**Work Done in a Force Field**

**Definition of Work Done**

**Work done** in Physics:

“Work is done upon an object whenever a force acts upon it to cause a displacement”

or WORK is defined as the product of force and distance moved in the direction of the force. If work done is w, distance covered is s and force is f, then mathematically,

Work done =force×distance W=f×s

The S.I unit of work done is Joules ( J ). Since unit of force ‘F’ is Newton (N), unit of distance ‘s’ is metre, the unit of work done is also Newton-Metre (Nm). Other units are kilojoules and megajoules. Note: If no distance is covered, work done is zero. Work done is a scalar quantity.

Every object on the earth’s surface is under the influence of the force of gravity. This force pulls the object towards its centre. The earth’s gravitational field is an example of force field. If a body is to be lifted vertically upwards, work has to be done against this force of gravity. The work done is given as

Work done =force×distance=m×g×h

Where m = mass of the body in kilogram, g = acceleration due to gravity and h is height in metres. If on the other hand, the body falls freely from a vertical height h to the ground, the work done is also mgh.

Work is said to be done whenever a force moves a body over a distance in the direction of the force. i.e.

work = force (F) × distance(d) moved in the direction of the force (f × d).

**Mathematically,**

Work done W(d)=F×d

The unit of work is joules with the symbol J.s

Work =F×dcosθ

Component of F along the direction of motion.

**Power**

**Definition of Power**

**Power **can be defined in a number of ways:

- Power is the time rate at which work is done.
- Power is energy expended with time.
- Power is work done in a given time interval. Its S.I unit is watt. Larger units are horse power (hp), kilowatt (kw) and megawatt (mw).

Mathematically, Power \((P) = {\text{work done(w) or energy expended} \over \text{

A 40kg girl climbing a flight of stairs expends energy at the rate of 50W. The time taken for her to reach a height of 20m is (t)}}\\ = \frac{w}{t}\\ =\frac{f \times s}{t} \\ = f \times v\)

Where f is force and v is velocity (i.e ^{s}/ _{t}). that means power can also be defined as the product of force and velocity. The instrument for measuring power is watt-metre.

**One horse power is equal to 746watts (1h.p = 746W)**.

**Example**

A machine is rated 2500watts. Calculate the power in horse power

**Solution**

1 horse power = 746watts

Therefore 2500watts=2500746=3.35 horse power

**The Interchangeability of Work and Energy**

Energy and work can be used interchangeably because they are almost the same thing. They have the same unit which is Joule. For example, if someone has energy, it means he can do some work and if someone can do some work, it means he has some energy. Thus work and energy cannot be separated.

**EVALUATION**

- Define work, energy and power. State their S.I units.
- Can energy and work be used interchangeably? Explain.

**Calculations on Work and Power**

**Example 1.**

A body of weight 300N climbs to the top of a hill of height 20m. What is the work done by the body against the force of gravity?

**Solution**

Force F = 300N, distance s = 20m

Work done =force×distance=f×s=300N×20m=600J

**Example 2.**

An object of mass 12kg is held at a height of 10m above the ground for 15 minutes. Calculate the work done within this period.

**Solution**

Since the body is not falling freely under gravity, acceleration due to gravity is zero. Hence work done is also zero.

**Example 3.**

A bag of rice of mass 50kg was pushed through a distance of 5m for 10seconds by a force of 500N. Calculate the work done.(g = 10ms^{-2})

**Solution**

m = 50.0kg, F= 500 N, s = 5m and t = 10 seconds.

Work done =force×distance=f×s=500N×5m=2500J

**Example 4.**

Calculate the power of a pump which lifts 1000kg of water through a vertical height of 2m in 10 seconds. ( g = 10ms^{-2})

**Solution**

Mass (m) = 1000kg, distance (s) = 2m, time (t) = 10s

Power =work donetime taken=force×distancetime=m×g×sT=1000×10×210=2000W

**Example 5.**

An engine develops a power of 750W while moving a car at constant velocity of 3ms^{-s}. Calculate the force exerted on the car by the engine.

**Solution**

Power = 750W, velocity = 3m/s, F = ?

Power =force×velocity

Force=PowerVelocity=7503=250N

**Example 6.**

A stone of mass 10kg falls from a height of 2.0m. Calculate the work done. (take g = 10ms^{2})

**Solution**

Mass (m) = 10kg, height (h) = 2.0m

Work done =mgh

=10×10×2=200J

**EVALUATION**

- Differentiate between work done and power.
- What other unit is used in measuring work done?
- A girl applied a force of 20N on an object for 5s. if the object remains stationary, calculate the work done
- A boy lifted up a bag of yam of weight 5N through a height of 2m in 10s. Calculate his power.

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