Question

Four movers pick up boxes. Each box has a different mass, and each mover applies a different amount of force to lift the box. Which box will have the greatest acceleration?(1 point).
Responses

a 20 kg box lifted with 40 N of force
a 20 kg box lifted with 40 N of force

a 20 kg box lifted with 60 N of force
a 20 kg box lifted with 60 N of force

a 10 kg box lifted with 60 N of force
a 10 kg box lifted with 60 N of force

a 10 kg box lifted with 40 N of force

Answer 1

To determine which box will have the greatest acceleration, we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration. We can rearrange this to find acceleration:

\[ a = \frac{F}{m} \]

Let's calculate the acceleration for each box.

1. **20 kg box lifted with 40 N of force:**
\[ a = \frac{40 \, \text{N}}{20 \, \text{kg}} = 2 \, \text{m/s}^2 \]

2. **20 kg box lifted with 60 N of force:**
\[ a = \frac{60 \, \text{N}}{20 \, \text{kg}} = 3 \, \text{m/s}^2 \]

3. **10 kg box lifted with 60 N of force:**
\[ a = \frac{60 \, \text{N}}{10 \, \text{kg}} = 6 \, \text{m/s}^2 \]

4. **10 kg box lifted with 40 N of force:**
\[ a = \frac{40 \, \text{N}}{10 \, \text{kg}} = 4 \, \text{m/s}^2 \]

Now we can compare the accelerations:
- 20 kg box with 40 N: \( 2 \, \text{m/s}^2 \)
- 20 kg box with 60 N: \( 3 \, \text{m/s}^2 \)
- 10 kg box with 60 N: \( 6 \, \text{m/s}^2 \)
- 10 kg box with 40 N: \( 4 \, \text{m/s}^2 \)

The box with the greatest acceleration is the **10 kg box lifted with 60 N of force**, which has an acceleration of \( 6 \, \text{m/s}^2 \).