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.
speed=2PI*radius/timeoneRev
a=v^2/r
To calculate the centripetal acceleration of the object, we can use the formula:
a = (v^2) / r
Where:
a is the centripetal acceleration
v is the velocity
r is the radius of the circular path
Since the object is moving at a constant speed in a circular path, we can find the velocity by dividing the circumference of the circle by the time it takes to make one full revolution.
The circumference of a circle is given by the formula:
C = 2 * π * r
In this case, the time taken to make one full revolution is 16.60 seconds, so the velocity can be calculated as:
v = C / t
Substituting the values, we have:
v = (2 * π * r) / t
Plugging in the known values, the velocity is:
v = (2 * π * 11.30) / 16.60
Now that we have the velocity, we can substitute it into the formula for centripetal acceleration. Plugging in the known values, we have:
a = (v^2) / r
Substituting the values, the centripetal acceleration is:
a = ((2 * π * 11.30) / 16.60)^2 / 11.30
Evaluating this expression will give us the centripetal acceleration of the object.
By performing the calculations, the centripetal acceleration of the object is approximately 7.06 m/s^2.