An amusement park ride consists of airplane shaped cars attached to steel rods. Each rod has a length of `20.0 m` and a cross-sectional area of `8.00 cm^(2)`. Young's modulus for steel is `2 xx 10^(11) N//m^(2)`.
a. How much is the rod stretched (in `mm`) when the ride is at rest ? (Assume that each car plus two people seated in it has a total weight of `2000 N`.)
b. When operating, the ride has a maximum angular speed of `sqrt(19/5) rad//s`. How much is the rod stretched (in mm) then?

Answer

`0.38mm`

Explanation

On sbstituting the values, we get `/_\l=(Fl_(0))/(YA)=2.5xx10^(-4)m=0.25mm`
b. The that each car exerts on the cable is `F=momega^(2)l_(0)=W/gomega^(2)l_(0)`. So,
`/_\l=(Fl_(0))/(YA)=(Womega^(2)l_(0)^(2))/(gYA)`
On substituting the value we get `3.8xx10^(-4)m=0.38mm`