Examine the scenarios.

Question

Scenario W: A force of 75 N moves a box 15 m.
Scenario X: A force of 100 N moves a box 12 m.
Scenario Y: A force of 50 N moves a box 20 m.
Scenario Z: A force of 25 N moves a box 45 m.

In which scenarios is the same amount of work done on the box?

W and X
W and Z
X and Y
Y and Z

Answer 1

To determine in which scenarios the same amount of work is done on the box, we can calculate the work done in each scenario using the formula:

\[ \text{Work} = \text{Force} \times \text{Distance} \]

Now, let's calculate the work done for each scenario:

Scenario W: \[ \text{Work} = 75 , \text{N} \times 15 , \text{m} = 1125 , \text{J} \]

Scenario X: \[ \text{Work} = 100 , \text{N} \times 12 , \text{m} = 1200 , \text{J} \]

Scenario Y: \[ \text{Work} = 50 , \text{N} \times 20 , \text{m} = 1000 , \text{J} \]

Scenario Z: \[ \text{Work} = 25 , \text{N} \times 45 , \text{m} = 1125 , \text{J} \]

Now we can summarize the work done in each scenario:

• W: 1125 J
• X: 1200 J
• Y: 1000 J
• Z: 1125 J

By comparing these values, we see that:

• Work done in W (1125 J) is equal to work done in Z (1125 J).
• Work done in X (1200 J) is different.
• Work done in Y (1000 J) is different.

Thus, the same amount of work is done in Scenario W and Scenario Z.