A 0.025kg rubber stopper is swung in a horizontal circle by a 0.95 meter threat that makes 25 revolutions every 15 minutes. a) what is the stoppers speed? b) what is the acceleration? c) what is the value of the centripetal force?
sorry not minutes but 15 seconds
T = 15/25 = .6 second
C = 2 pi R = 2 * 3.14 * .95 = 5.97 meter
a) v = C/T = 9.94 m/s
b) v^2/R = 9.94^2/.95 = 104 m/s^2
wow, 10 g
c) F = m a = .025*104 = 2.6 Newtons
thank you for your help
You are welcome.
To find the answers to these questions, we need to use the formulas related to circular motion. Let's go through each question one by one.
a) What is the stopper's speed?
The speed of an object moving in a circle is given by the formula:
speed = (2 * π * radius) / time
In this case, the stopper is making 25 revolutions in 15 minutes. To find the time for one revolution, we divide the total time by the number of revolutions:
time for one revolution = 15 minutes / 25 revolutions
Now, we have the time for one revolution and the radius given as 0.95 meters, so we can substitute these values in the formula to find the speed.
speed = (2 * π * 0.95) / (15 minutes / 25 revolutions)
Calculating this, we get:
speed ≈ 1.99 m/s
Therefore, the stopper's speed is approximately 1.99 m/s.
b) What is the acceleration?
The acceleration of an object moving in a circle is given by the formula:
acceleration = (speed^2) / radius
We already found the speed in the previous part as 1.99 m/s, and the radius is given as 0.95 meters. Substituting these values into the formula, we have:
acceleration = (1.99^2) / 0.95
Calculating this, we get:
acceleration ≈ 4.17 m/s^2
Therefore, the stopper's acceleration is approximately 4.17 m/s^2.
c) What is the value of the centripetal force?
The centripetal force is the inward force required to keep an object moving in a circle. It is given by the formula:
centripetal force = mass * acceleration
The mass of the rubber stopper is given as 0.025 kg, and we already found the acceleration in the previous part as 4.17 m/s^2. Substituting these values into the formula, we have:
centripetal force = 0.025 kg * 4.17 m/s^2
Calculating this, we get:
centripetal force ≈ 0.105 N
Therefore, the value of the centripetal force is approximately 0.105 N.