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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
11 days ago

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.**