To solve this, we use Newton's second law of motion:

$F = ma$

Where:

• $F$ is the net force,
• $m$ is the mass,
• $a$ is the acceleration.

Step 1: Calculate the mass of the box

From the first scenario, we know: $F = 50 \, \text{N}, \quad a = 2 \, \text{m/s}^2$ Rearranging $F = ma$ for $m$: $m = \frac{F}{a} = \frac{50}{2} = 25 \, \text{kg}$

Step 2: Find the acceleration for the new force

Now, when $F = 100 \, \text{N}$, the mass remains $25 \, \text{kg}$. Using $F = ma$: $a = \frac{F}{m} = \frac{100}{25} = 4 \, \text{m/s}^2$

Final Answer:

The acceleration of the box when the net force is doubled to 100 N is:

$\boxed{4 \, \text{m/s}^2}$

Would you like more details or have further questions?

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Relative Questions:

1. How does mass affect acceleration if the force remains constant?
2. What happens to the acceleration if both the force and mass are doubled?
3. Can you explain the relationship between net force and acceleration in everyday examples?
4. How would the result change if there was friction acting on the box?
5. What units are used for force, mass, and acceleration in the SI system?

Tip:

When solving problems using Newton's second law, always confirm that units are consistent (e.g., Newtons for force, kilograms for mass, meters per second squared for acceleration).