To calculate the power required to push the box up the ramp, we can use the formula for power:

$P = \frac{W}{t}$

Where:

• $P$ is the power (in watts),
• $W$ is the work done (in joules),
• $t$ is the time (in seconds).

Step 1: Calculate the work done

Work done is defined as the force applied times the distance over which the force is applied:

$W = F \times d$

Where:

• $F = 75 \, \text{N}$ is the force applied,
• $d = 3 \, \text{m}$ is the distance the box is pushed.

So,

$W = 75 \, \text{N} \times 3 \, \text{m} = 225 \, \text{J}$

Step 2: Calculate the power

Now, we can calculate the power required using the formula for power:

$P = \frac{W}{t} = \frac{225 \, \text{J}}{5.4 \, \text{s}} \approx 41.67 \, \text{W}$

Thus, the power required to push the box up the ramp is approximately 41.67 watts.

Would you like more details on this, or do you have any other questions?

Here are five related questions you might find interesting:

1. How does the angle of the ramp affect the power required to push the box?
2. What would be the power required if the force applied was doubled?
3. How would friction affect the work done in this scenario?
4. What is the relationship between force, work, and energy?
5. How can we calculate the efficiency of this process?

Tip: Power is often measured in watts, which is equivalent to joules per second.