Work and Power

Work and power are fundamental concepts of physics. This study material notes on work and power examine these concept’s definition, function and uses. Power and work are co-related to each other; Power is specifically used to refer to the rate at which work is done, and work means an object’s displacement.

Work

A work is said to be done when an application of force causes the displacement of an object. The SI unit in which work is determined is called Joules, i.e., 1 J = 1 N ⋅ m = 1 kg ⋅ m2/s2. Work is defined as a scalar quality as it only has magnitude and no directions.

Mathematical Formula: = (F cos θ )d = F.d 

The SI unit of work is Joule (J). On the other hand, in the CGS system, the unit of work is erg. The dimensional formula of work is ML2T-2.

For example: Suppose you are using a thread to pull a curtain over the floor; consider that the curtain is your system, and the force you are applying to pull the curtain is a type of external force. So, let’s say you are pulling on this curtain system by dragging it straight behind you, so the thread is parallel to the earth. If you use the thread to pull the curtain for 1 metre, then it is said that you are doing work on the curtain. 

So, the amount of the work you are doing equals the force you are using to pull the box times the distance you moved it. 

According to the work equation, if there is no displacement, then work done is 0, which means no work has been done. It implies that there is no work is done when:-

• Force = zero
• the displacement = 0
• force and displacement make 90-degree angles or are mutually perpendicular.

Work Done By a Constant Force

When a force acting on a body produces a displacement, then the work done by the force (W), i.e., W = FS cos θ.

Here F is a constant force

S is displacement to due to force

θ is the angle between force and displacement

Nature of Work Done

1) Positive Work

Work is a scalar quantity that may be positive or negative or even 0 as given below:

W = FS cos θ

Where θ is acute (< 90°), cos θ is positive, so work done is positive.

Ex:

1.  When a body falls freely under gravity, θ = 0°, cos θ = cos 0° = + 1 so the body falling freely is +ve.
2.  When a bull pulls a cart by applying a force along the rope at an acute angle, work done by the applied force is +ve.
3. When a spring is stretched, work done by the stretching force is +ve.

2) Negative Work

W = FS cos θ

Where θ is Obtuse (> 90°), cos θ is negative, so work done is negative.

Ex: When a body is thrown up, its motion is opposed by gravity

Energy

It is defined as the capacity or ability of a body to do work. If a body is capable of doing more work, it is said to possess more energy.

Factors Affecting Work

The factors that affect the work are:

• Force – It is defined as a push or a pull that can cause any object with a mass to change its velocity and acceleration.
• Displacement – The angle between the force vector and displacement vector.

Power

In physics, power measures the rate at which work is done or energy is transferred. An excellent example to understand it is that imagines a rock is being pushed and is moving in a specific direction; the rate at which the rock is being displaced in the direction of the force applied on it would be its power. The standard unit used to measure power is the watt (W). The formula for power is P= E/t (Where P stands for Power, E stands for energy in joule, and T stands for time in seconds). Power is also measured in horsepower (hp). Based on an interval of time, power is divided into two types; firstly, the amount of power used at a specific interval of time is known as the average power

 Pavg= W/t

 secondly, the amount of time used at a specific moment is known as instantaneous power

 Pinst=dW/dt.

Conclusion

This work and power study material discusses physics concepts that are extremely important from an examination point of view. The questions asked from this topic are theoretical and numerical, and the level of questions asked is almost easy to moderate. In this study material notes on work and power, we have studied definition, principle, formula, SI units and examples of work and power.