# Potential energy diagrams

## Presentation on theme: "Potential energy diagrams"— Presentation transcript:

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

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

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

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.

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.

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

Problem: a bullet of mass mb at speed vb, imbeds and stops within a sand bag of mass M. What is the maximum height of the sand bag?

Problem: a bullet of mass mb at speed vb, imbeds and stops within a sand bag of mass M. What is the maximum height of the sand bag? Right after collision bag+bullet moving at speed V Using conservation of energy after collision tells us how high the bag goes:

Problem: a bullet of mass mb at speed vb, 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.

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

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

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

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

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 600 S of E, while car B skidded at 600 N of E. vA vB vA’ 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?

vB’ vA vB vA’ Assume B’s scenario: vB = 0. Momentum in y = 0.
60 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: vB = vA/2. Exercise: show that final Kfinal < Kinitial in this scenario  Likely correct.

A. Only i. is true. B. Only ii. is true. C. i. and ii. are true.
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.

A. Only i. is true. B. Only ii. is true. C. i. and ii. are true.
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.

C12T.6 An object moving with speed v0 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 v0? A. v is about equal to v0 B. v noticeably less than v0 C. v is equal to v0/2 D. v is very small E. v  -v0

C12T.6 An object moving with speed v0 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 v0? A. v is about equal to v0 B. v noticeably less than v0 C. v is equal to v0/2 D. v is very small E. v  -v0