Question

Examine the scenarios.

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.**