Grade 7 → Energy, Work and Power ↓
Work done by force and its calculation
In our everyday lives, we talk about work all the time. However, the concept of work in physics is quite specific. When we discuss work in the context of physics, we are describing something very different from the everyday use of the word. Work in physics deals with forces and the displacements they cause.
What is work in physics?
In physics, work is done when a force causes an object to accelerate. For work to occur, three things must happen:
- A force must be applied to an object.
- The object must move in the direction of the force.
- The displacement of the object must be in the direction of the force.
The work done by a force is calculated using the following formula:
Work (W) = Force (F) x Distance (d) x cos(θ)Where:
- W is the work done (measured in joules, J).
- F is the force applied (in newtons, N).
- d is the distance over which the force is applied (in meters, m).
- θ is the angle between the force and the direction of motion.
Understanding the components
Let's look at each of these components in more detail:
Force (F)
Force is the push or pull applied to an object. It is measured in newtons (N). For example, when you push a shopping cart, you are applying force to it. The more force you apply, the more work you can do.
Distance (d)
Distance is the distance travelled by the object when the force is applied. In terms of work, it is important to note that the distance travelled must be in the direction of the force for work to be done. If the object does not move, no matter how much force is applied, no work is done.
Angle (θ)
The angle θ is important because it determines the component of the force that does the work. If the force is applied in the same direction as the motion, then θ is 0 degrees, and the formula simplifies to:
Work (W) = Force (F) x Distance (d)If the force is perpendicular to the direction of motion, such as moving a heavy object on a level surface, then θ is 90 degrees and no work is done in the direction of motion.
Example to show the work done
Example 1:
Imagine you are pulling a sled on snow. You apply a force of 10 N over a distance of 5 m in the same direction in which you are moving. How much work is done?
Since the force and velocity are in the same direction, θ is 0 degrees.
Work (W) = 10 N x 5 mx cos(0°)Since cos(0°) = 1, the calculation will be as follows:
Work (W) = 10 N x 5 m = 50 JHence 50 joules of work was done.
Visual example:
This diagram shows a force applied horizontally over a straight distance. The force vector and the distance are aligned.
Example 2:
Suppose you lift a box weighing 20 N to a height of 3 m. How much work will be done?
In this scenario, the force (20 N) is in the direction of the displacement (3 m upward), so θ is 0.
Work (W) = 20 N x 3 mx cos(0°)The simplification of which is as follows:
Work (W) = 20 N x 3 m = 60 JHence 60 joules of work was done.
No work situation
There are situations where force is applied but no work is done. This happens when:
- The force is perpendicular to the direction of motion.
- There is no displacement of the object.
Example 3:
If you push hard on a wall, but the wall doesn't move, you are applying a force, but since there is no displacement, no work is done.
Visualization of forces and work
It is often easier to understand how work is done with a visual aid. Below is an example to represent forces at an angle:
This diagram shows a force applied at an angle θ to the horizontal direction of motion. The horizontal component of the force does work, but the vertical component does not.
Conclusion
Understanding work in physics involves recognizing the interaction of force, distance, and the angle between them. Understanding these concepts allows us to calculate energy transfer in various scenarios, which is fundamental in physics and engineering.
As you continue to explore physics, remembering these basic concepts will help you understand more complex ideas related to energy, power, and machines.
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