Force and Displacement Work Calculation

This question asks us to calculate the work done on a body when a known force causes a specific displacement in the direction of the force.

Understanding Work Done in Physics

In physics, work is done when a force causes an object to move some distance. It's a measure of energy transfer. The amount of work done depends on three factors:

• The magnitude of the applied force (\(F\)).
• The magnitude of the displacement (\(d\)).
• The angle (\(\theta\)) between the direction of the force and the direction of the displacement.

The Formula for Work Done

The general formula to calculate work done is:

\( W = F \times d \times \cos(\theta) \)

Where:

• \(W\) represents the work done (measured in Joules, J).
• \(F\) represents the magnitude of the force (measured in Newtons, N).
• \(d\) represents the magnitude of the displacement (measured in meters, m).
• \(\theta\) is the angle between the force vector and the displacement vector.

Applying the Formula to the Problem

In this specific question, we are given:

• Force (\(F\)) = 10 Newtons (N)
• Displacement (\(d\)) = 2 meters (m)
• The displacement is stated to be in the direction of the force. This means the angle \(\theta\) between the force and displacement is 0 degrees (\(0^\circ\)).

Since \(\theta = 0^\circ\), the value of \(\cos(\theta)\) is \(\cos(0^\circ) = 1\).

Therefore, the formula simplifies to:

\( W = F \times d \times 1 \)

\( W = F \times d \)

Step-by-Step Calculation

1. Identify the given values:
   • Force, $F = 10 \, \text{N}
   • Displacement, $d = 2 \, \text{m}
2. Use the simplified work formula since force and displacement are in the same direction: \(W = F \times d\).
3. Substitute the values into the formula:

   \( W = 10 \, \text{N} \times 2 \, \text{m} \)

4. Calculate the result:

   \( W = 20 \, \text{N} \cdot \text{m} \)

5. Recognize that 1 Newton-meter (N·m) is equal to 1 Joule (J).
6. State the final answer:

   \( W = 20 \, \text{J} \)

Conclusion

The work done by the 10 Newton force resulting in a 2-meter displacement in the same direction is 20 Joules.