A child having a mass of 37 kg sits 0.2 m from the center of a merry-go-round that is rotating with a period of 36 s. What is the centripetal force acting on the child?
What is the centripetal force in Newtons?
circumference = 2 pi r
= 2 pi(.2)
speed = v = distance/time
= 2 pi (.2)/36
Ac = v^2/r
F = m Ac = 37 v^2/r
Oh my, I just noticed the Bob Pursley answered an almost identical question for you.
note w^2 r = v^2/r
and READ THE CHAPTER in your text on centripetal acceleration !
To calculate the centripetal force acting on the child, we can use the formula:
Centripetal Force (F) = mass (m) x angular velocity (ω)² x radius (r)
First, let's find the angular velocity (ω). The formula for angular velocity is:
Angular Velocity (ω) = 2π / period (T)
Given that the period (T) is 36 seconds, we can substitute this value into the formula to find the angular velocity (ω).
ω = 2π / 36
≈ 0.1745 rad/s (rounded to four decimal places)
Next, let's calculate the centripetal force (F). We are given the mass (m) of the child, which is 37 kg, and the radius (r) from the center of the merry-go-round to where the child is sitting, which is 0.2 m.
Substituting the values into the formula, we get:
F = m x ω² x r
= 37 kg x (0.1745 rad/s)² x 0.2 m
Calculating this expression, we find:
F ≈ 0.5068 N (rounded to four decimal places)
Therefore, the centripetal force acting on the child is approximately 0.5068 Newtons.