If a person moves a trolley horizontally for a distance of 10 m by applying a constant force of 50 N, what is the mechanical work done on the trolley in joule?

Introduction / Context:
This numerical physics question tests your understanding of the basic definition of mechanical work in translational motion. Work done by a constant force is one of the first applications of the concepts of force and displacement in mechanics. Examinations frequently ask such direct formula based questions to ensure that students remember the relation between force, displacement, and work along the direction of motion.

Given Data / Assumptions:
- Magnitude of the applied force, F = 50 N.- Displacement of the trolley in the direction of the force, s = 10 m.- The force acts in the same direction as the displacement.- We neglect friction and any other opposing forces for this simple calculation.- We want the work done in joule, the SI unit of work and energy.

Concept / Approach:
For motion in a straight line when a constant force acts in the same direction as the displacement, mechanical work W is defined by the relation W = F * s. Here F is the magnitude of the force and s is the displacement in the direction of that force. If the force is not along the displacement, we use W = F * s * cos(theta), but in this question the angle between force and displacement is zero, so cos(theta) = 1 and the simple product F * s is sufficient.

Step-by-Step Solution:
1. Identify the correct formula for work done by a constant force: W = F * s.2. Substitute the given force F = 50 N into the expression.3. Substitute the given displacement s = 10 m along the direction of the force.4. Multiply the two values: W = 50 * 10.5. Calculate the product: 50 * 10 = 500.6. Attach the correct unit: since 1 N * 1 m = 1 J, the work done is 500 J.

Verification / Alternative check:
A quick sense check can be done by comparing with smaller values. If the same force of 50 N moved the trolley only 1 m, the work would be 50 J. Moving it ten times farther with the same force should naturally lead to ten times more work, which is 500 J. This proportional reasoning matches the calculated result and confirms that the obtained value is reasonable.

Why Other Options Are Wrong:
- 0.2 J: This is far too small and could result from inverting the numbers or mishandling decimal places.- 5 J: This would correspond to a much smaller displacement, for example 0.1 m, and does not match 10 m of motion.- 20 J: This might come from mistakenly multiplying 2 * 10 instead of 50 * 10 or confusing force with mass.

Common Pitfalls:
Students sometimes forget that displacement must be in metre and force in newton for the answer to be directly in joule. Another common error is to divide instead of multiply, especially when other formulae in mechanics involve ratios. It is also important to note the direction: only the component of the force along the displacement contributes to work. In this question the wording clearly states that the trolley is moved by the force along the same direction, so no angle correction is needed.

Final Answer:
The work done on the trolley is 500 J.