Question

a particle of mass m moves io a circle of radius r. Its velocity v=k(s)^1/2. Calculate force on the particle

Answer 1

A particle of mass $m$ moves to a circle of radius $r$. Its velocity $v = k(s)^A / 2$. Calculate force on the particle.

Solution

we are given:

$$m, r, v = k(s)^{(1/2)}$$

For a circular motion:

The acceleration due to change in the direction is:

$$a = \frac{v^2}{r}$$

According to the Second Newton's Law:

$$F = m * a$$

Thus:

$$F = m * a = \frac{m * v^2}{r} = \frac{m * (k(s)^{(1/2)})^2}{r} = m k^2 \frac{|s|}{r}$$

Answer: $F = m k^2 \frac{|s|}{r}$

references:

1. http://en.wikipedia.org/wiki/Circular_motion#Formulas_for_uniform_circular_motion

2. http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_second_law