If a box of mass 25 kg is pushed 15 m by a force of ‘F’ N and work done in the process is 480 J. Find F:
32
Calculating Force from Work Done and Distance
The question asks us to find the force applied to a box given the work done and the distance it was pushed. We are provided with the mass of the box, the distance it moved, and the amount of work done during the process. We need to use the relationship between work, force, and distance to solve this problem.
Understanding Work, Force, and Distance
In physics, work done by a force on an object is defined as the product of the magnitude of the force and the distance moved by the object in the direction of the force. Mathematically, this is expressed by the formula:
\[W = F \times d\]
Where:
- \(W\) is the work done (measured in Joules, J)
- \(F\) is the magnitude of the force applied (measured in Newtons, N)
- \(d\) is the distance moved in the direction of the force (measured in meters, m)
In this specific problem, we are given the work done (\(W\)) and the distance (\(d\)), and we need to find the force (\(F\)). We can rearrange the formula to solve for \(F\):
\[F = \frac{W}{d}\]
Applying the Formula to Find the Force
Let's list the given values from the question:
- Mass of the box = 25 kg (Note: The mass is given but is not needed for the calculation of force using the work formula in this case, assuming the force is applied horizontally and only work against friction or accelerating the box is considered. Since we are given Work and Distance, the formula W=F*d is sufficient).
- Distance (\(d\)) = 15 m
- Work done (\(W\)) = 480 J
Now, we substitute these values into the rearranged formula for force:
\[F = \frac{W}{d}\]
\[F = \frac{480 \text{ J}}{15 \text{ m}}\]
Step-by-Step Calculation of Force
To find the value of F, we perform the division:
\[F = \frac{480}{15}\]
We can perform this division:
| 480 ÷ 15 | = 32 |
So, the force \(F\) is 32 Newtons.
Conclusion
The calculated force required to push the box is 32 N.
Revision Table: Key Concepts
| Concept | Definition/Formula | Unit |
|---|---|---|
| Work Done (\(W\)) | \(W = F \times d\) (when force and displacement are in the same direction) | Joules (J) |
| Force (\(F\)) | A push or a pull; \(F = \frac{W}{d}\) | Newtons (N) |
| Distance (\(d\)) | The length of the path covered; \(d = \frac{W}{F}\) | Meters (m) |
Additional Information on Work and Force
Work done is a scalar quantity, meaning it only has magnitude and no direction. The unit of work, the Joule (J), is defined as the work done when a force of one Newton moves an object through a distance of one meter (1 J = 1 N·m). Work is only done when a force causes displacement. If a force is applied but the object doesn't move, or if the force is applied perpendicular to the direction of motion, no work is done by that force.
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