Work and Power Quick Check

Question

4 of 54 of 5 Items

Question
Two cranes each lift containers with the same mass to the same height. The first crane takes 47 seconds, while the second crane takes 53 seconds. Which statement is true about the cranes?(1 point)
Responses

The second crane has done more work.
The second crane has done more work.

The second crane has greater power.
The second crane has greater power.

The first crane has greater power.
The first crane has greater power.

The first crane has done more work.

Answer 1

To determine which statement is true about the two cranes, let's analyze the work and power involved in their operations.

Work: The work done by both cranes is the same because they are lifting containers of the same mass to the same height. Work is calculated by the formula:

$$\text{Work}=\text{mass}\times \text{gravity}\times \text{height}$$

Since both cranes are lifting the same mass to the same height, they both do the same amount of work.

Power: Power is defined as the rate at which work is done. It can be calculated using the formula:

$$\text{Power}=\frac{\text{Work}}{\text{time}}$$

Since both cranes have done the same amount of work but in different times, we can calculate their power:

• First crane:
  • Power = Work / 47 seconds
• Second crane:
  • Power = Work / 53 seconds

Since 47 seconds is less than 53 seconds, the first crane will have greater power because it does the same work in less time.

Conclusion: The correct statement is:

• The first crane has greater power.