A stopper tied to the end of a string is swung in a horizontal circle. If the mass of the stopper is 13.0 g, and the string is 93.0 cm, and the stopper revolves at a constant speed 10 times in 11.8s?
You left out the question. What do they want you to calculate? The tension in the string?
If so, multiply the mass by the centripetal acceleration.
They want to find the angular velocity...so please post the answere
To find the centripetal acceleration, you can start by finding the centripetal force acting on the stopper. The centripetal force is given by the equation:
Fc = (m * v^2) / r
Where Fc is the centripetal force, m is the mass of the stopper, v is the velocity, and r is the radius of the circular motion.
First, convert the mass of the stopper from grams to kilograms:
m = 13.0 g / 1000 = 0.013 kg
Next, find the velocity of the stopper. Since the stopper completes 10 revolutions in 11.8 seconds, you can find the time it takes for one revolution:
time per revolution = 11.8 seconds / 10 = 1.18 seconds
To find the velocity, divide the circumference of the circular path by the time per revolution:
v = 2 * π * r / time per revolution
Since the radius is given in centimeters, convert it to meters:
r = 93.0 cm / 100 = 0.93 m
Now, substitute the values into the equation to find the velocity:
v = 2 * π * 0.93 m / 1.18 s = 4.97 m/s
Finally, substitute the values for mass and velocity into the centripetal force equation to find the centripetal force:
Fc = (0.013 kg * (4.97 m/s)^2) / 0.93 m = 0.036 N
Therefore, the centripetal force acting on the stopper is 0.036 N.