mrubber stopper = 0.07Kg
mmetal washers = 0.196Kg
radius = 1.0m
total time = 12 seconds
# of revolutions = 10 revolutions
With this data, calculate the centripetal Force (Fc) (to 2 decimals) of the rubber stopper in its "orbit".
To calculate the centripetal force (Fc) of the rubber stopper, we can use the formula:
Fc = (m * v^2) / r
where:
- Fc is the centripetal force
- m is the mass of the rubber stopper
- v is the linear velocity of the rubber stopper
- r is the radius of the orbit
First, let's calculate the linear velocity (v) of the rubber stopper using the given information.
# of revolutions = 10 revolutions
total time = 12 seconds
To find the linear velocity (v), we need to find the circumference of the circular path (orbit) travelled by the rubber stopper. The circumference can be calculated using the formula:
C = 2πr
where:
- C is the circumference
- π (pi) is a mathematical constant approximately equal to 3.14
- r is the radius of the orbit
Given that the radius (r) is 1.0m, the circumference (C) is:
C = 2 * π * r
C = 2 * 3.14 * 1.0
C = 6.28 meters
Next, let's find the linear velocity (v) using the formula:
v = C / t
where:
- v is the linear velocity
- C is the circumference
- t is the total time taken to complete the revolutions
Given that the circumference (C) is 6.28 meters and the total time (t) is 12 seconds, the linear velocity (v) is:
v = 6.28 / 12
v ≈ 0.52 meters/second (rounded to 2 decimal places)
Now that we have the linear velocity (v) and the radius (r), we can calculate the centripetal force (Fc) using the formula mentioned earlier:
Fc = (m * v^2) / r
Given that the mass (m) of the rubber stopper is 0.07 Kg, the centripetal force (Fc) is:
Fc = (0.07 * (0.52)^2) / 1.0
Fc ≈ 0.019 Newtons (rounded to 2 decimal places)
Therefore, the centripetal force (Fc) of the rubber stopper in its orbit is approximately 0.019 Newtons.