Youngs Modulus and angular speed.

In summary, an amusement park ride consists of airplane-shaped cars attached to steel rods with 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. The ride has a maximum angular speed of 7.50 rev/min. However, without knowing the angle or radius of the circle, it is impossible to determine the amount the rod is stretched. The two unknowns of radius and angle are related, with the radius being the circle created by the masses swinging and the angle being the angle between the rod and its vertical support. After further consideration, the answer to the problem was obtained
  • #1
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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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  • #2
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. )
 
  • #3
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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FAQ: Youngs Modulus and angular speed.

What is Young's Modulus?

Young's Modulus, also known as the elastic modulus, is a measure of the stiffness of a material. It is defined as the ratio of stress (force per unit area) to strain (change in length per unit length) in a material when it is subjected to tensile or compressive forces.

How is Young's Modulus calculated?

Young's Modulus is calculated by dividing the applied stress by the resulting strain. The units of Young's Modulus are either pascals (Pa) or newtons per square meter (N/m²).

What factors affect the value of Young's Modulus?

The value of Young's Modulus can be affected by a variety of factors, including the type of material, the temperature, and the presence of impurities or defects in the material.

What is angular speed?

Angular speed, also known as rotational speed, is a measure of how fast an object is rotating around a fixed axis. It is defined as the change in angular displacement (in radians) per unit time.

How is angular speed related to Young's Modulus?

Angular speed is not directly related to Young's Modulus. However, the stiffness of a material (as measured by Young's Modulus) can affect the angular speed of an object rotating around that material. A stiffer material will require more force to deform it, which can result in a slower angular speed.

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