A towline used to tow hang gliders is 500 m long and \(10 mm^{2} \) in cross-sectional area. It is found to stretch 10 m under a tension equal to one-fourth the weight of an 100 kg glider-pilot combination. What is Young’s modulus for the material used to make the towline?
2.
A brass wire \((Yb = 9\times 10^{10} \,Pa)\) and a steel wire \((Ys = 20\times 10^{10} \,Pa)\) are both used (in parallel) to support a single mass of 1000 kg. Both wires have a length of 2 m and a cross-sectional area of \(1 mm^{2}\text{.}\)
What is the change in length of each wire?
What is the tension in each wire?
What is the stress in each wire?
What is the strain in each wire?
How much elastic potential energy is stored in each wire?
3.
The deepest part of the ocean is about 11 km and has a pressure of about 1000 atm. If the bulk modulus of sea water is \(2.2\times 10^{9} \,Pa\) and the surface density of sea water is \(1.03\times 10^{3} \,kg/m^{2}\text{,}\) what is the density of sea water at the bottom of the ocean?
4.
A horizontal rod of negligible mass and of length 1 m is supported on each end by a wire of length 1 m and diameter 0.1 mm. The wire on the left has a diameter of 0.1 mm and is made of aluminum \((Y = 7.0\times 10^{10} \,N/m^{2})\text{.}\) The wire on the the right has a diameter of 0.2 mm and is made of copper \((Y = 11\times 10^{10} \,N/m^{2})\text{.}\) A mass of 1 kg is then suspended from the rod.
Where should the mass be located in order to produce equal stresses in the two wires?
Where should it be located to produce equal strains?
5.
A lead block 50.0 cm long, 10.0 cm wide, and 10.0 cm thick, has a force of \(2\times 10^{5} \,N\) placed on it. Find the stress, the strain, and the change in length if
the block is standing upright, and
the block is lying flat.
6.
A coil spring stretches by 4.50 cm when a mass of 250 g is suspended from it. What force is necessary to stretch the spring an additional 2.50 cm?
7.
Find the ratio of the density of water at the bottom of a 50.0 m lake to the density of water at the surface of the lake. The pressure at the bottom of the lake is \(4.90 \times 10^{5} \,N/m^{2}.\) The bulk modulus for water is \(0.21 \times 10^{10} \,N/m^{2}.\)
