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)
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 40 N of force
a 20 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 the acceleration (a) of an object is equal to the net force (F) acting on it divided by its mass (m):

\[ a = \frac{F_{\text{net}}}{m} \]

First, we need to calculate the net force for each box. The net force can be calculated by subtracting the gravitational force (weight) from the applied force. The weight of an object can be calculated using the formula:

\[ F_{\text{weight}} = m \cdot g \]

Where \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).

Now let's calculate the net force and acceleration for each box:

1. **20 kg box lifted with 60 N of force**:
- Weight: \( F_{\text{weight}} = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N} \)
- Net force: \( F_{\text{net}} = 60 \, \text{N} - 196 \, \text{N} = -136 \, \text{N} \) (it doesn't accelerate upward, it accelerates downward)

2. **10 kg box lifted with 60 N of force**:
- Weight: \( F_{\text{weight}} = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N} \)
- Net force: \( F_{\text{net}} = 60 \, \text{N} - 98 \, \text{N} = -38 \, \text{N} \)

3. **10 kg box lifted with 40 N of force**:
- Weight: \( F_{\text{weight}} = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N} \)
- Net force: \( F_{\text{net}} = 40 \, \text{N} - 98 \, \text{N} = -58 \, \text{N} \)

4. **20 kg box lifted with 40 N of force**:
- Weight: \( F_{\text{weight}} = 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N} \)
- Net force: \( F_{\text{net}} = 40 \, \text{N} - 196 \, \text{N} = -156 \, \text{N} \)

Now let's calculate the acceleration for the boxes that have a positive net force:

For boxes 1, 2, and 3, since they have negative net forces, they are not accelerating upwards.

The box that will have the least negative acceleration (or greatest upward acceleration) is:

2. **10 kg box lifted with 60 N of force**:
- Net force: \( -38 \, \text{N} \)
- Acceleration: \( a = \frac{-38 \, \text{N}}{10 \, \text{kg}} = -3.8 \, \text{m/s}^2 \)

This box will be accelerated downward, but it will have the 'greatest acceleration' in terms of the least magnitude in the downward direction compared to the others.

Since none of the boxes provide a positive net force to create an upward acceleration, strictly speaking, none can be said to have a 'greater' upward acceleration than others.

However, based on the net forces calculated above, if the question was asking for the box with the least amount of downward acceleration, it would be the **10 kg box lifted with 60 N of force** having the least negative force.