Simple rotation/elasticity problem

ninjagowoowoo

An amusement park ride consists of airplane-shaped cars attached to steel rods. Each rod has a length of 14.0 m and a cross-sectional area of 0.000780m^2. When operating, the ride has a maximum angular speed of 8.00 rev/min. How much is the rod stretched?

Take the Young's modulus for the rod to be Y = 2×10^11 Pa and the free fall acceleration to be g = 9.80 m/s^2

Umm... Im really just stumped on this one. Really its just the rotation part thats messing me up. What outward force would be caused by the rotation? Would the rotation even change the amount stretched from a still position? Haha, I would really appreciate a push in the right direction.

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OlderDan

Homework Helper
The cars are going around in circles. Each car is subject to a centripetal force provided by the rods. The rods are being stretched by the force of the car and attachment at the axis of rotation.

Was the rotation axis specified? Is the motion horizontal?

ninjagowoowoo

ok so to find the tensile force, I will use the centripetal force. so F=(mv^2)/R. And v=R(omega). So F=R(omega)^2(m). But to find this force wouldn't I need to know the radius of the rotation?

FredGarvin

ninjagowoowoo said:
Each rod has a length of 14.0 m
You'll have to decide if you want to assume that the rods are horizontal at the time you are interested in. I would simply because it would make things easier.

ninjagowoowoo

Nope still not working. using the formula for F that I gave earlier, and that
changeinlength = F(originallength)/(crosssectionalarea)(modulus)
I get that:
change in length = r(omega^2)m(orig length) / AY where Y is the modulus.
so I use the following values:
R = 14m
omega = 3015.92895rad/s (converted from rev/min)
m = 203.0612245 (1990N/9.8m/s/s)
orig length = 14m
A = 0.00078m^2
Y=2*10^11
and when i plug in the numbers I get a rediculous number (2320.602127m). Any other suggestions?

OlderDan

Homework Helper
ninjagowoowoo said:
omega = 3015.92895rad/s (converted from rev/min)

and when i plug in the numbers I get a rediculous number (2320.602127m). Any other suggestions?
See if you can fix that ridiculous value for omega
I did not check the rest of your calculation

ninjagowoowoo

well if it was in rev/min wouldnt i have to convert it to rad/s?

*(2pi*60)???

Last edited:

OlderDan

Homework Helper
$$\omega = \frac{8\ \ rev}{min} \cdot \frac{2\pi\ \ rad}{rev} \cdot \frac{1\ \ min}{60\ \ sec}$$

Usually a good idea to write units.

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