Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lecture 24

Ex.6

This is a one dimensional problem. A particle of mass m is attracted to the origin with a force of magnitude

2x

kFx

If a particle starts at x=A, moving to the right with velocity V0, where will it turn around? Could there be no solution?

x=0 x=A xV0

Quiz

A particle can only move along the x axis. Forces act on it so that its potential energy function is

42

21 4

1

2

1)( xkxkxU

where k1 and k2 are positive. The particle is started at x=a with zero velocity.

a)Where is the velocity a maximum? What is its magnitude?

b) Where else will the velocity be zero?c)What is the force on the particle as a function

of x?

Second exam Tuesday, October 21

105 Heldenfels

Section 801 and half of 802 start at 7 pm

Section 803 and half of 802 start at 8:15 pm

Work Energy Theorem

22

222

1

initialfinalr

r

total

mVmVrdFW

22

2222

11

22

11

initialfinalyx

yx

totaly

yx

yx

totalx

mVmVdyFdxF

If a force can be written as the gradient (slope) of some scalar function, that force is conservative.

U(x) is called the potential energy function for the force F

If such a function exists, then the force is conservative

1D case:dx

dUFx

)]()([ 12

2

1

2

1

xUxUdxdx

dU

FdxW

x

x

x

x

veconservati

veconservatiW does NOT depend on path!

1D case:dx

dUF

conW does NOT depend on path!

)]()([ 12 xUxUW con

If Fx(x) is known, you can find the potential energy function as

CdxxFxU x )()(

or

112221 ,0 UKUKW nc If

112221 UKUKW nc

Kinematics:

dt

dVa

dt

dVa y

yx

x ;

dt

dyV

dt

dxV yx ;

If is given, you can find anda

V

r

daVdtaV yyxx ;

dtVydtVx yx ;

ty

Newton’s 2nd Law

amF

xx maF yy maF

Work does not depend on the choice of coordinates! You can calculate work of each force in the most convenient system of coordinates.

Do not forget to work with components!

Usually there are several ways to solve the problem. Indicate the law or the theorem you use!

We will have a regular class on Wednesday!

Help Session:When: tonight at 7:00 pm

Where:Room 207 James J. Cain Engineering/Physics Lab Building

Spence St.

Have a great day!

Hw: Be prepared for the test

Good luck!