Question

How to calculate work done and power of a 48 N force pushing a 2 kg object 3m along a frictionable horizontal surface?

Answer 1

To calculate the work done and power generated by a force acting on an object, we can use the following formulas:

### Work Done (W)
The work done by a force is calculated using the formula:

\[
W = F \times d \times \cos(\theta)
\]

where:
- \( W \) = work done (in joules)
- \( F \) = magnitude of the force applied (in newtons)
- \( d \) = distance moved in the direction of the force (in meters)
- \( \theta \) = angle between the force and the direction of motion

In this case:
- The force \( F = 48 \, \text{N} \)
- The distance \( d = 3 \, \text{m} \)
- Since the force is pushing in the same direction as the motion, \( \theta = 0^\circ \) (so \( \cos(0) = 1 \)).

Putting these values into the formula:

\[
W = 48 \, \text{N} \times 3 \, \text{m} \times \cos(0^\circ)
\]
\[
W = 48 \, \text{N} \times 3 \, \text{m} \times 1
\]
\[
W = 144 \, \text{J}
\]

### Power (P)
Power is the rate of doing work and is given by the formula:

\[
P = \frac{W}{t}
\]

where:
- \( P \) = power (in watts)
- \( W \) = work done (in joules)
- \( t \) = time taken (in seconds)

To calculate power, we need to know the time taken to move the object. If you can provide the time \( t \), we can calculate the power. If you don't have the time, you cannot determine the power without it.

Assuming you get the time taken (let's call it \( t \) seconds), you would calculate the power like this:

\[
P = \frac{144 \, \text{J}}{t}
\]

### Summary
- The work done by the force is **144 J**.
- To find the power, you need to divide the work done by the time taken to move the object (in seconds).