Exam 15: Solids

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?

The architect of a trendy new inner-city townhouse in Adelaide wants a staircase where the steps stick out from a wall and are only supported at the wall end. If each step is made of steel and is 1.5 cm thick, 30 cm wide and 1.2 m wide, and a person weighing 120 kg stands on the end of them, by how much will the end of the step bend? Young's modulus for steel is 2.0x1011 N m-2.

A torque of 1 N m is applied to one end of a solid rubber cylinder of radius 5 cm and length 30 cm. By what angle does the end rotate?

Consider two adjacent water molecules in an ice crystal. Assume that the binding energy connecting them follows a Lennard-Jones potential with a potential well depth of 9.6x10-21 J. How much energy must you put into the system to increase the separation of the two molecules by 10% from the equilibrium spacing?

A heavy crate containing artworks from the National Gallery of Victoria is to be shipped to London to be part of an exhibition. The artworks are securely fastened in a cubic crate 1 m on a side. This crate is placed on top of a rubber mat in the back of a cargo plane. The rubber mat has an uncompressed thickness of 1 cm and a Young's Modulus of 100 000 N m-2. When the crate is placed on the rubber, the mat is compressed by 0.1 mm. How much elastic energy is stored in the rubber in this situation?

Imagine that a new monorail system is being planned for Sydney. The trains will run on elevated tracks, 20 m high. A single square concrete post supports each segment of the track. Each segment of track needs to be able to withstand a sideways force of 100 000N without moving sideways by more than 1 mm. How wide must the concrete support post be? You may assume that the force shears the concrete support posts. The shear modulus of concrete is 2.2x109 N m-2.

Find the minimum diameter of a steel wire 18 m long that will stretch no more than 9 mm when a load of 380 kg is hung on the lower end. (Y steel = 2.0 *1011 N/m²).

A 20-m long steel wire (cross-section 1.0 cm², Young's modulus 2.0 * 1011 N/m²), is subjected to a load of 25 000 N. How much will the wire stretch under the load?

When a particular crystal increases in temperature by 30K, the average spacing between its atoms increases by 2%. How does the density change?

Consider two adjacent water molecules in an ice crystal. Assume that the binding energy connecting them follows a Lennard-Jones potential with a potential well depth of 9.6x10-21 J, and the equilibrium atomic spacing is 3.196x10-10 m. How much force must you apply to one of the molecules to increase the separation of the two atoms by 10% from the equilibrium spacing? Assume that the other molecule is fixed in position.

How large a force is necessary to stretch a 2.0-mm diameter copper wire (Y = 11*1010 N/m²) by 1.0%?

A steel bridge strut decreases in radius by 5% when put under load. By what percentage does it increase in length, if the Poisson ratio for steel is 0.3?

A metal cylinder of length 1 m and radius 10 cm is stretched so that its length increases by 10%. If the Poisson ratio for this metal is 0.3, what is its radius while it is stretched?

You have been asked to help suspend a road-sign over a narrow Hobart street. The sign has a mass of 100 kg and will need to be suspended from the end of a 5-m long steel beam which will be attached at the other end to a building. If the beam has a square cross-section, how thick will it need to be to carry the weight without sagging by more than a centimetre? Young's modulus for steel is 2.0x1011 N m-2.

A shear force is applied to a cube of glass, 10 cm on a side, such that the top of the cube is displaced sideways relative to the bottom. If the shear force is 10 000N, by how much does the top of the cube move relative to the bottom? The shear modulus of glass is 3x1010 N m-2.

At a building site in Perth, a tower crane is lifting a 300 kg pallet of bricks upwards at a steady speed. The cable from which the bricks are suspended has a circular cross-section of radius 1 cm. What is the tensile stress in this cable?

The four tyres of an automobile are inflated to a gauge pressure of 2.0 * 105 N/m² (29 PSI). Each of the four tyres has an area of 0.024 m² that is in contact with the ground. Determine the weight of the auto.

Iron has a molar mass of 55.85 g/mol and a density of 7.87 g cm-3.If the atoms are arranged in a cubic grid, what is the typical distance between adjacent atoms?

A glass sphere of radius 10 cm is placed in a pressure chamber. Its radius is observed to decrease by 0.1 mm. What is the pressure in the chamber (in atmospheres)? The bulk modulus of glass is 5x1010 N m-2.

In a particular form of Silicon, the atoms are arranged in a rectangular grid of spacing 2x10-10 m. Each atom weighs 4.7x10-26 kg. What is the density of this form of Silicon, in g cm-3?