Energy

Warm Up:

Forces

Distances and Displacements Compared

Describing work done

$$\text{work done}=\text{Force}\times \text{displacement in the direction of the force}$$

$$W=Fs$$

• where
• $W$ is the work done in joules, J;
• $F$ is the driving force in newtons, N;
• and
• $s$ is the displacement in metres, m.

This formula fits well with experience. Over a given distance the greater the force applied the more the effort (the more work is done). Similarly, for a given force, the greater the distance the more the effort (so more work done)

Notice that this formula requires that the force and displacement are parallel.

A more general formula with the force and the displacement with an angle, $\theta$ between them is

$$W=Fscos\theta$$

This can be written in a more compact form using the scalar (or dot) product

$$W=\mathbf{F}\cdot \mathbf{s}$$

Where here the force and the displacement are both written as vectors.

Note: work done can be thought of as energy transferred or simply just energy.

The Rearrangements.

Questions:

work done
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Follow-on material:

Efficiency

In terms of energy is ...

... and in terms of power ...

Questions:

Efficiency Worksheet
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Power

Prerequisite Materials

Mechanical Power:

Work can be done very quickly or rather slowly; there can be difference rates at which work is done.

Power is the rate at which work is done or the work/time ratio. The equation for rate of doing work or power is:

or

The SI unit of power is the Watt. As implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time, that is, joule/second or J/s.

Machines do work on objects in a given time therefore have a certain power. This power gives the rate at which the machine can do work on a process. A car engine is an example of a machine that is given a power. The power equation implies that a more powerful engine can do the same amount of work in less time. That is, power and time are inversely proportional for a given amount of work.

Questions:

Power Worksheets, Questions and Revision
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An Alternate Formula for Power

Given that:

Work done is:

where $F$ is the force displacing an object by $s$.

Combining the equations for work with that for power

Since the expression for velocity is

The expression for power can be rewritten as

This new equation for power shows that a powerful machines are both strong (i.e., large force) and/or fast (i.e., high velocity).

An Equation for Electrical Power

$P=IV$

For more see Work Energy Power from revisionmaths.com

Power Equations

$$P=\frac{\Delta E}{\Delta t}$$

• where
• $P$ is the power developed in watts, $W$;
• $\Delta E$ is the energy transferred in joules, $J$;
• and
• $\Delta t$ is the time taken for the transfer in seconds, $s$.

The Rearrangements:

$$\Delta E=P\Delta t$$

$$\Delta t=\frac{\Delta E}{P}$$