Lecture 09: Work and Potential Energy II

Physics 2210Fall Semester 2014

Today's Concepts:a) Energy and Frictionb) Potential Energy and Force

Mechanics Lecture 8, Slide 2

Unit 9: Prelecture Feedback

Mechanics Lecture 8, Slide 3

● Block sliding down the ramp checkpoint.● Macroscopic work● Connection between force and potential

energy.● Please keep going through problems like

the homework

Energy and Friction

● Last time: Mechanical Energy (K+U) is a constant of the motion for conservative forces.

● Today: Change in mechanical energy is equal to work done by nonconservative forces.

Last Time:Generalize mechanical energy conservation to conservative systems including springs:

Spring P.E. K.E.

Gravitational P.E.

Energy and Friction

● Last time: Mechanical Energy (K+U) is a constant of the motion for conservative forces.

● Today: Change in mechanical energy is equal to work done by nonconservative forces.

Mechanics Lecture 9, Slide 7

Macroscopic Work done by Friction

Macroscopic Work:

This is not a new idea – it’s the same “work” you are used to.

Applied to big (i.e. macroscopic) objectsrather than point particles (picky detail)

We call it “macroscopic” to distinguish it from “microscopic”.

Mechanics Lecture 9, Slide 8

∫ ⋅=b

a

ldFW

Mechanics Lecture 9, Slide 9

Mechanics Lecture 9, Slide 10

ff

Mechanics Lecture 9, Slide 11

“Heat” is just the kinetic energy of the atoms!

Mechanics Lecture 9, Slide 12

“Heat” is just the kinetic energy of the atoms!

Mechanics Lecture 9, Slide 13

This is how the conservative “fundamental forces”(gravity, electromagnetism...) give rise to nonconservative macroscopic forces

Example: A block of mass 12 kg has an initial velocity of 1.0 m/s to the right as it slides across the floor with a coefficient of kinetic friction

k = 0.45. How far does it travel

before coming to rest? Solve via:a) 2nd law and kinematics equationsb) Work-energy theorem

H

N1

mg

N2

mg

µ mg

must be negative

m

Mechanics Lecture 9, Slide 15

Conservative and Nonconservative Forces

A block of mass m, initially held at rest on a frictionless ramp a vertical distance H above the floor, slides down

the ramp and onto a floor where friction causes it to stop a distance r from the bottom of the ramp. The coefficient

of kinetic friction between the box and the floor is µk. What is the macroscopic work done on the block by

friction during this process?

A) mgH B) –mgH C) µk mgD D) 0

D

m

CheckPoint

Mechanics Lecture 9, Slide 16

H

What is the macroscopic work done on the block by friction during this process?

A) mgH B) –mgH C) µk mgD D) 0

B) All of the potential energy goes to kinetic as it slides down the ramp, then the friction does

negative work to slow the box to stop

C) Since the floor has friction, the work done by the block by friction is the normal force times

the coefficient of kinetic friction times the distance.

Mechanics Lecture 9, Slide 17

CheckPoint

D

m

H

A block of mass m, initially held at rest on a frictionless ramp a vertical distance H above the floor, slides down

the ramp and onto a floor where friction causes it to stop a distance D from the bottom of the ramp. The coefficient

of kinetic friction between the box and the floor is µk. What is the total macroscopic work done on the block by

all forces during this process?

A) mgH B) –mgH C) µk mgD D) 0

CheckPoint

Mechanics Lecture 9, Slide 18

D

m

HtotWK =∆

What is the total macroscopic work done on the block by all forces during this process?

A) mgH B) –mgH C) µk mgD D) 0

D) total work is equal to the change in kinetic energy. since the box starts and ends at rest, the

change in kinetic energy is zero.

Mechanics Lecture 9, Slide 19

CheckPoint

D

m

HtotWK =∆

Potential Energy vs. Force

Mechanics Lecture 9, Slide 20

dx

xdUxF

)()( −=

Suppose the potential energy of some object U as a function of x looks like the plot shown below.

Where is the force on the object biggest in the –x direction?

A) (a) B) (b) C) (c) D) (d)

U(x)

x

(a) (b) (c) (d)

CheckPoint

Mechanics Lecture 9, Slide 21

Suppose the potential energy of some object U as a function of x looks like the plot shown below.

Where is the force on the object biggest in the –x direction?

A) (a) B) (b) C) (c) D) (d)

U(x)

x

(a) (b) (c) (d)

CheckPoint

Mechanics Lecture 9, Slide 22

dx

xdUxF

)()( −=

Suppose the potential energy of some object U as a function of x looks like the plot shown below.

Where is the force on the object zero?A) (a) B) (b) C) (c) D) (d)

U(x)

x

(a) (b) (c) (d)

Flashcard Question

Mechanics Lecture 9, Slide 23

dx

xdUxF

)()( −=

Suppose the potential energy of some object U as a function of x looks like the plot shown below.

Where is the force on the object in the +x direction?A) To the left of (b) B) To the right of (b) C) Nowhere

U(x)

x

(a) (b) (c) (d)

Flashcard Question

Mechanics Lecture 9, Slide 24

dx

xdUxF

)()( −=

HW Example

● What is work done by tension before the incline?● What is the speed of the block before the incline?● What is the work done by friction after traveling up the incline?● What is the work done by gravity after traveling up the incline?● How far does the block travel before coming to rest?

Homework Example

● How far will you get with some initial speed?● If you have the minimum speed 11,068 m/s required,

what is your speed when you reach the moon?● Which effects minimum speed? m

earth, r

earth, m

ship?

HW Example: Potential Energy in Earth-Moon System

HW Example: Potential Energy in Earth-Moon System