How to Calculate Work

In our day-to-day life, we consider any physical or mental labor as work. However, the scientific definition of "work" is entirely different. If we look at two instances in the scientific way, you "work" hard for your exams, yet no work is done. However, if you throw a rock, you have done some "work". If you're curious to know more and want to learn how to calculate the amount of work done when a force acts on an object, this tutorial will answer your questions.

Edit Steps

Edit Part One: Deriving the Formula

Learn the definition of work. Work is said to be equal to the product of Force, Displacement and Cosine of the angle between the Force vector and the Direction of movement.

Derive the formula.
- Imagine a train car on a straight rail is being pulled by a force through a rope.
- Consider a constant Force, "F" acting on that car.
- Let the car be displaced (moved) through a distance, "d" in the direction movement.
- Let α (alpha) be the angle between the direction of force and the direction of movement. Force is a vector quantity, which means its magnitude and direction can be represented through a vector. In this example, the direction of force vector is the rope.
- Let "W " be the "Work" done.
  - Work= Force × Displacement × Cosine of α
  - W = F × d × Cos(α)

Know the two conditions that should be satisfied for work to be done.
- A force must act on an object.
- Displacement must take place.

If either of the conditions is not satisfied, then work is not done. Which means Work = 0.

Edit Part Two:Working out the Formula

Proceed with the formula. Memorize the formula and learn what each letter stands for. A quick recap is given below.
- W is Work done. The SI unit of Work is Joule (J).
- F is the Force applied. The SI unit of Force is Newton (N).
- d is the displacement (often written as s). In this formula, displacement's unit is metre (m).
- α is the angle between the direction of force and the direction of movement. The unit of α can be either radian (rad) or degree(°).

Understand what "1 J of Work" means. 1 J is the Work to be done on an object when a Force of 1 N displaces it by 1 m along the line of action of Force.

Work only has magnitude and no direction. Thus, Work is not a vector quantity.

Edit Part Three: Practicing the Formula

Try out a problem. For example:
- A train car is pulled by a Force of 10 N, which displaces it by 2 m in the direction of force. Calculate the Work done in this case.
  - F = 10 N
  - d = 2 m
  - α = 0° ⇔ Cos(α) = 1 (Since the car is pull in the direction of Force)
  - W = F × d × Cos(α) = 10 N × 2 m × 1 = 20 J
  - Thus, the Work done is 20 J.
- A train car is pulled by a rope, by a Force of 10 N, which displaces it by 2 m. The rope and the rail make an angle of 60°. Calculate the Work done in this case.
  - F = 10 N
  - d = 2 m
  - α = 60° ⇔ Cos(α) = 1/2 = 0.5
  - W = F × d × Cos(α) = 10 N × 2 m × 0.5 = 10 J
  - Thus, the Work done is 10 J.

Practice. Though the formula is pretty simple, it forms the basis for deriving the formulas for calculating kinetic and potential energy. As such, it's essential that you're thoroughly conversant with this formula and the way of working it.

Try out different problems. If you keep practicing, you'll find that you can remember the formula with ease and work it out quickly. For example, here are some more problems to figure out:
- A force of 7 N acts on an object. The displacement is 8 m, in the direction of the force. What is the Work done?
- A pair of bullocks exerts a force of 140 N on a plough. The field is being ploughed is 15 m long. Calculate the Work done in ploughing the length of the field.

Edit Tips

Keep practicing, and try again if you don't succeed at first.

Learn the following points about work:
- Work done by a force can either be positive or negative. (In this sense, the terms positive or negative carry their mathematical meaning, not the everyday meaning.)
- Work done is negative when the force acts opposite to the direction of displacement.
- Work done is positive when the force is in the direction of displacement.