Swing ride

Classical Mechanics Level 3

In a swing ride, passengers experience a radially outward centrifugal force which deflects the chain by some angle with the vertical.

For this problem, assume the following simple model of the swing.

The seats are attached to a rotating disk of radius R = 0.4 m R= 0.4 \text{ m} by chains of length l = 3.30 m l = 3.30\text{ m} . When the disk rotates, the chains are deflected by an angle of α = 4 5 ∘ \alpha = 45^\circ . Calculate the number of times the swing ride rotates per minute.


Details and Assumptions:

  • The gravitational acceleration is g = 10 m/s 2 . g = 10\text{ m/s}^2.
  • The mass of the seat is very large compared to that of the chain.


The answer is 12.

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Markus Michelmann by Markus Michelmann , 35, Germany

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1 solution

Markus Michelmann
Sep 10, 2017

We need to consider the parallelogram of the centrifugal force and gravity.

The total force vector must be parallel to the chain, so that for an angle α = 4 5 ∘ \alpha = 45^\circ both forces must be equal:

F cf = m ω 2 r = m g = F g → ω = g r F_\text{cf} = m \omega^2 r = m g = F_\text{g} \quad \rightarrow \quad \omega = \sqrt{\frac{g}{r}}

The radial distance r = R + sin ⁡ ( α ) l r = R + \sin(\alpha) l , therefore, the value of the angular frequency is

ω = g R + l / 2 = 12 rpm \omega = \sqrt{\frac{g}{R + l/ \sqrt{2}}} = 12 \,\text{rpm}

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Please check the answer it's got wrong calculation please check it

Agrim Agrawal - 2 years, 7 months ago

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