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
velocity = circumference / period
v = (2 * π * 11.30 m) / 16.60 s
plug it in and crank the crank
To calculate the centripetal acceleration of the object, you can start by finding the velocity of the object. The velocity can be determined using the formula:
Velocity = (2 * π * radius) / time period
Given:
Radius (r) = 11.30 m
Time period (T) = 16.60 seconds
Substituting the values into the formula:
Velocity = (2 * 3.14159 * 11.30 m) / 16.60 s
Calculating:
Velocity = 23.87 m/s (rounded to two decimal places)
Now that you have the velocity, you can substitute it into the formula for centripetal acceleration:
Centripetal acceleration (a) = (velocity^2) / radius
Substituting the values:
Centripetal acceleration = (23.87 m/s)^2 / 11.30 m
Calculating:
Centripetal acceleration = 50.61 m/s^2 (rounded to three significant figures)
Therefore, the centripetal acceleration of the object is 50.61 m/s² (rounded to three significant figures).
To calculate the centripetal acceleration of the object, you need to determine the velocity of the object first. In this case, you are given the mass, the radius, and the time it takes for the object to complete one revolution.
To find the velocity, you can use the formula v = (2πr) / t, where r is the radius of the circular path and t is the time it takes for one revolution.
Given:
Mass (m) = 12.5 kg
Radius (r) = 11.30 m
Time (t) = 16.60 s
First, substitute the values into the formula:
v = (2π * 11.30 m) / 16.60 s
Next, evaluate the expression:
v ≈ 6.80 m/s
Now that you have the velocity, you can calculate the centripetal acceleration using the formula a = v^2 / r, where v is the velocity and r is the radius of the circular path.
Substituting the values:
a = (6.80 m/s)^2 / 11.30 m
Calculating:
a ≈ 4.08 m/s^2
Therefore, the centripetal acceleration of the object is approximately 4.08 m/s^2.