Youngs Modulus and angular speed.

AI Thread Summary
The discussion revolves around calculating the stretch of a steel rod in an amusement park ride, given its dimensions and the weight of the cars and passengers. The maximum angular speed of the ride is 7.50 revolutions per minute, but the problem lacks specific values for the angle and radius, creating two unknowns. The relationship between the tension in the rod, the gravitational force, and the angular motion is explored through equations involving the angle and radius. The user initially struggles with the problem but ultimately finds the solution after further contemplation. The interaction highlights the importance of understanding the relationships between physical quantities in rotational motion.
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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
 
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