Work, Energy, and Power

The change in energy of a system by mechanical means:

Work

What mechanical means does work use to change the energy of a system?

Pushing or pulling

How to calculate work?

Force times displacement in the direction of force

Equation for calculating work:

Fd, where F is applied force in N, and d is distance moved by object in m

Unit for work:

Joules (J)

Is work a scalar or vector quantity?

Scalar

Can work have positive, negative, and neutral signs?

Yes

What does work with positive sign mean?

It is in the same direction as force

What does work with negative sign mean?

It is in the opposite direction of force

How to calculate work done by gravity?

W=mgh

If an object is moving downward, what is the sign of work done by gravity?

Positive

If an object is moving upward, what is the sign of work done by gravity?

Negative

What force is used to stretch a spring?

Applied force

What force tries to restore the spring after it is stretched?

Spring force

How to find work done by stretching a spring?

Applied force x change in length

Equation for finding work done by stretching force:

kx²

Why is the equation for finding work done by a stretching force kx²?

The work done by stretching a spring is applied force x change in length, and applied force = kx according to Hooke’s law

How to find the angle theta?

cos theta = FAx / FA

How to find FAx?

FA cos theta

What is the work done by FAy?

0

Why is the work done by FAy zero?

Because FA cos 90 d = 0

The sum of potential energy and kinetic energy:

Mechanical energy

Energy possessed by an object due to its position or shape?

Potential energy

Different types of potential energy:

Gravitational potential energy, elastic potential energy

Energy that an object has relative to its position in the earth’s gravitational field:

Gravitational potential energy

How to calculate gravitational potential energy?

Mass x gravitational field strength x height

The energy possessed by elastic materials:

Elastic potential energy

Example of elastic materials:

Spring

Hooke’s law:

F=kx

What does the area of a load-extension graph represent?

Work done by stretching or compressing the spring

Equation for finding area of a load-extension graph:

1/2 (x)(F)

Equation for calculating work done by stretching or compressing a spring:

½ (k) (x²)

Why is work done by stretching or compressing a spring calculated using ½ (k)(x²)?

Because F=kx, and W=1/2(Fx), so W=1/2(kx(x)), or W=1/2kx²

Energy possessed by an object due to its motion:

Kinetic energy

Equation for calculating kinetic energy:

1/2mv², where m = mass and v = velocity

Rate of doing work:

Power

How to calculate average power?

Work done in J over time in seconds

What is the unit for power?

J/s or watt (W)

kW = ? W

1000

MW = ? W

10^6

How to further break down the equation average power = work done / time?

Average power = (force x distance)/time

How to calculate power of a moving object?

Fv, where F = force and v = velocity

What does the principle of conservation of energy state?

Energy can never be created or destroyed but the total energy always remains constant

What does the work-energy theorem state?

The amount of work done on a system is equal to the energy added to the system

Why is work = change in kinetic energy for a block changing from one velocity to another?

Vf² = Vi² + 2ad, so Vf² = Vi² + 2ad, or Vf²-Vi²=2ad, and F=ma, so a =F/m, so (Vf-Vi)²=2Fd/m, so m(delta v)²=2Fd, so 1/2m(delta v)²=Fd, so change in kinetic energy = work

How is work = potential energy?

Potential energy = mgh, and mg = F and h = d, so potential energy = Fd = work

What does the area of force-distance graph represent?

Work

What condition must be true for area of force-distance graph to equal work?

Force must be constant

If force must be constant for area of force-distance graph to equal amount of work done, what does this mean about the calculated work?

It represents average work

Which type of collision do theoretical models exhibit?

Elastic

Types of collisions:

Elastic and inelastic

What happens to the momentum of a system where no external force acts?

Constant

The collision of 2 objects that do not stick to each other after collision:

Elastic collision

What is collision called if kinetic energy is conserved?

Elastic

Why are collisions in real life inelastic?

Energy is loss to sound, friction, or deformation

Is energy conserved in most collisions in real life?

No

A collision in which the kinetic energy is not conserved:

Inelastic collision