Phys141 Principles of Physical Science

Chapter 4 Work and Energy

Instructor: Li Ma

Office: NBC 126Phone: (713) 313-7028Email: malx@tsu.edu

Webpage: http://itscience.tsu.edu/ma

Department of Computer Science & PhysicsTexas Southern University, Houston

Sept. 20, 2004

Topics To Be Discussed

WorkKinetic Energy and Potential EnergyConservation of EnergyPower

About Work & Energy

Common meaning of Work– Work is done to accomplish some task or

job– When work is done, energy is expended

Mechanically, Work involves force & motion

Energy is a concept, is abstract, is stored work

Work

The work done by a constant force F acting on an object is the product of the magnitude of the force (or component of force) and the parallel distance d through which the object moves while the force is applied

W = F·d

Work (cont)

If only apply force but no motion, then there is technically no work

Only the component of force in the direction of motion has contribution to work

Example:

d

F

Fh

Fv

W = Fh·d

Work (cont)

Unit of Work– In Metric system: N·m, or joule (J)– In British system: pound·foot (ft·lb)

Newton’s third law force pair– When the force is applied, work is done

against this force pair– Moving box forward: do work against

friction– Lifting the box: do work against gravity

Energy

Common sense:– when work is done, some physical quantity

changes: work against gravity, height is changed; work against friction, heat is produced; etc.

With concept of energy:– When work is done, there is a change in

energy, and the amount of work done is equal to the change in energy

Energy (cont)

Energy is described as a property possessed by an object or system

Energy is ability to do work:– An object or system that possess energy

has the ability or capability to do workUnit of Energy

– Same as work

Work and Energy

Doing work is the process by which energy is transferred from one object to another:– When work is done by a system, the

amount of energy of the system decreases– When work is done on a system, the

system gains energyBoth work and energy are scalar

quantities

Work and Energy (cont)

One scenario: when work is done on an object (at rest initially), the object’s velocity changes

d = ½a·t2, v = a·t, F = m·a, W = F·dW = m·a·d = m·a·(½a·t2) = ½ m·(a·t)2 = ½ m·v2

So W = ½ mv2

This amount of work is now energy of motion, or kinetic energy

Work and Energy (cont)

Another scenario: when work is done on an object, the object’s position changes

There is also a change in energy, since the object has potential ability to leave that position and do work

This amount of work is energy of position, or potential energy

Kinetic & Potential energy: two forms of Mechanical energy

Kinetic Energy

Kinetic energy is the energy an object possesses because of its motion, or simply stated, it is energy of motion:

kinetic energy = ½ x mass x (velocity)2

Ek = ½ mv2

Kinetic Energy (cont)

If the work done goes into changing the kinetic energy, then

work = change in kinetic energy

W = ΔEk = Ek2 – Ek1

So W = ½ mv22 - ½ mv2

1

Potential Energy

An object does not have to be in motion to have energy

Potential energy is the energy an object has because of its position or location, or simply, it is energy of position

Examples: lifted weight, compressed or stretched spring, drawn bowstring

Potential Energy (cont)

One scenario: Lift an object at a (slow) constant velocity up to a height h from the ground (or saying sea level)

Work is done against gravity

Work = weight x height

W = m·g·h (W = F·d)

Gravitational Potential Energy

The object has potential ability to do work, it has energy

Gravitational potential energy is equal to the work done against gravity

gravitational potential energy = weight x height

Ep = m·g·h

More generally, Ep = m·g·Δh

Conservation of Energy

Understanding of conservation– Energy can be neither created nor

destroyed– Energy can change from one form to

another, but the amount remains constant– Energy is always conserved

The total energy of an isolated system remains constant

Conservation of Mechanical Energy

Ideal systems– Energy is only in two forms: kinetic and

potentialConservation of mechanical energy

– The mechanical energy of the ideal system remains constant

Initial Energy = Final Energy

(Ek + Ep)1 = (Ek + Ep)2

(½ mv2 + mgh)1 = (½ mv2 + mgh)2

Conservation of Mechanical Energy (cont)

Want the velocity of a freely falling object when fallen a height of Δh:– velocity and acceleration:

Vt = gt, Δh = ½ gt2 (Δh = d)

=> Vt = (2gΔh) ½

– Conservation of mechanical energy:

(½ mv2 + mgh)i = (½ mv2 + mgh)t

½ m(v2t - v2

i ) = mg(hi - ht)

=> Vt = (2gΔh) ½

Power

Do same thing in different amount of time: the rate at which the work is done is different

Power is the time rate of doing work

power = work / time

P = W/t = F·d/tUnit: watt in the SI, 1 W = 1 J/s

Power (cont)

The greater the power of an engine or motor, the faster it can do work

Power may be thought of as energy produced or consumed divided by the time taken

P = E/t

=> E = p·t