What is the ratio of the acceleration produced when two forces of 6N and 4N act on a body in the same direction compared to when they act in opposite directions?

To find the ratio of the accelerations, we can use Newton’s second law of motion, which states that force equals mass times acceleration (F = ma). The total force acting on the body will change depending on whether the forces are acting in the same direction or in opposite directions.

1. **Forces Acting in the Same Direction:**
When the two forces of 6N and 4N act in the same direction, the total force (F_same) is the sum of the two forces:

F_same = 6N + 4N = 10N

Using Newton’s second law:

a_same = F_same / m = 10N / m

2. **Forces Acting in Opposite Directions:**
When the forces act in opposite directions, the total force (F_opposite) is the difference between the two forces:

F_opposite = 6N – 4N = 2N

Using Newton’s second law again:

a_opposite = F_opposite / m = 2N / m

3. **Finding the Ratio:**
The ratio of the accelerations when the forces are acting in the same direction to when they are acting in opposite directions is:

Ratio = a_same / a_opposite = (10N / m) / (2N / m)

Since mass (m) cancels out, we have:

Ratio = 10N / 2N = 5

So the ratio of the accelerations is **5:1**. This means that the acceleration is five times greater when the two forces are acting in the same direction compared to when they are acting in opposite directions.