How much centripetal force is needed to keep a 0.20 kg ball on a 1.50 m string moving in a circular path with a speed of 3.0 m/s?
1.2N
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 object (0.20 kg)
v = velocity of the object (3.0 m/s)
r = radius of the circular path (1.50 m)
Plugging in the values:
F = (0.20 kg * (3.0 m/s)^2) / 1.50 m
Simplifying:
F = (0.20 kg * 9.0 m^2/s^2) / 1.50 m
F = 1.2 kg * m/s^2
Therefore, the centripetal force needed to keep the ball on a 1.50 m string moving in a circular path with a speed of 3.0 m/s is 1.2 N (Newton).
To find the centripetal force needed to keep the ball moving in a circular path, you can use the centripetal force formula:
F = (m * v²) / r
where:
F = centripetal force
m = mass of the ball (0.20 kg)
v = speed of the ball (3.0 m/s)
r = radius of the circular path (1.50 m)
Let's substitute the given values into the formula:
F = (0.20 kg * (3.0 m/s)²) / 1.50 m
First, calculate the square of the velocity:
(3.0 m/s)² = 9.0 m²/s²
Now, substitute this value into the formula:
F = (0.20 kg * 9.0 m²/s²) / 1.50 m
Simplify the formula:
F = (1.8 kg·m²/s²) / 1.50 m
Now, divide the values:
F = 1.2 kg·m²/s²
Therefore, the amount of centripetal force needed to keep the 0.20 kg ball on a 1.50 m string moving in a circular path with a speed of 3.0 m/s is 1.2 kg·m²/s².