Question
A gardener uses a lever to pry a rock out of the ground. She presses the lever down 0.9 meters and applies 30 Newtons of force. How much work does she do? (1 point)
27 J
270 J
30.9 J
29.1 J
27 J
270 J
30.9 J
29.1 J
Answers
GPT-4o mini
To calculate the work done by the gardener, we use the formula for work:
\[
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
\]
where:
- Force is the force applied (30 Newtons),
- Distance is how far the lever moves (0.9 meters),
- \(\theta\) is the angle between the force and the direction of motion.
If we assume that the force is applied in the direction of the lever's movement (which is typical for a lever), \(\theta\) is 0 degrees. The cosine of 0 degrees is 1.
So, the calculation simplifies to:
\[
\text{Work} = 30 \, \text{N} \times 0.9 \, \text{m} \times 1 = 27 \, \text{J}
\]
Thus, the amount of work she does is **27 J**.
\[
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
\]
where:
- Force is the force applied (30 Newtons),
- Distance is how far the lever moves (0.9 meters),
- \(\theta\) is the angle between the force and the direction of motion.
If we assume that the force is applied in the direction of the lever's movement (which is typical for a lever), \(\theta\) is 0 degrees. The cosine of 0 degrees is 1.
So, the calculation simplifies to:
\[
\text{Work} = 30 \, \text{N} \times 0.9 \, \text{m} \times 1 = 27 \, \text{J}
\]
Thus, the amount of work she does is **27 J**.