how much centripetal force is needed to keep a 0.23 kg ball on a 1.68m string moving in a circular path with a speed of 3.0 m/s

f = m v^2 / r ... mass , times velocity squared , divided by the radius

To calculate the centripetal force needed to keep the ball moving in a circular path, we can use the formula:

F = (m * v^2) / r

Where:
F = Centripetal force
m = mass of the ball (0.23 kg)
v = velocity of the ball (3.0 m/s)
r = radius of the circular path (1.68 m)

Substituting the given values into the formula, we get:

F = (0.23 kg * (3.0 m/s)^2) / 1.68 m

First, calculate the value inside the parentheses:

(3.0 m/s)^2 = 9.0 m^2/s^2

Now, substitute the value into the formula:

F = (0.23 kg * 9.0 m^2/s^2) / 1.68 m

Calculate the numerator:

0.23 kg * 9.0 m^2/s^2 = 2.07 kg·m^2/s^2

Now, divide the numerator by the denominator:

F = 2.07 kg·m^2/s^2 / 1.68 m

Finally, calculate the centripetal force:

F ≈ 1.232 kg·m/s^2 or 1.232 Newtons

Therefore, approximately 1.232 Newtons of centripetal force is needed to keep the 0.23 kg ball on a 1.68 m string moving in a circular path with a speed of 3.0 m/s.