Lecture 07: Work and Kinetic Energy

Physics 2210Fall Semester 2014

Announcements

● Schedule next few weeks:● 9/08 – Unit 3● 9/10 – Unit 4● 9/15 – Unit 5 (guest lecturer)● 9/17 – Unit 6 (guest lecturer)● 9/22 – Unit 7, Exam Review

● work practice exam in discussion● 9/24 – Exam 1, Units 1-6● 9/25 – Unit 7 HW due

Unit 7: Prelecture Feedback

Mechanics Lecture 6, Slide 3

● Review dot product● Derive relation between work and K.E.● Review all checkpoint problems● “Work” through examples ● Why is “work” relevant?

The Dot (also “scalar”, “inner”) Product of Two Vectors

Mechanics Lecture 7, Slide 4

Work-Kinetic Energy Theorem

Mechanics Lecture 7, Slide 5

The net work done on a body is equal to the change in kinetic energy of the body

Formal definition of work(“Force times distance” generalized)

Formal definition of kinetic energy

Flashcard Question

A lighter car and a heavier van, each initially at rest, are pushed with the same constant force F. After both vehicles travel a distance d, which of the following statements is true? (Ignore friction)

Mechanics Lecture 7, Slide 6

A) They will have the same velocityB) They will have the same kinetic energy

C) They will have the same momentum

F d

F d

car

van

Flashcard Question

A lighter car and a heavier van, each initially at rest, are pushed with the same constant force F. After both vehicles travel a distance d, which of the following statements is true? (Ignore friction)

Mechanics Lecture 7, Slide 7

A) They will have the same velocityB) They will have the same kinetic energy

C) They will have the same momentum

F d

F d

car

van

Example: I lift an object of mass m, starting at rest, and place it at rest on a table of height h.

1) What is the work done by gravity?2) What is the work done by me?3) What is the change in kinetic energy?4) Do the answers above depend on the path taken by the object?

Work-Kinetic Energy Theorem

If there are several forces acting then W is the work done by the net (total) force:

Mechanics Lecture 7, Slide 9

You can just add up the work done by each force

KWNET ∆=...21 ++= WW

TOTNET WW =

Example: I drop an object of mass m, from a height h, starting at rest. What is its speed v when it hits the floor... a) As calculated by 1D kinematics? b) As calculated by the Work-KE theorem?

H

Free Fall Frictionless incline String

CheckPoint Three objects having the same

mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string.

Mechanics Lecture 7, Slide 11

In which case does the

object have the biggest

net work done on it by

all forces during its motion?

A) Free Fall B) Incline C) String D) All the same

H

Free Fall Frictionless incline String

CheckPoint Three objects having the same

mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string.

Mechanics Lecture 7, Slide 12

In which case does the

object have the biggest

net work done on it by

all forces during its motion?

A) Free Fall B) Incline C) String D) All the same

Flashcard QuestionThree objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. What is the relationship between their velocities when they reach the bottom?

H

Free Fall Frictionless incline String

A) vf > vi > vs B) vf > vs > vi C) vf = vs = vi

Mechanics Lecture 7, Slide 13

Flashcard QuestionThree objects having the same mass begin at the same height, and all move down the same vertical distance H. One falls straight down, one slides down a frictionless inclined plane, and one swings on the end of a string. What is the relationship between their velocities when they reach the bottom?

H

Free Fall Frictionless incline String

A) vf > vi > vs B) vf > vs > vi C) vf = vs = vi

Mechanics Lecture 7, Slide 14

CheckPoint

A car drives up a hill with constant speed. Which statement best describes the total work WTOT done on the car by all forces as it moves up the hill?

A) WTOT > 0

B) WTOT

= 0

C) WTOT < 0

v

Mechanics Lecture 7, Slide 15

CheckPoint

A car drives up a hill with constant speed. Which statement best describes the total work WTOT done on the car by all forces as it moves up the hill?

A) WTOT > 0

B) WTOT

= 0

C) WTOT < 0

v

Mechanics Lecture 7, Slide 16

CheckPoint

A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives.

µS

a

The work done on the box by the static frictional force as the truck moves a distance D is:

A) Positive B) Negative C) Zero

Mechanics Lecture 7, Slide 17

CheckPoint

A box sits on the horizontal bed of a moving truck. Static friction between the box and the truck keeps the box from sliding around as the truck drives.

µS

a

The work done on the box by the static frictional force as the truck moves a distance D is:

A) Positive B) Negative C) Zero

Mechanics Lecture 7, Slide 18

Physics 211 Lecture 7, Slide 19

Work done by a Spring

Physics 211 Lecture 7, Slide 20

I am confused about the positive work and negative work and also the positive and negative forces for the spring problems.

In this example the spring does negative work since F and ∆x are in opposite direction. The axes don’t matter.

Use the formula to get the magnitude of the work

Use a picture to get the sign (look at directions)

Example: Simple Gravitational Orbit

A space telescope of mass 10,000 kg is in a stable orbit above the Earth at an altitude h = 3,630 km. The radius and mass of the Earth are R

E = 6,370 km and

ME = 6.0x1024 kg, respectively.

Newton's gravitational constant is G=6.672x10-11 Nm2/kg2. (a) what is the acceleration of the space telescope? (b) if the telescope's mass were to increase, what would need to happen to its speed in order to maintain the same orbit?

Example

I move an object from the surface of the Earth to a height of one Earth radius above the Earth, and to a position on the far side of the Earth from the launch position. The object is at rest with respect to the Earth before and after the move.

What is the work that I must do on the object? If the object were instead moved to “infinity” (or at

least very, very far away), what work must I do?

Exam Details● Coverage: Units 1-6

● 1D Kinematics● 2D Kinematics● Relative and Circular Motion● Newton's Laws● Free Body Diagrams● Friction

● Problem types: Multiple choice & workout.● Study recommendations:

● Review homework● See practice exam on course webpage● Solve problems, problems, problems...

● Allowed materials● Calculator (not on cell phone)● Straightedge● Blue or black pen required for regrade● Equation sheet will be provided

1D Kinematics

● Precise “physicist” definitions of words you use every day.

● Differential and integral representations.

● Graphical representation.

2D Kinematics

● Generalize 1D kinematics to 2 or 3D

● Vectors, vector addition and subtraction.

● Projectile motion:● Horizontal constant v● Vertical constant a

● Horizontal and vertical independent

Relative and Circular Motion

● Kinematics may be described in different coordinate systems.

● These systems may be in relative motion.

● Circular motion at constant linear speed is accelerated motion. Acceleration is towards center of circle.

Newton's Laws

● 2nd Law: define force in terms of mass and acceleration.

● 1st Law: Special case of 2nd. “Inertia”

● 3rd Law: forces come in pairs, but act in opposite directions.

Free-Body Diagrams

● Tool for generating equations that relate knowns to unknowns.

● Useful for many types of forces

● Support forces● Spring forces● Gravity (near Earth

and far from Earth).● Friction

Friction

● Contact force between two objects. Parallel to adjoining surface.

● Two types:● Kinetic (moving)● Static (at rest)