chapter 6 - work, power, and efficiency

8/13/2019 Chapter 6 - Work, Power, And Efficiency

1/33

Chapter 6 Work, Power, and

Efficiency

Unit 3 Momentum and Energy


2/33

Types of Energy

Physicists classify energy into two fundamentaltypes: kinetic energy and potential energy.

Kinetic energy is the energy of motion.

Potential energy is the energy that is stored (or has

the potential to be used).

In this chapter, we will focus on one type of energy

called mechanical energy.


3/33

Types of Energy

Mechanical energy is a combination of kinetic andpotential energy.

A baseball that has been thrown like a parabola

through the air has both kinetic and potential energyit has kinetic energy because it is moving, and it

has potential energy because it is high in the air.

The force of gravity acts on the ball, causing it to fall

to the ground. As it falls, its speed increases and it

gains kinetic energy.


4/33


5/33

Defining Work

What are some examples of doing work on anobject?

For work to exists, there is always a force exerted on

the object causing it to move a certain distance.


6/33

Defining Work

You know from experience that it takes more work tomove a heavy table than a light one.

It also takes more work to move it to a new building

than to move it across the room.

The amount of work depends on both the magnitude

of the force, and the displacement of the object.


7/33

Defining Work


8/33

Defining Work

The unit of work (Nm) is called a Joule, J.

One Joule of work is created by exerting exactly one

Newton of force on a object, causing it to move

exactly one meter.


9/33

Defining Work

The definition for work depends on the individualforces acting on the object, and not on the net force.

If you are pushing a wooden box across the floor,

BOTH the applied force and the force of friction aredoing work.

You can calculate each of these forces individually

we do not need to use the net force.


10/33

Model Problem

A Physics student is rearranging her room. Shedecides to move her desk across the room, a total

distance of 3.00m. She moves the desk at a

constant velocity by exerting a horizontal force of

2.00x10

2

N. Calculate the amount of work the studentdid on the desk in moving it across the room.


11/33

Zero Work

Physicists define work very precisely.

The work done on an object can ONLY be calculated

when the force and displacement vectors are

parallel.

This can be shown through three cases:


12/33

Zero Work

Case 1: Applying a force that does not cause motion

If you were to push on a house, it likely wouldnt move.

Thus, according to the equation for work, the work

done on the house is zero because the displacementis zero.

Your muscles feel as though theyve done work, but in

the case of Physics, they did not do any work on thehouse.


13/33

Zero Work

Case II: Uniform Motion in the Absence of a Force

What do Newtons first law and inertia say about an

object in motion?

A hockey puck sliding on a frictionless surface at

constant speed is moving, but the work done is zero

because there is no force required to continue the

motion.


14/33

Zero Work

Case III: Applying a Force that is Perpendicular toMotion

If you are carrying a textbook, your hand is applying a

force directly upward (against gravity), keeping thetextbook up.

But, if you are walking forward, the books motion is

forward, which is perpendicular to the force acting onthe book.

Thus, the work done by you hand on the textbook iszero.


15/33

Zero Work

In the third case, it is important to note that yourhand does do work on the textbook to accelerate it

when you begin to move, but once you and the

textbook are moving at constant velocity, you are no

longer doing work on the book.


16/33

Model Problem

A child ties a ball to the end of a 1.0m string andswings the ball in a circle. If the string exerts a 10N

force on the ball, how much work does the string do

on the ball during a swing of one complete circle?


17/33

Work Done by Changing Forces

So far weve only talked about work when it pertainsto constant motion.

However, out definition of work (W=Fd) applies to

all cases, including situations where the forcechanges.

Mathematically, solving problems with changing

forces is beyond our current knowledge, but insteadwe can do so graphically.


18/33


A force-vs-position graph can allow you to determinethe work thats been done regardless of if the force

remains constant.

The work is given by the area under the curve!


19/33



20/33



21/33

Constant Force at an Angle

To determine the work done on an object when theforce applied is at an angle, we must first find the

component of the force that is parallel to the

direction of motion.

For the work done where the x-component of the

force is parallel to the direction of the motion, we can

use:

W = Fcosd = Fdcos


22/33

Positive and Negative Work

Can a force and direction still be parallel even if theypoint in opposite directions?

If they point in different directions, it simply means

that the angle is 180.


23/33

Positive and Negative Feet

Negative work done by an external force reduces theenergy of a mass.

The energy does not disappearit is lost to the

surroundings in the form of heat or thermal energy.

Positive work adds energy to an object, while

negative work removes energy from an object.


24/33

Model Problem

Consider a weight lifter bench-pressing a barbellweighing 6.50x102N through a height of 0.55m.

There are two distinct motions: (1) when the barbell

is lifted up and (2) when the barbell is lowered back

down. Calculate the work done on the barbell during

each of the two motions.


25/33

Kinetic Energy

The energy of motion is called kinetic energy.

We can think intuitively about what quantifies kinetic

energyif a bowling ball and a golf ball were rolling

towards you with the same velocity, which would youwant to avoid more?

Since both balls have the same velocity, the mass

must be contributing to the kinetic energy of theballs.


26/33

Kinetic Energy

A Dutch mathematician and physicist namesChristian Huygens looked for a quantity involving

both mass and velocity that was characteristic of an

objects motion.

He experimented using the collisions of rigid balls

(similar to billiard balls).

He discovered that if he calculated the product of themass and the square of the velocity for each ball,

and then added those products together, the totals

were the same before and after the collisions.


27/33

Kinetic Energy


28/33

Model Problem

A 0.200kg hockey puck, initially at rest, is accelerated

to 27.0m/s. Calculate the kinetic energy of the

hockey puck (a) at rest and (b) in motion.


29/33

Work and Kinetic Energy

The relationship between doing work on an object

and the resulting kinetic energy of the object is called

the work-kinetic energy theorem.

This is quite intuitiveif you saw a hockey puck atrest on the ice and a moment later saw it hurtling

though the air, you would conclude that someone did

work on the puck by exerting a large force over a

short distance.

This correctly shows that doing work on an object

give the object an increased velocity, or kinetic

energy.


30/33


So, we have to find a relationship between work and

the energy of motion.


31/33



32/33

Model Problem

A Physics student does work on a 2.5kg curling stone

by exerting 400N of force horizontally over a

distance of 1.5m.

(a) Calculate the work done by the student on the

curling stone.(b) Assuming the stone started from rest, calculate

the velocity of the stone at the point of release if the

ice is frictionless.


33/33

Model Problem

chapter 6 - work, power, and efficiency

Documents