Two children, with masses m 1 = 32.0 kg and m 2 = 44.0 kg, are swinging on a tir

Question

Two children, with masses

m1 = 32.0 kg

and

m2 = 44.0 kg,

are swinging on a tire swing attached to a tree overhanging a pond. The mass of the tire is negligible. At the lowest point of the swinging motion, the tension in each of the three vertical

4.45-m-long

chains supporting the swing is

320 N.

(a) What is the speed of the children at the lowest point of the swinging motion?
m/s

(b) What is the force exerted on each child by the tire at the lowest point of the swinging motion? (Enter the magnitude.)

Explanation / Answer

given m1 = 32 kg
m2 = 44 kg
l = 4.45 m
T in each rope = 320 N
number of roped = n = 3

a. speed of the swing at its lowest point = v
from force balance
(m1 + m2)v^2/l + (m1 + m2)g = 3T
hence
v = 3.54 m/s

b. force exerted by the tyre on the child = Fn1, Fn2
Fn1 = m1v^2/l + mg = 404.0348764 N
Fn2 = m2v^2/l + m2g = 555.547955 N

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