Youngs Modulus and angular speed.

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SUMMARY

The discussion focuses on calculating the stretch of a steel rod in an amusement park ride, given its dimensions and the weight of the cars. The rod measures 14.2 m in length and has a cross-sectional area of 7.80 cm², supporting a total weight of 1950 N. The maximum angular speed of the ride is 7.50 revolutions per minute. The relationship between the radius of the circular motion and the angle of the rod is crucial for solving the problem, as indicated by the equations Tcos(theta) = mg and Tsin(theta) = mv²/r.

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An amusement park ride consists of airplane-shaped cars attached to steel rods. Each rod has a length of 14.2 m and a cross-sectional area of 7.80 cm^2. Each car plus two people seated in it has a total weight of 1950 N.

When operating, the ride has a maximum angular speed of 7.50 rev/min. How much is the rod stretched then?

This problem does not give an angle or a radius of the circle, so I have two unknowns and can't get an answer.

So far I have

Tcos(theta) = mg

Tsin(theta) =mv^2/r
 
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Your unknowns are r and theta

Are they related in anyway? (I'm assuming yes - they usually are, but I can't actually picture from your post whether I'm right. )
 
r is the radius of the circle created as the masses on the rods swing in a circle.

theta is the angle between the rod and its vertical support (perpendicular to the ground) as the masses swing outward




EDIT: What you said got me to thinking and I got the answer now. Thanks
 
Last edited:

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