Question

The force of attraction, F of a body varies directly as its mass m and inversely as the square of the distance d from the body. When m=8 kilograms and d=5 meters, F=100 Newtons. Find F when m=2 kilograms and d=15 meters.

Answer 1

The force of attraction when the mass is 2 kilograms and distance is 15 meters is found using the constant of proportionality obtained from the given values, resulting in approximately 0.56 Newtons.

Step-by-step explanation:

The force of attraction, F, varies directly as its mass, m, and inversely as the square of the distance, d, from the body. Given that at m=8 kilograms and d=5 meters, F=100 Newtons, we can find a constant of proportionality.

Use the equation F = k * (m/d2) to find k as follows:

100 = k * (8/52)

k = 100 * 52 / 8 = 500 / 8 = 62.5

Now, to find F when m=2 kilograms and d=15 meters, plug the values into the equation:

F = 62.5 * (2/152) = 62.5 * (2/225) = 0.5556 (approx)

Therefore, the force F when m=2 kilograms and d=15 meters is approximately 0.56 Newtons.