To calculate the work done when lifting a rock, we can use the formula:

$\text{Work} = \text{Force} \times \text{Distance}$

In this case:

1. Force is equal to the weight of the rock, which is given by the product of the mass of the rock and the acceleration due to gravity:

$\text{Force} = m \times g$

2. Distance is the height to which the rock is lifted.

Given:

• Mass ($m$) = 290 kg
• Acceleration due to gravity ($g$) = 9.8 m/s²
• Height ($h$) = 5 m

Now, let's calculate the force:

$\text{Force} = 290 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 2842 \, \text{N}$

Finally, the work done:

$\text{Work} = 2842 \, \text{N} \times 5 \, \text{m} = 14210 \, \text{J}$

So, the work done is 14,210 joules (J).

Would you like more details or have any questions? Here are five related questions you might find interesting:

1. What is the work done if the mass of the rock was doubled?
2. How does the work change if the height was reduced to 2.5 meters?
3. What if the hoist lifts the rock at a constant speed? Does the work done change?
4. How would the work done be affected if the rock was lifted on the Moon, where gravity is weaker?
5. Can work be done if the rock is lifted vertically but then returns to its original position?

Tip: Remember, work is a scalar quantity; it has magnitude but no direction!