Find the minimum diameter of an I = 15.4 m long brass wire that will stretch no more than 7.83 mm when a mass of 335 kg is hung on the lower end. (Hint: The Young's modulus of brass is 91.0 GPa.)

An amusement park ride consists of airplane-shaped cars attached to steel rods. Each rod has length 15m and cross-sectional area 8.00cm2. Take Young's modulus for steel to be Y=2.0×1011Pa. How much is the rod stretched (change in length of ΔL) when the ride is at rest? Assume that each car with two people seated in it has a total weight of 1900N. When the ride is operating, it has a maximum angular speed of ω=8.0rev/min. How much is the rod stretched then?

A 1.25 m long cable has a diameter 3.50 mm with a Young’s Modulus, E, of 9.75 x 109 N/m2 . When the wire is placed under tension, it experiences a stress of 202.52 x 106 N/m2 , the length of the cable extends by 36.35 mm. Calculate the force that the cable experiences under tension and the strain energy density (U/V) due to deformation. Give your answers in newtons (N) to 2 decimal places for the force; and in joules per cubic metre (J/m3 ) for the strain energy density to 2 decimal places. Assume the cable is solid and the material is homogeneous.