What is Work and Power - It's Introduction, Types, Formula, Examples

Work:

Suppose you apply a constant horizontal force to a heavy box to move it across a concrete floor. You have done work to move the crate and that the farther you move it, the more work you will do. Think of work as the price you pay, in effort, to make something move against a resistance. At the heart of the concept of work is the notion of movement against resistance, be it the resistance produced by gravity, or friction, or inertia, or whatever. Work can be done on a body to get it moving, to keep it moving, or to change the way it is moving. Work is done to overcome, to move against the resistance of, some force.

Work is defined as the change in the energy of a system resulting from the application of a force acting over a distance.

It's not just about being tired. It's about successfully using your energy to cause a specific kind of action. For it to count as work in the physics sense, two things must happen together. You have to push or pull means you have to apply a Force. The thing you push must move in the direction you're pushing means displacement. If either one is missing, you did zero work.

If the force and the distance moved are in the same direction, then work is the applied force multiplied by the distance gives us,

work = force × distance
W = Fd

where W is the work and d is the distance moved. The units of work will be units of force multiplied by units of distance or newton meters (Nm) in the metric system. We call this unit a joule (J). The joule is the basic metric unit of energy, 1 J = 1 N·m.

e.g.
1. Pushing a stalled car and it starts rolling. You applied a force and the car moved in the direction of your push. In this case, you transferred your energy to the object to make it move. That's work.
2. Pushing against a solid brick wall until you sweat. You applied a huge force, but the wall did not move. No displacement means no work. Walking around holding your shopping bags. You are applying an upward force, but the bags are moving horizontally. The direction of the force and the direction of motion are perpendicular. Since you aren't fighting gravity by moving them up or down, you're doing no work on the bags horizontally. You are doing work with your legs to move yourself, but not on the bags.

Force applied at an angle:

What if the force acting on an object is neither perpendicular nor parallel to the direction of the object’s motion? In this case, we do not use the total force in computing work. Instead, we use only that portion or component of the force in the direction of the motion.

Suppose you are moving a box horizontally by pulling on a rope that is inclined at an angle, not parallel to the ground. You're not using all your effort to move the box. Because you are pulling at an angle, you are wasting some of your effort on the vertical lift. To move the box, you must pull harder than if you were pulling perfectly horizontally to produce the same amount of horizontal force. When you pull on an inclined rope, your pulling force points along the rope.

That force at an angle split into two separate effects or components: horizontal component i.e Fcosθ and vertical component Fsinθ. Of you didn't get it then study vector.

A Horizontal Component: 

This part of your force pulls the box forward, working to overcome friction and actually move it horizontally. This part does useful work.

A Vertical Component: 

This part of your force pulls the box upwards, slightly lifting it off the ground. This part does NO work for horizontal movement.

Only the component of the force in the direction of motion or in horizontal contributes to the work. The vertical component just adds downward force but doesn't help with horizontal movement.

e.g. Imagine you are pulling the rope with a force of 50 Newtons at an angle θ.

Your total force vector is along the rope
This force can be split into two imaginary arrows:

Horizontal arrow i.e.
F horizontal = 50 N × cos(θ)) &

Vertical arrow i.e.
F_vertical = 50 N × sin(θ))

Types of Work :-

• Based on the Angle between Force and Displacement
• Based on the Force Doing the Work

1. Based on the Angle between Force and Displacement:

Work is strictly defined by the formula Work = Force × Displacement × cos(θ). The work is often distinguished by the the direction of the force relative to the direction of motionand the nature of the force doing the work i.e. angle θ.

• Positive Work if θ < 90°. 

The force is helping the motion. It adds energy to the object. Pushing a car to make it go faster. The force is in the same direction as the motion. i.e. W = +F × d.

• Zero Work if θ = 90°.

The force prevents the object from moving in another direction but doesn't speed it up or slow it down. It doesn't change the object's energy. Carrying a box while walking horizontally. The upward force is perpendicular to the horizontal motion. i.e. W = 0.

• Negative Work if θ > 90°.

The force is opposing the motion. It removes energy from the object. Sliding a box to a stop. Friction acts opposite to the direction of motion, slowing it down. i.e.W = -F × d

2. Based on the Force Doing the Work:

• Work Done by a Conservative Force: 

The work done is independent of the path taken; it only depends on the start and end points. The energy can be recovered.

▪︎Gravitational Work: 

Work done by gravity e.g., lifting or lowering an object.

▪︎Spring Work: 

Work done by compressing or stretching a spring.

• Work Done by a Non-Conservative Force:

The work done depends on the path taken. This work generally dissipates energy as heat, sound, etc., and cannot be easily recovered.

▪︎Work Done by Friction: 

Always negative, as it opposes motion and turns kinetic energy into heat.

▪︎Work Done by a Person or Engine: 

An external force that adds or removes energy from a system.

Power:

When you want a day’s labor and are concerned about getting every minute’s worth, you buy a certain amount of work per hour. That’s the practical language of industry, and it was in the beginning of the Industrial Revolution that the idea of power became quantified. In simple language, Power is not about the task, but it's about the Speed. If Work is the total amount of a task done like lifting 50 boxes, then Power is how fast you can do that task.

Power measures the rate at which work is done or energy is transferred. Power is found by dividing the amount of work done by the time required.

                      Work          W
Power (P) = ----------- = ---------
                      Time           ​​ t

  
We computed a work value of 200 J for moving a crate 4 m across the floor using a force of 50 N. If the crate is in motion for 10 seconds, the power is found by dividing 200 J by 10 seconds, yielding a power of 20 J/s. A joule per second (J/s) is also called as watt (W). Another unit of power still used to describe the power of automobile engines is horsepower (hp). One horsepower is equal to 746 watts, or 0.746 kilowatt (kW).

Example:-

1. Imagine two people lifting the same 100 kg weight from the floor to a table. The work done is fighting gravity to lift the weight up is identical for both people. Person A is a bodybuilder. He will lift the weight in 2 seconds.
Person B is out of shape. He will struggle, but will take 10 seconds to lift the same weight the same height. Who is more powerful? Person A is. They did the same amount of work but in much less time. That's what power is.

2. Why Horsepower matters in car engines. This is the perfect real-world example of power. We want to move a 1,500 kg car from a stop to a speed of 100 km/h. This is a fixed amount of energy required. A small economy car might take 15 seconds to accelerate to 100 km/h. A powerful sports car might take 4 seconds to accelerate to 100 km/h. They both did the same work. They accelerated the same mass to the same speed, but the sports car's engine did it much faster. The sports car's engine has a higher power output. It can transfer chemical energy I.e. from fuel into kinetic energy means motion at a fast rate.

Power means How quickly can you get the job done?

• High Power means a huge amount of energy is being transferred or work is being done in a very short time. Think of sports car acceleration and bodybuilder lifting weight.
• Low Power means the same amount of energy is being transferred or work is being done slowly over a long time. Think of a economy car, out of shape person

Types of Power:

Power is classified based on how it is measured or the form of energy being transferred.

• Based on Measurement:

▪︎ Average Power:

The average rate at which work is done or energy is transferred over a long time period. P_avg = Total Work / Total Time Your monthly electricity bill is based on the average power you used each day.

▪︎ Instantaneous Power:

The power at a specific moment in time. It's the rate of work done in an infinitesimally small time interval. P = Force × Velocity
The power output of a car engine exactly at the moment you slam the accelerator.

2. Based on the Form of Energy:

▪︎ Mechanical Power: 

Power associated with moving parts and forces.
Example: The power output of a car's engine (horsepower), a cyclist pedaling, a wind turbine spinning.

▪︎ Electrical Power: 

Power associated with the flow of electric charge. This is what utilities provide and what most appliances use.
Formula: P = Voltage × Current
Example: A 60W light bulb, a 1200W microwave oven.

▪︎ Human Power:

The power a human can generate physically.

Example: A healthy adult can sustain about 100 watts of power for a full day. In short bursts, a person can output over 1000 watts!