Question

A student is investigating mass and acceleration. The student applies the same force of 40 N force to two boxes that have the same size and shape. Box 1 experiences an acceleration of 10 m/s^2 and box 2 experiences an acceleration of 5m/s^2.

Answer 1

To analyze the situation involving the two boxes, we can apply Newton's second law of motion, which states that the force applied to an object is equal to the mass of that object multiplied by its acceleration (F = m * a).

Given:
- Force (F) = 40 N
- Acceleration of Box 1 (a₁) = 10 m/s²
- Acceleration of Box 2 (a₂) = 5 m/s²

Using the formula \( F = m \cdot a \), we can rearrange the equation to solve for mass \( m \):

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

### For Box 1:

\[
m_1 = \frac{F}{a_1} = \frac{40 \text{ N}}{10 \text{ m/s}^2} = 4 \text{ kg}
\]

### For Box 2:

\[
m_2 = \frac{F}{a_2} = \frac{40 \text{ N}}{5 \text{ m/s}^2} = 8 \text{ kg}
\]

### Summary:
- The mass of Box 1 (m₁) is 4 kg.
- The mass of Box 2 (m₂) is 8 kg.

This means that even though both boxes have the same size and shape, Box 1 has a lower mass than Box 2, which accounts for the difference in acceleration when the same force is applied to both.