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?

a. a 20 kg box lifted with 60 N of force
b. a 10 kg box lifted with 40 N of force
c. a 20 kg box lifted with 40 N of force
d. a 10 kg box lifted with 60 N of force

Answer 1

To determine which box will have the greatest acceleration, we can use Newton's second law, which states:

\[ F = ma \]

Where:
- \( F \) is the net force applied to the object,
- \( m \) is the mass of the object,
- \( a \) is the acceleration.

First, we need to find the net force on each of the boxes, which can be calculated as the applied force minus the weight of the box (weight = mass × gravity, and we generally take gravity as \( g = 9.8 \, \text{m/s}^2 \)).

Let's calculate the net force for each option:

### a. 20 kg box lifted with 60 N of force
- Weight = \( 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N} \)
- Net Force = \( 60 \, \text{N} - 196 \, \text{N} = -136 \, \text{N} \) (the box will not accelerate upward)

### b. 10 kg box lifted with 40 N of force
- Weight = \( 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N} \)
- Net Force = \( 40 \, \text{N} - 98 \, \text{N} = -58 \, \text{N} \) (the box will not accelerate upward)

### c. 20 kg box lifted with 40 N of force
- Weight = \( 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 196 \, \text{N} \)
- Net Force = \( 40 \, \text{N} - 196 \, \text{N} = -156 \, \text{N} \) (the box will not accelerate upward)

### d. 10 kg box lifted with 60 N of force
- Weight = \( 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N} \)
- Net Force = \( 60 \, \text{N} - 98 \, \text{N} = -38 \, \text{N} \) (the box will not accelerate upward)

Now we see that all the net forces are negative, meaning all the boxes are not accelerating upward—they are all heavy enough that the weight exceeds the applied force.

However, if we consider the positive net force relative to the applied force:

- Box **a** does not accelerate upward (negative net force).
- Box **b** does not accelerate upward (negative net force).
- Box **c** does not accelerate upward (negative net force).
- Box **d** does not accelerate upward (negative net force).

None of the boxes will accelerate upward. However, if we look at the box that could potentially accelerate the highest relative to its applied force:

The net force of the box lifted with the most positive excess over its weight would have been box **d**, if it had a greater applied force or lower weight.

So the best choice among the situations laid out is **d**, the 10 kg box lifted with 60 N of force, as it has the least negative net force among the options, indicating it is closest to being able to accelerate.

**Answer: d. a 10 kg box lifted with 60 N of force**