W = F × d × cos(θ). When force and displacement are in same direction, cos0° = 1. W = 50 J.

A 10 N Force Moves a Box 5 m — Calculate Work Done

Question

A force of 10 N acts on a box and moves it 5 m in the direction of the force. Calculate the work done.

Solution — Step by Step

Work is defined as force multiplied by displacement, but only the component of force along the displacement counts. The full formula is:

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

Here, $\theta$ is the angle between the force vector and the displacement vector.

The force acts in the same direction as the displacement — the box moves the way we push it. So $\theta = 0°$ .

We need $\cos 0°$ , which equals 1. This means the entire force contributes to doing work — no component is “wasted” sideways.

W = 10 \times 5 \times \cos 0°

W = 10 \times 5 \times 1

W = \mathbf{50 \text{ J}}

The work done is 50 joules.

Why This Works

Work measures energy transfer. When we push a box and it moves in our push direction, we’re handing over our energy directly into the box’s motion — that’s why $\cos\theta = 1$ gives us the maximum possible work for that force and distance.

The joule (J) is the SI unit of work. One joule means one newton of force moving something one metre. So $10\ \text{N} \times 5\ \text{m} = 50\ \text{J}$ is clean, no conversion needed.

This is a Class 9 NCERT staple — it tests whether you understand that the angle between force and displacement is the key idea, not just multiplying two numbers blindly.

Alternative Method

For Class 9, NCERT often writes the formula without $\cos\theta$ in the introductory section, as:

W = F \times s

This simplified form assumes force and displacement are in the same direction (which is the most common board exam case). Substituting:

W = 10\ \text{N} \times 5\ \text{m} = 50\ \text{J}

Use $W = F \times s$ only when the force is parallel to displacement. The moment the problem mentions a force at an angle (like “a force of 10 N at 60° to the horizontal”), you must bring in $\cos\theta$ .

Same answer, simpler route — but know why it’s simplified.

Common Mistake

Students often write the unit as “N·m” instead of “J” in the final answer. Both are technically the same thing ( $1\ \text{J} = 1\ \text{N·m}$ ), but board examiners want joules (J) as the unit for work and energy. Writing “N·m” can cost you the unit mark in CBSE.

A second trap: some students forget to check who does the work. The question asks for work done by the applied force — 50 J. If it asked for work done by friction (assuming a rough surface), that would be negative. Always read what the question is asking.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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