Energy Work and Linear Momentum

8/12/2019 Energy Work and Linear Momentum

1/33

Energy Work and

Linear Momentum

Chamila Sumathiratna-FIVT


2/33

Energy and Work Energy is the

ability to dowork

Work is beingdone wheneversome physicalforce is being

used to movean object somedistance


3/33

Forms of EnergyO Forms of Mechanical Energy

O Potential energy

O Kinetic energy

O Strain energy/elastic potential energy


4/33

Calculating Kinetic EnergyO Calculating kinetic energy.

If we know the mass of an object and its

velocity we can determine the amount of kineticenergy possessed by using the following

formula:

O kinetic energy = 1/2 (mass of

object)(velocity of object) 2

O or KE = 1/2 mV 2


5/33

Potential EnergyO The amount of

energy contained in

an object at rest dueto its height.

O Potential Energy =

(mass)(gravity)(heigh

t)

O PE= mgh


6/33

Elastic Potential Energy

O Force exerted ona spring

F=kx

O Where k is springconstant

O Work done orenergy stored inthe spring is the

area under thecurve in graph


7/33

Conservation of EnergyO When a closed

system is considered

energy cannot becreated or destroyed

O Can only be

transferred from one

form to the other.


8/33

Application


9/33

Work Done

O Definition of work

When an object undergoes a displacement with

magnitude along a straight line, while a constantforce with magnitude F, making an angle with s

acts on the object, the work done by the force on the

object is (F cos ) s


10/33

ApplicationO A person pushes a car 19 m.

If he pushes with a constantforce with magnitude 210 N,

how much work does he doon the car

O (a) if he pushes in thedirection the car is heading

andO (b) if he pushes at 30 to

that direction?


11/33

Momentum

Momentum= Mass x Velocity


12/33

Momentum

Momentum is a vector quantity


13/33

Change of MomentumO In order to stop

the vehicle, need

to bring themomentum to

zero.

O Time taken to

stop the vehiclemay differ

Take a long time to stop.

How about the force required??

Take a short time to stop

How about the force required??


14/33

ImpulseO Impulse is force

applied into time

that the force isapplied

O Impulse = change in

momentum


15/33

Application


16/33

Same Impulse

O Impulse for all three situations are same.


17/33

Conservation of momentum


18/33

The law of conservation of

linear momentum


19/33

Elastic and Inelastic Collisions


20/33

Elastic and Inelastic collisionsKinetic

energy isconserved

Kinetic

energy is

NOTconserved


21/33

Application-perfectly elastic

There are two elastic balls green and red.The Green

ball come at 3m/s and hit on red ball which is initiallyat rest. After collision green ball comes to rest and

red ball travels at v m/s. find v.


22/33

Application-perfectly inelastic

Find the velocity of the two balls

sticked together


23/33


24/33

Angular MomentumO Linear momentum=

mass x velocity

O Angular momentum=Linear momentum x radius

of rotation

P=mv kgm/s

L=rmv kgm 2/s


25/33

ApplicationO What is the angular

momentum of a

100 g mass tied tothe end of a 0.75 m

long string and

spun overhead

once per second?

O L=rmv

O Can be applied for a

point mass


26/33

Rotational Inertia/moment of

inertia


27/33

Moment of Inertia

O Which has more

rotational inertia?O If the mass is

distributed further

from axis of

rotation, moment ofinertia will be larger


28/33

Conservation of Angular

Momentum vs conservation oflinear momentum

O In the absence of

any net externaltorque, the totalangularmomentumof a closed system is

conserved..

O In the absence of

any net external

force, the total linearmomentum of a

closed system is

conserved..


29/33

Contd,


30/33

Equation for Angular

MomentumO Linear momentum P=mv kgm/s

O Angular momentum L=rmv kgm 2/s

O

v=rO Again L=rm(r)

L= mr L= I

I=moment of inertiaAngular momentum=moment of inertia x angularvelocity


31/33

ApplicationO What is the moment of

inertia of the followingpoint masses arranged

in a square?

O a) about the x-axis?

O b) about the y-axis?

O c) about the z-axis?


32/33

ApplicationO I door= Ms

2/3.

O Find the angular

velocity of thecompound unit

O Find kinetic energy in

two situations


33/33

ApplicationAn acrobat stands at the center of a turntable,

holding his arms extended horizontally, with a

5.0 kg dumbbell in each hand in figure . He is

set rotating about a vertical axis, making one

revolution in 2.0 s. His moment of inertia

(without the dumbbells) is 3.0 kg m2 when his

arms are outstretched, and drops to 2.2 kg m2when his arms are pulled in close to his chest.

The dumbells are 1.0 m from the axis initially

and 0.20 m from it at the end.

O Find the acrobats new angular velocity if he

pulls the dumbbells close to his chest, and

O Compare the final total kinetic energy withthe initial value.

Documents

Energy Work and Linear Momentum