a child is twirling a 0.0120 kg ball on a string in a horizontal circle whose radius is 0.100m. The ball travels once around the circle in 0.500s. Determine the centripetal force acting on the ball
omega = radians/s = 2 pi/.5 = 4 pi
Ac = omega^2 R = (4 pi)^2 * .1
F = m Ac = .012 (4 pi)^2 (.1)
increases as omega^2 so 2^2 = 4 times
To determine the centripetal force acting on the ball, you can use the centripetal force formula:
F = (m * v^2) / r
where:
F is the centripetal force (in Newtons)
m is the mass of the ball (in kilograms)
v is the velocity of the ball (in meters per second)
r is the radius of the circle (in meters)
Given:
m = 0.0120 kg
r = 0.100 m
T (time for one revolution) = 0.500 s
To find the velocity (v), you can use the formula:
v = 2πr / T
Substituting the values:
v = (2 * 3.14159 * 0.100) / 0.500 ≈ 1.257 m/s
Now you can calculate the centripetal force:
F = (0.0120 kg * (1.257 m/s)^2) / 0.100 m
F ≈ 0.019 N
So, the centripetal force acting on the ball is approximately 0.019 Newtons.
To determine the centripetal force acting on the ball, we can use the formula for centripetal force:
F = (m * v^2) / r
where:
- F is the centripetal force
- m is the mass of the ball (0.0120 kg)
- v is the velocity of the ball
- r is the radius of the circle (0.100 m)
In this case, the ball travels once around the circle in 0.500 seconds, so we can calculate the velocity of the ball using the formula:
v = 2πr / t
where:
- v is the velocity
- r is the radius of the circle (0.100 m)
- t is the time taken to complete one revolution (0.500 s)
First, calculate the velocity:
v = (2 * 3.14 * 0.100 m) / 0.500 s
v = 12.57 m/s
Next, substitute the values into the formula for centripetal force:
F = (0.0120 kg * (12.57 m/s)^2) / 0.100 m
F = (0.0120 kg * 157.87 m^2/s^2) / 0.100 m
F = 1.8944 N
Therefore, the centripetal force acting on the ball is approximately 1.8944 Newtons.