If 1,200 J of work is done in pushing a trolley by 20 m, what was the force (in N) employed?
60
Calculating Force from Work and Distance
The question asks us to determine the force employed when a known amount of work is done over a specific distance. This involves the fundamental physics concept of work done by a constant force.
Understanding Work Done
Work is done when a force applied to an object causes displacement in the direction of the force. The amount of work done depends on the magnitude of the force and the distance over which it acts.
The relationship between work, force, and distance is given by the formula:
\(W = F \times d\)
Where:
- \(W\) is the work done
- \(F\) is the force applied
- \(d\) is the distance moved in the direction of the force
Applying the Formula to Find Force
We are given the following information:
- Work done (\(W\)) = 1,200 J (Joules)
- Distance moved (\(d\)) = 20 m (meters)
We need to find the force (\(F\)) in Newtons (N).
To find the force, we can rearrange the work formula:
\(F = \frac{W}{d}\)
Step-by-Step Calculation
Now, let's substitute the given values into the rearranged formula:
\(F = \frac{1200 \text{ J}}{20 \text{ m}}\)
Performing the division:
\(F = 60 \text{ N}\)
So, the force employed was 60 Newtons.
Comparing with Options
Let's check our calculated force against the given options:
- Option 1: 120 N
- Option 2: 90 N
- Option 3: 60 N
- Option 4: 30 N
Our calculated force of 60 N matches Option 3.
Revision Table: Work, Force, and Distance
| Concept | Symbol | Unit (SI) | Formula |
|---|---|---|---|
| Work Done | \(W\) | Joule (J) | \(W = F \times d\) (when force is constant and parallel to displacement) |
| Force | \(F\) | Newton (N) | \(F = \frac{W}{d}\) |
| Distance/Displacement | \(d\) | Meter (m) | \(d = \frac{W}{F}\) |
Additional Information on Work and Force
It's important to remember a few key points about work:
- Work is a scalar quantity, meaning it only has magnitude, not direction.
- Work can be positive (force and displacement in the same direction), negative (force and displacement in opposite directions), or zero (force perpendicular to displacement, or no displacement).
- The formula \(W = F \times d\) is a simplified version that applies when the force is constant and acts purely in the direction of the displacement. If the force and displacement are not parallel, or if the force is not constant, more advanced methods (like using dot products or integration) are needed to calculate the work done.
- In this specific problem, we assume the force is applied in the direction the trolley is pushed, making the calculation straightforward.
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