A large merry-go-round completes one revolution every 10.5 s. Compute the acceleration of a child seated on it, a distance of 5.20 m from its center. what is the magnitude?
a= w^2*r=(2PI/10.5)^2 * 5.2
To find the acceleration of the child seated on the merry-go-round, we need to use the formula for centripetal acceleration:
a = (v^2) / r
where:
a = acceleration
v = velocity
r = radius
First, let's find the velocity of the child. The velocity is equal to the circumference of the circle divided by the time it takes to complete one revolution.
v = (2 * π * r) / t
Substituting the values:
r = 5.20 m (distance from the center)
t = 10.5 s (time taken for one revolution)
v = (2 * π * 5.20) / 10.5
To calculate the magnitude of the acceleration, we will substitute this value into the centripetal acceleration formula.
a = (v^2) / r
Substituting the values:
v = [(2 * π * 5.20) / 10.5]
r = 5.20 m
a = [(2 * π * 5.20) / 10.5]^2 / 5.20
Now we can calculate the magnitude of the acceleration.
To compute the acceleration of a child seated on a merry-go-round, we need to use the formula for centripetal acceleration:
a = (v^2) / r
where "a" represents the acceleration, "v" represents the velocity, and "r" represents the radius of the circular motion.
Since the merry-go-round completes one revolution every 10.5 s, we can calculate the velocity by dividing the circumference of the circle (2 * π * r) by the time taken:
v = (2 * π * r) / t
Substituting the given values, we have:
v = (2 * 3.14 * 5.20 m) / 10.5 s
Now we can calculate the velocity:
v ≈ 3.08 m/s
Next, we can substitute the velocity and radius into the formula for centripetal acceleration:
a = (3.08 m/s)^2 / 5.20 m
Now we can calculate the acceleration:
a ≈ 1.83 m/s^2
Therefore, the magnitude of the acceleration of the child seated 5.20 m from the center is approximately 1.83 m/s^2.