WORK, ENERGY AND SECOND LAW

PRESENTED BY: FAROOQ MUSTAFA (169) ADIL ZAHOOR

(176) DAIYAL ZAHEER (182) M.BILAL ARSHAD (183) MOHTASIM NAWAZ (187)

AGENDA:-

• NEWTONS SECOND LAW• WORK • ENERGY • WORK-ENERGY THEOREM

Newton’s Second Law

Force equals mass times acceleration.

F = ma

Acceleration: a measurement of how quickly an object is changing velocity.

What does F = ma mean?

Acceleration is inversely proportional to mass

Acceleration is directly proportional to force

In other words….

Large Force = Large AccelerationF

a

In other words…..using the same amount of force….

FLarge Mass

a

Small acceleration

FSmall Mass

Large acceleration

a

WORK

DEFINATION

When a force “F” is applied to a body and it covers some distance “d” than a work is done on a body.

Work = Force x distance

W (Joules) = F (N) Δx (m)

Work is measured in Newton-meters (Nm), more commonly called joules (J).

1 J = 1 Nm

W = Fd

Is there working being done?

This is great! I’m getting paid

for doing no work!

Force and distance in same direction = + work

Force and distance in opposite directions = - work

CAN YOU DO NEGATIVE WORKING?

W = Fd(cos ө)

…so when the applied force is perpendicular to the distance, you end up with zero work!

CALCULATION OF WORK

Just as velocities may be integrated over time to obtain a total distance, by the fundamental theorem of calculus, the total work along a path is similarly the time-integral of instantaneous power applied along the trajectory of the point of application.

Work is the result of a force on a point that moves through a distance. As the point moves it follows a curve X with a velocity v at each instant. The small amount of work δW that occurs over an instant of time δt is given by

where the F.v is the power over the instant δt. The sum of these small amounts of work over the trajectory of the point yields the work.

WORK DONE BY A CONSTANT FORCE

WORK DONE BY A SPRING

A horizontal spring exerts a force F=(kx, 0, 0) that is proportional to its deflection in the x direction. The work of this spring on a body moving along the space curve X(t) = (x(t), y(t), z(t)), is calculated using its velocity, V=(vx, vy, vz), to obtain

For convenience, consider contact with the spring occurs at t=0, then the integral of the product of the distance x and the x-velocity, xvx, is (1/2)x2.

WORK DONE BY A GRAVITY

Gravity exerts a constant downward force F=(0, 0, W) on the center of mass of a body moving near the surface of the earth. The work of gravity on a body moving along a trajectory X(t) = (x(t), y(t), z(t)), such as the track of a roller coaster is calculated using its velocity, V=(vx, vy, vz), to obtain.

where the integral of the vertical component of velocity is the vertical distance. Notice that the work of gravity depends only on the vertical movement of the curve X(t).

20

THE WORK-ENERGY THEOREM

When a net external force does work W on an object, the kinetic energy of the object changes from its initial value of KE0 to a final value of KEf, the difference between the two values being equal to the work:

20

20 2

1

2

1mvmvKEKEW ff

The work done in lifting the mass gave the mass gravitational potential energy.

Potential energy then becomes kinetic energy. Kinetic energy then does work to push stake into ground.

Mechanical Energy

Mechanical energy is the energy which is possessed by an object due to its motion or its stored energy of position.

Mechanical energy can be either kinetic energy or potential energy.

The 1st Law of Thermodynamics and the Law of Conservation of Energy state that the algebraic sum of these energy changes and transfers must add up to zero, accounting for all changes relative to the system.

W + Q = ∆E

EQW

So for mechanics neglecting Q

W = ∆Ek + ∆Eg + ∆Eel+ ∆Echem+∆Eint

Potential and Kinetic Energy

How is all energy divided?

PotentialEnergy

Kinetic

Energy

All Energy

Gravitation

PotentialEnergy

ElasticPotentia

lEnergy

ChemicalPotentialEnergy

What is Potential Energy?

o Energy that is stored and waiting to be used later

What is Kinetic Energy?

o Energy an object has due to its motion

o K.E. = .5(mass x speed2)

Energy Storage Mode Equations:

1) EK = ½mv2

2) Eg = mgh

3) Eel = ½kx2