Deck 15: Solids

Question 1

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 atoms by 10% from the equilibrium spacing?

A)0.2x10-21 J
B)0.4x10-21 J
C)0.9x10-21 J
D)1.8x10-21 J
E)9.6x10-21 J

Answer 1

1.8x10-21 J

Question 2

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

A)Increases by 6%.
B)Increases by 2%.
C)Remains the same.
D)Decreases by 2%.
E)Decreases by 6%.

Answer 2

Decreases by 6%.

Question 3

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?

A)0.32 g cm-3.
B)1.3 g cm-3.
C)3.3 g cm-3.
D)5.8 g cm-3.
E)33.2 g cm-3.

Answer 3

5.8 g cm-3.

Question 4

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. One of the molecules is pulled outwards to a position 10% further out than the equilibrium position and then released from rest. What is its initial acceleration? Assume that the other molecule is fixed in position, and that the mass of a water molecule is 2.99x10-26 kg.

A)2.7x10=15 m s-2.
B)1.3x10-12 m s-2.
C)2.7 m s-2.
D)1.3x1012 m s-2.
E)2.7x1015 m s-1.

Question 5

Which one of the following cannot be a definition of an elastic modulus?

A) $-V_{i} \frac{\Delta P}{\Delta V}$
B) $\frac{F h}{A \Delta x}$
C) $\frac{F L_{i}}{A \triangle L}$
D) $V_{i} \frac{\Delta V}{\Delta P}$
E) $\frac{\text { stress }}{\text { strain }}$

Question 6

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 aircraft weighs 8 tonnes, and the cable will be 5 m long, and has a radius of 1 cm. Steel has a Young's Modulus of 2x1011 N m-2. By how much will the cable stretch (in mm) when it is supporting the whole weight of the aircraft?

A)0.08.
B)0.8.
C)3.2.
D)7.7.
E)32.0.

Question 7

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 8

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 weigh 800 kg and are securely fastened in 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 2 cm and a Young's Modulus of 100 000 N m-2. By how much will the mat be compressed when the crate is placed on it?

A)0.03 mm.
B)0.3 mm.
C)3 mm.
D)0.1 mm.
E)1 mm.

Question 9

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)0.0%.
B)5.0%.
C)15.0%.
D)16.7%.
E)30.0%.

Question 10

How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume by 1.0%? The bulk modulus of water is 2.0 *109 N/m² and 1 ATM = 1.0 *105 N/m².

A)50 ATM
B)100 ATM
C)1100 ATM
D)400 ATM
E)200 ATM

Question 11

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?

A)11.0 cm.
B)10.3 cm.
C)10 cm.
D)9.7 cm.
E)9.0 cm.

Question 12

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.

A)3.0x10-11 N
B)5.4x10-11 N
C)8.0x10-11 N
D)3.2x10-10 N
E)9.6x10-10 N

Question 13

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)2.3x10-11 m.
B)1.0x10-10 m.
C)2.3x10-10 m.
D)1.0x10-9 m.
E)2.3x10-9 m.

Question 14

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

A)2.1 kN
B)3.5 kN
C)6.9 kN
D)11 kN
E)5.4 kN

Question 15

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, by what percentage does its volume increase?

A)0.0%.
B)3.7%.
C)3.0%.
D)1.0%.
E)-3.0%.

Question 16

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?

A)9.4x106 N m-2.
B)9.5x105 N m-2.
C)95 N m-2.
D)936 N m-2.
E)9.4x104 N m-2.

Question 17

Stress is proportional to strain means that:

A)stress = constant * strain.
B)stress = (constant 1) * strain + constant 2.
C)stress = $\frac{\text { constant }}{\text { strain }}$ .
D)stress = $\frac{\text { constant } 1}{\text { strain }}+\text { constant } 2$ .
E)stress * strain = constant.

Question 18

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?

A)0.025 J.
B)0.25 J.
C)2.5 J.
D)25 J.
E)250 J.

Question 19

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?

A)0.25 cm
B)2.5 cm
C)12.5 cm
D)25 cm
E)1.25 cm

Question 20

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)0.2x10-21 J
B)0.4x10-21 J
C)0.9x10-21 J
D)1.8x10-21 J
E)9.6x10-21 J

Question 21

For safety in climbing, a mountaineer uses a 50-m long nylon rope that is 1.0 cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6 m. Find the Young's modulus for the rope material.

Question 22

If 1.0 m3 of concrete weighs 5 *104 N, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? (The compression strength of concrete is 1.7 * 107 N/m²)

Question 23

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.

Question 24

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.

A)0.33 μm.
B)1.0 μm.
C)3.3 μm.
D)10.0 μm.
E)33.3 μm.

Question 25

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?

A)0.3 degrees.
B)5 degrees.
C)10 degrees.
D)17.5 degrees.
E)20 degrees.

Question 26

A steel beam is to be installed on a spacecraft. By what percentage will its volume increase when placed in a vacuum? You may assume that the temperature remains the same and that the bulk modulus of steel is 6.0x1010 N m-2.

A)1.7x10-6 %.
B)1.7x10-8 %.
C)1.7x10-5 %.
D)1.7x10-4 %.
E)1.7x10-3 %.

Question 27

You wish to suspend a sculpture by a single wire high over the atrium of a new art gallery. You wish the state to rotate in the breeze. Your architect has given you a choice of several wires that you could use. Which will allow the sculpture to rotate most easily? The shear modulus of copper is 4.2x1010 N m-2 and that of steel is 8.4x1010 N m-2.

A)Solid copper wire, 1 mm in radius.
B)Hollow copper wire, inside radius 1 mm, outside radius 1.5 mm.
C)Solid steel wire, 0.8 mm in radius.
D)Hollow steel wire, inside radius 0.8 mm, outside radius 0.9 mm.
E)All the other answers are equally good.

Question 28

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.

A)1480 ATM
B)14 800 ATM
C)1500 ATM
D)150 ATM
E)15 ATM

Question 29

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)10 cm.
B)7 cm.
C)4 cm.
D)1 cm.
E)0.5 cm.

Question 30

Imagine that you are helping out with the stage design for an amateur theatrical performance. You have to support a heavy set of lights on the end of a wooden plank. The plank is 3 m long, 1 cm thick and 10 cm wide. One end of the plank will be bolted to a bracket on the theatre wall, and the plank will extend horizontally over the stage, with the lamps screwed onto the end. You are worried that the weight of the lights might bend the plank too much and cause it to break. Initially you set up the plank in a flat orientation (with the width horizontal), and the tip bent by 5 cm when weighed down, which was too much. You are considering rotating the plank by 90° (so the width is vertical). How much would you expect the tip to bend in this orientation?

A)5 cm.
B)0.5 cm.
C)0.05 cm.
D)50 cm.
E)1.0 cm.

Question 31

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? The shear modulus of rubber is 105 N m-2.

A)0.3 degrees.
B)5 degrees.
C)10 degrees.
D)17.5 degrees.
E)20 degrees.

Question 32

Imagine that a diamond necklace was sunk with the Titanic, and is now lying at a depth of 4 km in the North Atlantic Ocean. What would the percentage change in the volume of the diamond be, due to the water pressure? The bulk modulus of Diamond is 4.42x1011 N m-2 and the density of seawater can be assumed to be 1000 kg m-3.

A)0.004%.
B)0.009%.
C)0.04%.
D)0.09%.
E)0.4%.

Question 33

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)20 cm.
B)15 cm.
C)12.5 cm.
D)10 cm.
E)7.5 cm.

Question 34

Imagine that a new monorail system is being planned for Sydney. The trains will run on elevated tracks, 15 m high. A single square concrete post, 5 cm on a side, supports each segment of the track. How much of a sideways force can the track segments withstand without moving sideways by more than 1 mm? You may assume that the force shears the concrete support posts. The shear modulus of concrete is 2.2x109 N m-2.

A)14 700 000 N.
B)1 470 000 N.
C)147 000 N.
D)14 700 N.
E)1470 N.

Question 35

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.

A)100 cm.
B)95 cm.
C)90 cm.
D)75 cm.
E)32 cm.

Question 36

When a given torque is applied to a 1-m long copper wire, the end rotates by 10°. If half the torque were applied to a 2-m long length of the same wire, by what angle would the end rotate?

A)5 degrees.
B)7.1 degrees.
C)10 degrees.
D)14.1 degrees.
E)20 degrees.

Question 37

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).