Question
A child of mass m swings in a swing supported by two chains, each of length R.
The mass of the swing’s seat is negligible. If the tension in each chain at the
lowest point is T, find:
4.1 the child’s speed at the lowest point;
4.2 the force exerted by the seat on the child at the lowest point.
The mass of the swing’s seat is negligible. If the tension in each chain at the
lowest point is T, find:
4.1 the child’s speed at the lowest point;
4.2 the force exerted by the seat on the child at the lowest point.
Answers
Anonymous
Lets swing a ball on the end of ONE string and divide call it 2 T
You were not told what angle or height so I will say dropped from height h.
m g h = (1/2) m v^2
so at the bottom v = sqrt (2gh)
then the centripetal acceleration = v^2/R
and 2 T = m g + m v^2/R
2 T= m (g + 2 g h/R) = mg (1 +2 h/R) = force up on child if sat has no mass :)
Now if you were given maximum angle theta instead of height h then
h = R - R cos theta = R(1-cos theta)
if theta is small cos theta = 1 -theta^2/2 +.....
so
h = (R /2)theta^2 note theta in radians
You were not told what angle or height so I will say dropped from height h.
m g h = (1/2) m v^2
so at the bottom v = sqrt (2gh)
then the centripetal acceleration = v^2/R
and 2 T = m g + m v^2/R
2 T= m (g + 2 g h/R) = mg (1 +2 h/R) = force up on child if sat has no mass :)
Now if you were given maximum angle theta instead of height h then
h = R - R cos theta = R(1-cos theta)
if theta is small cos theta = 1 -theta^2/2 +.....
so
h = (R /2)theta^2 note theta in radians