A weightlifter lifts a weight of 500N from the ground over her head, a distance of 1.8m. How much work has been done to move the weight?

1. ### Break Down the Problem

To calculate the work done by the weightlifter, we need to identify the parameters involved in the work formula.

• Force (F): 500 N (the weight being lifted)
• Distance (d): 1.8 m (the height the weight is lifted)

2. ### Relevant Concepts

The work done ($W$) against gravity can be calculated using the formula: $W = F \times d \times \cos(\theta)$ where:

• $W$ is the work done,
• $F$ is the force applied,
• $d$ is the distance the object moves,
• $\theta$ is the angle between the force and the direction of motion.

In this case, since the weightlifter is lifting vertically, $\theta = 0^\circ$ and $\cos(0^\circ) = 1$.

3. ### Analysis and Detail

Plugging the values into the work done formula: $W = F \times d \times \cos(0^\circ) = F \times d$ $W = 500 \, \text{N} \times 1.8 \, \text{m}$ $W = 900 \, \text{J}$

4. ### Verify and Summarize

We have calculated the work done as $900 \, \text{J}$. The values for force and distance were correctly identified, and the calculations were carried out step-by-step following the work formula, confirming that the work done by the weightlifter to lift the weight is indeed $900 \, \text{J}$.

Final Answer

The work done to move the weight is $900 \, \text{J}$.