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?
To find the centripetal force needed to keep the ball moving in a circular path, we can use the formula:
Fc = (m * v^2) / r
Where:
- Fc is the centripetal force
- m is the mass of the ball (0.20 kg)
- v is the speed of the ball (3.0 m/s)
- r is the radius of the circular path (1.50 m)
Substituting the values into the formula:
Fc = (0.20 kg * (3.0 m/s)^2) / 1.50 m
First, calculate (3.0 m/s)^2:
(3.0 m/s)^2 = 9.0 m^2/s^2
Now, substitute this value back into the formula:
Fc = (0.20 kg * 9.0 m^2/s^2) / 1.50 m
Next, calculate the numerator:
0.20 kg * 9.0 m^2/s^2 = 1.8 kg * m^2/s^2
Finally, divide the numerator by the denominator:
Fc = 1.8 kg * m^2/s^2 / 1.50 m
Simplifying the equation:
Fc = 1.2 kg * m/s^2
Therefore, the 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 N (newtons).
M*V^2/R
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