Topic 2 Mechanics

2.3 Work, Energy and Power

Work

James Prescott Joule defined the concept of work using a simple intuitive guess.

Physical work clearly depends on the force used to do that work.

Joule's insight was to say simply that the only factors affecting the amount of work done are the size of the force, and how far the object is moved in the direction of the force.

Calculating Work Done

Work done is given by

Where:W is work done in joules (J)

F is the force applied in newtons (N)

s is the displacement in (m)

is the angle between F and s.

Calculate the work done in:Pushing a 40kg box, 8m across a floor against a 15N friction force.

Lifting a 20kg box up on to a shelf 2m high.

Calculating Work Done

Calculate the work done in:Swimming 25m against a 30N current.

Dragging a 10kg box 30m across a warehouse using a 150N force applied by a rope at:0o to the horizontal

30o to the horizontal

60o to the horizontal

Moving a 15kg box up a flight of 13 stairs. Each stair is 15cm high and has a tread length of 20cm.

Measuring Work Done

In all the above cases, it is assumed that:The force applied is constant

The speed of the object is constantThere is no force causing acceleration.

If this is not the case then a force-displacement graph can be used.The area under the graph will give the product of the force and displacement; i.e. the work done.

Kinetic Energy

Kinetic energy is the energy of a massive body due to its motion.

It is given by:

The kinetic energy of a body is a scalar quantity measured in joules (J)

Gravitational Potential Energy

When work is done on an object to move it in a gravitational field there will be a change in gravitational potential energy.

Absolute Gravitational Potential Energy is a relative quantity and is defined as being zero at infinity (see Unit 6.1)

In all real-world situations we are able to define our own zero and so work with Change in gravitational Potential Energy.

Gravitational Potential Energy

Gravitational Potential Energy is defined as:

It is a scalar quantity measured in joules (J)Technically absolute GPE is always a negative quantity.

If working in a situation where g is variable, then a graph is generally used to find the area gh.

The Principle of Conservation of Energy

Energy can neither be created nor destroyed; it can only be transferred or transformed from one form into another.

This means that the total energy of a closed system must always remain constant.

Types of Energy

There are 5 main forms of energyKinetic energy of motion

Radiant energy carried by em waves

Internal energy of molecular vibrations / motions.

PotentialGravitational Potential energy stored in a gravity field.

Electrostatic Potential energy stored in an electrical field.

Elastic Potential - energy stored in stressed inter-molecular bonds.

Chemical Potential energy stored in intra-molecular bonds

Nuclear Potential energy stored in intra-atomic bonds.

Rest Mass energy stored in matter

Transferring Energy

There are just 2 ways to transfer energy.

Through Work done by a force

Through Heating due to a temperature difference.

Practice

A ball of mass 250g is placed at the top of a smooth ramp 3m high and released. It rolls across a horizontal sandpit for 1.8m once it reaches the bottom of the ramp.

Calculate:The GPE released as the ball rolls down the ramp

The speed of the ball at the bottom of the ramp

The average value of the friction force of the sand.

Power

Power is defined as the rate of doing work

Power is measured in Watts (W)

Power

Efficiency is defined as the ratio of useful work out to total work input.

Collisions Energy and Momentum

In order to explain most collisions and explosions the concepts of Energy and Momentum need to be used together.

In all collisions and explosions momentum is conserved if no external force acts.

In elastic collisions the total kinetic energy of the system is also conserved.

In inelastic collisions the total kinetic energy is not conserved; some energy will be transferred to sound, internal energy or stored as elastic energy.

In an explosion, the total momentum is always zero.