At the Australian War Memorial in Canberra, a large historic aircraft is to be put on display. The plan is to suspend it by a steel cable from the roof. The cable will be 5 m long, and has a radius of 5 mm. Steel has a Young's Modulus of 2x1011 N m-2. The cable stretches 3 mm when it is supporting the weight of the aircraft. How much elastic energy is stored in the cable in this situation?
A)0.3 J.
B)28 kJ.
C)540 kJ.
D)4.5 J.
E)14.1 J.

Question

Quizplus · Accepted Answer

The elastic energy stored in a cable is given by the formula:

E = (1/2) * (stress) * (strain) * (volume)

The stress can be calculated using the Young's modulus:

stress = (force/area) = (mass * gravity/area) = (mass * 9.81/area)

The area of the cable can be calculated using its radius:

area = π * (radius)^2

The volume of the cable is simply its length:

volume = length = 5 m

The strain is given as 3 mm/mm, or 0.003.

Putting it all together:

stress = (10000 kg * 9.81 m/s^2)/(π * (0.005 m)^2) = 1.989 x 10^9 N/m^2

strain = 0.003

volume = 5 m

E = (1/2) * (1.989 x 10^9 N/m^2) * (0.003) * (5 m) = 14.1 J

Therefore, the elastic energy stored in the cable is 14.1 J, which corresponds to choice E.

At the Australian War Memorial in Canberra, a Large Historic