Find the work done on a box if it is pushed with a horizontal force of 1.5 N for a distance of 1.2 m. Give your answer to two decimal places.

Question

BlackTom AI · Accepted Answer

Work done by a constant force equals the dot product of force and displacement: W = F · d = F d cosθ. Here the force is horizontal and the box moves horizontally, so the angle θ between force and displacement is 0° and cos0° = 1.

Step-by-step reasoning:
1. Identify the quantities: magnitude of force F = 1.5 N, displacement d = 1.2 m, angle θ = 0° (force parallel to displacement).
2. Apply the formula: W = F d cosθ.
3. Substitute the numbers: W = (1.5 N) × (1.2 m) × cos0°.
4. Evaluate cos0° = 1, so W = 1.5 × 1.2 × 1 = 1.8.
5. Include units: N·m which is equivalent to joules (J). So W = 1.8 J.
6. Round to two decimal places as requested: 1.80 J.

Intermediate arithmetic shown: 1.5 × 1.2 = (15 × 12) / 100 = 180 / 100 = 1.8.

Why this answer is correct: the force is entirely in the direction of motion, so all of the applied force contributes to work; there is no component to ignore or additional factors (like friction or vertical displacement) mentioned. The computation directly follows the definition of mechanical work for constant force.

Common incorrect approaches and why they are wrong:
- Multiplying by mass or g: unnecessary here because no change in potential energy or acceleration information is required.
- Using W = 1.5 + 1.2 or other arithmetic errors: wrong operation.
- Forgetting to convert units: units are already SI (N and m), so no conversion needed.
- Reporting 1.8 without two decimals: formatting error — the question requests two decimal places.

Conclusion: The work done is 1.80 J, which matches the provided correct answer 1.80.

Find the work done on a box if it is pushed with a horizontal force of 1.5 N for a distance of 1.2 m. Give your answer to two decimal places.数值题

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