A portable machine requires a force of 500 N to move it. How much work is done if the machine is moved 40 m, and what average power is utilized if the movement takes 50 s?

Solution:  To find the work done, we use the formula for work:

$𝑊=\overrightarrow{𝐹}\cdot \overrightarrow{𝑑}\cdot \cos (𝜃)$

Given:

• Force ($\overrightarrow{𝐹}$) = 500 N
• Displacement ($\overrightarrow{𝑑}$) = 40 m
• Angle ($𝜃$) = We assume the force is applied in the direction of displacement, so $𝜃=0^{\circ }$ (cosine of 0 is 1).

Plugging the values into the formula:

$𝑊=500\text{N}\times 40\text{m}\times \cos (0^{\circ })$

$𝑊=500\text{N}\times 40\text{m}\times 1$

$𝑊=20000\text{J}$

So, the work done in moving the machine 40 m is 20,000 joules (J).

To find the average power utilized, we use the formula for power:

$𝑃=\frac{𝑊}{𝑡}$

Given:

• Work ($𝑊$) = 20,000 J
• Time ($𝑡$) = 50 s

Plugging the values into the formula:

$𝑃=\frac{20000\text{J}}{50\text{s}}$

$𝑃=400\text{W}$

So, the average power utilized during the movement, if it takes 50 seconds, is 400 watts (W).