How can I calculate the elongation of a steel rod in an amusement park ride?

In summary, when the amusement park ride is in operation, the rods are stretched by the free fall acceleration. The tension in the rods is also responsible for the centripetal acceleration of the ride.
  • #1
superdave
150
3
An amusement park ride consists of airplane-shaped cars attached to steel rods. Each rod has a length of 14.5 m and a cross-sectional area of 8.25 {\rm cm}^{2}.

yf_Figure_11_51.jpg


When operating, the ride has a maximum angular speed of 8.50 rev/min. How much is the rod stretched then?
Take the Young's modulus for the rod to be Y = 2.00×1011 Pa and the free fall acceleration to be g = 9.80 m/s^2

Assume that each car plus two people seated in it has a total weight of 1930 N.

Now, I somehow need to find theta or r using only omega. I'm not really sure how to do this.
 
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  • #2
Hint: The only two forces acting on a plane with its cargo are the tension in the rod and gravity. The vector sum of these two forces is horizontal and that force is causing the plane to go in a circle.
 
  • #3
superdave said:
An amusement park ride consists of airplane-shaped cars attached to steel rods. Each rod has a length of 14.5 m and a cross-sectional area of 8.25 {\rm cm}^{2}.

yf_Figure_11_51.jpg


When operating, the ride has a maximum angular speed of 8.50 rev/min. How much is the rod stretched then?
Take the Young's modulus for the rod to be Y = 2.00×1011 Pa and the free fall acceleration to be g = 9.80 m/s^2

Assume that each car plus two people seated in it has a total weight of 1930 N.

Now, I somehow need to find theta or r using only omega. I'm not really sure how to do this.
you should take a FBD of the car ,and examine the forces acting on it. In the y direction, there is no movement. In the x direction, the horizontal component of the tension force provides the centripetal acceleration. Write the centripetal force equation in terms of omega (where omega =v/r), do a little trig, and solve for T. Show your work, please. I then presume you are familiar with the formula for length expansion under load?
 

1. What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness or elasticity 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 linear elastic material.

2. How is Young's modulus calculated?

Young's modulus is calculated by dividing the stress applied to a material by the strain it experiences. The resulting value is measured in pascals (Pa) or newtons per square meter (N/m^2).

3. What is the relationship between Young's modulus and rotation?

Young's modulus and rotation are related through the concept of torsion, which is the twisting of a material when an external torque is applied. Young's modulus is used to calculate the torsional stiffness of a material, which determines how much it will twist under a given torque.

4. What factors affect Young's modulus?

The factors that affect Young's modulus include the type of material, its microstructure, temperature, and strain rate. Generally, stiffer materials have higher Young's moduli.

5. Why is Young's modulus important in materials science?

Young's modulus is an important parameter in materials science as it provides information about a material's ability to resist deformation under stress. It is often used to compare the mechanical properties of different materials and is essential for designing and engineering structures that can withstand external forces.

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