Understanding Work in Physics Through Simple Examples

When we talk about work in physics, it's important to know what it means and how it works in real life. Work is when you use force to move something. We can think of it like this:

Work = Force × Distance × Cosine(Angle)

In this formula:

• Work (W) is the amount of work done.
• Force (F) is how hard you push or pull something.
• Distance (d) is how far the object moves.
• Angle (θ) is the angle between the direction of the force and the direction of movement.

Let’s look at some easy examples to understand this better.

Example 1: Pushing a Box Across the Floor

Imagine you want to push a box across a flat floor. The box weighs 50 kg, and you push it with a force of 100 Newtons (N) straight forward, which is at an angle of 0 degrees. The box moves 4 meters.

In this case, since everything is in the same direction (θ = 0), we can simplify our formula to just:

Work = Force × Distance

So, plugging in our numbers:

Work = 100 N × 4 m = 400 Joules (J)

That means you did 400 joules of work on the box.

Now, let’s change it up. What if you push the same box with the same force but at a 30-degree angle?

We will use our formula again:

Work = Force × Distance × Cosine(30 degrees)

The cosine of 30 degrees is about 0.866. So, we calculate:

Work = 100 N × 4 m × 0.866 ≈ 346.4 J

Now you only do about 346.4 joules of work because not all of the force helps the box move in the direction you want.

Example 2: Lifting a Weight

Next, let’s say you lift a 10 kg weight straight up to a height of 3 meters. You need to use force to overcome gravity. The force due to gravity on the weight can be calculated like this:

Weight = Mass × Gravity (where Gravity ≈ 9.81 m/s²)

So, the weight is:

Weight = 10 kg × 9.81 m/s² = 98.1 N

Now, to find out how much work you did lifting the weight:

Work = Force × Distance

Here, Force is 98.1 N and Distance is 3 m:

Work = 98.1 N × 3 m = 294.3 J

Thus, you do about 294.3 joules of work when lifting the weight.

Example 3: Pulling a Sled Up a Hill

Now, let’s think about pulling a sled up a slope. The sled weighs 15 kg, and the hill is angled at 20 degrees. You pull with a force of 80 N up the hill for 5 meters.

First, we need the force of gravity acting on the sled, which we can find just like before:

Weight = Mass × Gravity = 15 kg × 9.81 m/s² = 147.15 N

Next, we calculate how much force you need to fight against gravity while you pull the sled. This is found by using:

Force = Weight × Sine(20 degrees)

The sine of 20 degrees is about 0.342. So, we calculate:

Force = 147.15 N × 0.342 ≈ 50.4 N

Now, the work you do against gravity is:

Work = Force × Distance = 50.4 N × 5 m = 252 J

But we also need to find the total work done with the force you applied:

Total Work = Applied Force × Distance

Total Work = 80 N × 5 m = 400 J

So, you did a total of 400 joules of work to pull the sled, and 252 joules of that was to fight against gravity.

Example 4: Compressing Gas with an Air Compressor

Let’s consider an air compressor that is compressing gas. Suppose it pushes with a force of 500 N while the piston moves in by 0.1 m.

To find the work done on the gas, we use:

Work = Force × Distance

So, substituting in our numbers:

Work = 500 N × 0.1 m = 50 J

Here, 50 joules of work was done on the gas while it was being compressed.

Conclusion: Why Work Matters in Real Life

These examples help us see how work works in different situations. Whether you are pushing a box, lifting weights, pulling a sled, or running a compressor, work is everywhere!

Understanding work helps us see how energy is used in our daily lives and in machines. Learning how to calculate work is a key skill in physics. It helps connect what we learn in theory to what we experience in the real world.