwards at a constant speed v. The string does not slip on the pulley. At what rate is the motor doing work on the block and pulley? m M

13 m M Pulley rotating at constant angular velocity, thus no work needed. Power is mg dh/dt:

14 On an icy road one day, a car with mass m (car A) traveling due E hits another car of mass 2m (car B) in the center of an intersection. After the accident, marks in the ice show that car A skidded at an angle of 60 0 S of E, while car B skidded at 60 0 N of E. vAvA vBvB vA’vA’ vB’vB’ 60 The driver of car A claims in court to have been traveling the speed limit of 40 mi/h, but car B ran the stoplight was moving N at 20 mi/h. The driver of car B does not dispute that A was moving at 40 mi/h, but claims car B was stalled in the center of the intersection at the time of the accident, so A should have had plenty of time to stop. Which story is more consistent with the physical facts?

15 vAvA vBvB vA’vA’ vB’vB’ 60 Assume B’s scenario: v B = 0. Momentum in y = 0. Momentum in x: Kinetic energy of A stayed unchanged. K of B increased. Where did energy come from? Scenario is unlikely. Assume A’s scenario: v B = v A /2. Exercise: show that final K final < K initial in this scenario  Likely correct.

16 C12T.4 i. Momentum is not conserved in an inelastic collision ii. Energy is not conserved in an inelastic collision A. Only i. is true. B. Only ii. is true. C. i. and ii. are true. D. i. and ii. are false.

17 C12T.4 i. Momentum is not conserved in an inelastic collision ii. Energy is not conserved in an inelastic collision A. Only i. is true. B. Only ii. is true. C. i. and ii. are true. D. i. and ii. are false.

18 C12T.6 An object moving with speed v 0 collides head-on 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 noticeably less than v 0 C. v is equal to v 0 /2 D. v is very small E. v  -v 0

19 C12T.6 An object moving with speed v 0 collides head-on 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 noticeably less than v 0 C. v is equal to v 0 /2 D. v is very small E. v  -v 0


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