Consider an object with a mass of 12.5 kg moving at a constant speed in a circular path with a radius of <11.30> m. The object makes one full revolution in <16.60> seconds. Calculate the centripetal acceleration of the object. Give your answer in m/s2 and with 3 significant figures.
I know you have to use the equation ( a=v^2/r) but I don't know how to figure out the Velocity in the equation. I am confused
Ac = v^2/R = omega^2 R
well circumference = 2 pi R
= 22.6 pi meters
does that circumference in 16.6 seconds
so
v = 22.6 pi/16.6 meters/second
so
Ac = (22 pi/16.6)^2 / 11.3
the mass has nothing to do with it unless you want the tension in a string :)
To calculate the centripetal acceleration of the object, you need to find the velocity first. The velocity can be calculated by dividing the distance traveled by the time taken to travel that distance. In this case, as the object makes one full revolution, the distance traveled is equal to the circumference of the circular path.
The circumference of a circle is given by the formula:
Circumference = 2 * π * radius
In this case, the radius is 11.30 m. So the circumference would be:
Circumference = 2 * π * 11.30
Next, you need to find the time taken to make one full revolution, which is given as 16.60 seconds.
Now you can find the velocity using the formula:
Velocity = Circumference / Time
Substituting the values, you get:
Velocity = (2 * π * 11.30) / 16.60
Calculate the value of Velocity using a calculator or computer software.
Now that you have the value of the velocity, you can use the formula for centripetal acceleration, which is:
Centripetal Acceleration = (Velocity^2) / Radius
Substitute the values:
Centripetal Acceleration = (Velocity^2) / 11.30
Again, calculate the value of Centripetal Acceleration using a calculator or computer software, and round it to three significant figures.
Note: Make sure to use the appropriate units while plugging in the values and round the final answer to three significant figures as requested.