physics 218, lecture x1 physics 218 lecture 10 dr. david toback

Physics 218, Lecture X 1

Physics 218Lecture 10 Dr. David Toback


Overview: Chapters 6 & 7

Combine Chapter 6 & 7 into four lectures

Today we’ll cover Work:• Intuitive understanding• The math and multiple ways to

calculate workNext time:• How much energy does it take to

accomplish a task?


Why are we learning this stuff?

This is Fundamental to Engineering

• How much work can a machine do? (today)

• How much energy does it take to accomplish a task? (next time)


Work

• The word “Work” means something specific in Physics (Kinda like Force)

• The amount of Work we do is the amount of Forcing we do over some distance

• Example: If we are accelerating a car for 1 mile, then there is a force and a distance We do Work


Calculating the work

• Work is done only if the force (or some component of it) is in the same (or opposite) direction as the displacement

• Work is the force done Parallel to the displacement


Work for Constant Forces

The Math: Work can be complicated. Start with a simple case.

For constant forces, the work is:

…(more on this later)

W=F.d


1 Dimension Example

Pull a box with a constant force of 30N for 50m where the force and the displacement are in the same direction

How much work is done on the box?

W = F.d = 30N . 50m= 1500 N . m = 1500 Joules


What if the Force and the Displacement aren’t in the same

direction?


Force

Displacement

2 Dim: Force Parallel to Displacement

Force

Displacement

Rotate

F|| = Fcos

W = F||d = F.d = Fdcoswhere is the angle between the net Force and the net displacement. You can think of this as the force component in the direction of the displacement.


Work done and Work experienced

• Something subtle: The amount of work YOU do on a body may not be the same as the work done ON a body

• Only the NET force on the object is used in the total work calculation

• Add up all the work done on an object to find the total work done!


Examples• Holding a bag of groceries in place

– Is it heavy?– Will you get tired holding it?– Are you doing “Work?”

• Moving a bag of groceries with constant speed across a room– Is it heavy?– Will you get tired doing it?– Are you doing “Work?”

• Lifting a bag of groceries a height h with constant speed?– Work by you?– Work on the bag?


Groceries: With the math• Holding a bag of groceries

– W=F.d = Fdcos=(0)*(0)*cos = 0

• Moving a bag of groceries with constant speed across a room– Force exerted by you = mg, Net Force on bag = 0– Work on bag= F.d = Fdcos=0*dcos=0– Work exerted by you =Fdcos=mgd*cos(900)=0

• Lifting a bag of groceries a height h with constant speed?– Work on bag = Fd*cos = (0)*h*(00) = 0– Work by you =Fdcos=(mg)hcos(00)=mgh


Work in Two Dimensions

You pull a crate of mass M a distance X along a horizontal floor with a constant force. Your pull has magnitude FP, and acts at an angle of . The floor is rough and has coefficient of friction . Determine:

• The work done by each force

• The net work on the crate

X


What if the Force is changing direction?

What if the Force is changing magnitude?


What if the force or direction isn’t constant?

I exert a force over a distance for awhile, then exert a different force over a different distance (or direction) for awhile. Do this a number of times. How much work did I do?

Need to add up all the little pieces of

work!


Fancy sum notationIntegral

Find the work: CalculusTo find the total work, we must sum up all the little pieces of work (i.e., F.d). If the force is continually changing, then we have to take smaller and smaller lengths to add. In the limit, this sum becomes an integral.

b

a

xdF


Use an Integral for a Constant Force

FdFFd| FxFdx x dFW dxx

dd

0000

Assume a constant Force, F, doing work in the same direction, starting at x=0 and continuing for a distance d. What is the work?

Region of integrationW=Fd


Non-Constant Force: Springs• Springs are a good example of

the types of problems we come back to over and over again!

• Hooke’s Law

• Force is NOT CONSTANT over a distance

Some constantDisplacement

xkF


Work done to stretch a Spring

How much work do you do to stretch a spring, at constant velocity, from x=0 to x=D?

D


This Week

• Next Lecture: More on Work and Energy

• Finish the reading for Chapter 7

• Recitation on Chapter 5, with HW5 due Monday

• Get caught up on your homework


Examples• While you are lifting up a bottle with mass m, the

bottle moves a distance d with constant velocity. As you lift it:– What is the force you exert? – What is the work done by you?– What is the work done by gravity?– What is the net work?

• You push a box with Force F on a rough floor with coefficient of friction for a distance d, and the box moves with constant velocity. As it moves:– What is the work done by you?– What is the work done by friction?– What is the net work?


Exam 1 Results• Overall:

• Mean=50/75 (after bonus) or ~66%• This was a hard exam… We’ll probably

curve it. • Preliminary curve… will change

• >85% => A• >75% =>B• Between 40 and 52 out of 75 => C• <40/75 in the D or F range

• Remember: Exam 1 only worth 75 points


Does the Earth do work on the Moon?


Simple Case

Start with our spherical cow:–Constant Forces in a single direction

• Work is the force done Parallel to the displacement

• Work is done only if the force (or some component of it) is in the same (or opposite) direction as the displacement


Hiker

A hiker carries a backpack of mass M with constant speed up a hill of angle and height h.

Determine:

• The work done by the hiker

• The work done by gravity

• The work on the backpack


Simple Example with Unit Vectors

A woman pulls a box of mass M with Force FP in the direction for a distance d. Ignore friction

Find the work using unit vectors

physics 218, lecture x1 physics 218 lecture 10 dr. david toback

Documents

work work

displacement work

word work

lecture x7 work

lecture x14 work

lecture x11 work

displacement slide

total work calculation