WORK DONE BY A CONSTANT FORCE

Understanding Work in Science

In science, work is defined as the product of force and displacement. When a constant force acts on an object in the direction of its displacement, the work done (W) can be expressed using the formula:

$W = F \times s$

Where:

• $W$ = Work done
• $F$ = Force applied (in Newtons)
• $s$ = Displacement (in meters)

Important Points

• Work done has magnitude only. It does not have a direction.
• The unit of work is Newton meter (N·m), which is also known as Joule (J). Thus, $1 J$ is defined as the work done when a force of $1 N$ displaces an object by $1 m$.

Example Calculation

If $F = 1 N$ and $s = 1 m$:

• Work done $W = 1 N \times 1 m = 1 J$

More Examples

1. Example 1: A force of 5 N displaces an object 2 m in the direction of the force.

   • Work done $W = 5 N \times 2 m = 10 N·m = 10 J$.

2. Question Example: A force of 7 N acts on an object which is displaced 8 m in the direction of the force.

   • Work done: $W = 7 N \times 8 m = 56 J$.

When is Work Considered Done?

To determine if work is done, consider:

• If the force (F) acting on an object is non-zero.
• If the displacement (s) also has occurred.
• If either force or displacement is zero, then no work is done.

Positive and Negative Work

1. Positive Work: Occurs when the force is in the direction of displacement.

   • Example: A baby pulling a toy car.

2. Negative Work: Occurs when the force is in the opposite direction to displacement.

   • Example: A car stopping when a retarding force is applied.

Activity: Lifting an Object

1. Lift an Object: Apply a force upward to lift it.
2. Forces to Consider:
   • Your applied force (upward) - Positive work is done.
   • Gravity (downward force) - Negative work is done.

More Example Calculations

1. Example 2: A porter lifts luggage weighing 15 kg from the ground to a height of 1.5 m.
   • Given: $m = 15 kg$, $g = 10 m/s^2$, $s = 1.5 m$.
   • Calculating work:
   • Force $F = mg = 15 kg \times 10 m/s^2 = 150 N$
   • Work done $W = F \times s = 150 N \times 1.5 m = 225 J$.

Questions for Practice

1. When do we say that work is done?

   • When a force causes an object to be displaced.

2. Write an expression for the work done when a force acts in the direction of displacement.

   • $W = F \times s$

3. Define 1 J of work.

   • 1 Joule is the work done when a force of 1 Newton displaces the object by 1 meter in the direction of the force.

4. A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field?

   • Work done $W = F \times s = 140 N \times 15 m = 2100 J$.

5. If an object is displaced 10 m with no force acting on it, how much work is done?

   • Answer: Work done $W = 0$ since the force is zero.

Conclusion

Understanding the concept of work is crucial in physics. It's about the force applied, the distance moved, and the direction of both. Always remember: If both force and displacement are aligned, work is positive, if they are opposite, work is negative.