# Work and Energy

When it comes to physics, work and energy mean something different from what we normally use these words for. In physics, work is the energy transfer that happens when you move an object with force. So, when you push a box across the floor, you are doing work.

## How can we calculate the work done and what are its units?

We can calculate work done on an object using the following formula:

W = F·d

Here:

W = work done.F = force applied.d = distance covered in the direction of the force applied.

Work has the SI unit of Joules (Nm). According to the formula, work can only be done if the object on which the force is applied moves in the same direction as the force. If you apply force on an object and there is no displacement, you have done no work regardless of how tired you feel.

## What if the force applied does not move an object in the direction of the force?

While calculating the work done on an object, we must also bear in mind that only the component of the force that is parallel to the direction of the movement is taken into consideration. If you apply a force on a box, and your arms are parallel to the floor, all your efforts will contribute to the work done on the box.

When you push an object at an angle, only the part of the force that's parallel to the movement counts as work done. If the force is perpendicular to the direction of the motion, it doesn't count. To figure out how much work is done when the force is at an angle, we use the formula W = F·dcos(θ), where θ is the angle from the horizontal. If the angle is 0 degrees, the equation is W = F⋅d. If the angle is 90 degrees and the force is downward, there's no work done. If the force is upward, the object will move up if the force is strong enough.

## Can there be both positive and negative work?

You might think that work is what makes an object move, but it's actually the dot product of two vector quantities: force and displacement. This makes work a scalar quantity, which means it has a magnitude but no specific direction. Like temperature, work can be positive or negative. It's positive when the force and displacement are in the same direction, and negative when they're in opposite directions.

## Energy and its units

As we previously mentioned, work done is the transfer of energy to an object. This means that energy is a crucial element in determining the total amount of work done. Energy is the capacity of a body to perform work and is measured in Joules (Nm). It's simply a property of a system that can be transferred to another system. The amount of energy a body has will determine how much work it can do.

## Concept of Work and Energy

This theorem states that whenever work is done on an object, there will be a change in the kinetic energy of that object. Kinetic energy happens to be the energy of motion. But how can we prove this theorem?

First of all, we are going to make a few assumptions, even though these assumptions are not required to derive the formula to prove the work-energy theorem. They just make the calculations much simpler.

Suppose you have forces acting on an object whose direction is the same as the displacement. Theta will be zero in this case, which reduces the equation to:

W = F·d

Figure 3. Net force in the direction of the movement.

As we are dealing with the Wnet total work on an object, we can rewrite the above formula as:

Wnet = Fnet·d

Fnet is the total net force applied to an object. We also know that the net force is equal to the product of mass and acceleration. Hence:

Fnet = ∑F= ma

Wnet = m·a·d

The above equation has acceleration, which is why we need to rewrite it in the velocity v form. Recall from the kinematics equations that:

vf2 = vi2 + 2·a·d

a·d = Vf2 - Vi22

Vf in the above equation is the final velocity, Vi is the initial velocity, a is the acceleration, and d is the displacement. To use the above kinematic equation, we need to assume the acceleration to be constant. In that case, the Fnet applied is constant as well.

Putting the values into the Wnet equation yields:

Wnet=m·a·d

a·d=vf2-vi22

Wnet = m(vf2 - vi22) = 12mvf2 - 12mvi2

This quantity of 1/2⋅m⋅v2 is what we call kinetic energy. Finally, we can write the work-energy theorem as:

Wnet = ∆KE

Work and Energy - Key takeaways Work done can be calculated as the dot product of force and displacement vectors. Work done on an object depends only on the component of the force that is parallel to the direction of the movement. Work can be positive or negative. Energy is the capacity of an object to perform work. The work-energy theorem states that whenever work is done on an object, there is a change in the kinetic energy of that object.

## Work and Energy

**Are work, power, and energy scalar or vector quantities?**

They are scalar quantities.

**Are energy and work the same thing, explain?**

Energy is the ability of a body to do work, while work is the amount of energy transferred to a body in the same direction of the movement.

**What are the units of work and energy?**

The units of work and energy are Joules.

**What is the relationship between work, energy, and power?**

Whenever work is done on an object, there is a change in the kinetic energy of that object. In relation, power is the rate of doing work or work done per unit time.