Question

Many amusement parks have a ride with swings that are attached to a large spinning disk. As the speed of the spinning disk increases the swings flair out. On one ride the swings are at a radius of 15.8 m when the ride completes one revolution in 9.1 seconds. To determine the angle of the chain, follow the steps below.

A. Draw the free body diagram for the swing with the chain at an angle. Write the Newton’s 2nd law equations.

B. What is the vertical component of the tension of the chain in terms of the mass of the swing?

C. What is the centripetal acceleration of the swing? D. What is the angle of the chain relative to the vertical?

Answer 1

Here is the free body diagram

so,

Writing Newton's second law

In y direction

Tcos = mg ------------- (1)

In x direction

Tsin = mv² / r --------- (2)

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vertical component of the tension of the chain in terms of the mass of the swing

Tcos = mg

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What is the centripetal acceleration of the swing

v² / r

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from (1)

T = mg/cos

put this in (2)

(mg / cos) * sin = mv² / r

gtan = v² / r

tan = v² / rg

= arctan ( v² / rg)

where v = 2r / T

so

= arctan (4 ² r / T²g)

= arctan ( 4 ² * 15.8 / 9.1² * 9.8)

= arctan ( 0.7686)

= 37.54 degree