Question 1

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.

Accepted Answer

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

Question 2

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.

Accepted Answer

3.51 *108

Question 3

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?

Accepted Answer

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

Question 4

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.

Accepted Answer

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

Question 5

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?

Accepted Answer

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

Question 6

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?

Accepted Answer

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

Question 7

Stress is proportional to strain means that:

Accepted Answer

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. 
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 8

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?

Accepted Answer

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

Question 9

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.

Accepted Answer

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

Question 10

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.

Accepted Answer

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

Question 11

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?

Accepted Answer

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

Question 12

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.

Accepted Answer

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

Question 13

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

Accepted Answer

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)  $\frac{\text { stress }}{\text { strain }}$ 
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 14

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.

Accepted Answer

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. 
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 15

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)

Accepted Answer

The answer of If 1.0 m3 of concrete weighs 5...

Question 16

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.

Accepted Answer

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. 
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 17

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?

Accepted Answer

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 
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

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.

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.

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.

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 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?

Stress is proportional to strain means that:

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.

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

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)

Physics and Measurement

Motion in One Dimension

Motion in Two Dimensions

Forces and Newtons Laws

Further Applications of Newtons Laws

Work, Force and Energy

Conservation of Energy

Linear Momentum and Collisions

Rotational Motion

Energy and Momentum in Rotating Systems

Gravity

Special Relativity

Fluid Statics

Fluid Dynamics

Oscillatory Motion

Wave Motion

Superposition and Interference

Heat and Temperature

Energy Transfer Processes and Thermodynamics

The Kinetic Theory of Gases

The Second Law of Thermodynamics, Heat Engines and Entropy

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Exam 15: Solids

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.

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.

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.

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 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?

Stress is proportional to strain means that:

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.

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

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)

Physics and Measurement

Motion in One Dimension

Motion in Two Dimensions

Forces and Newtons Laws

Further Applications of Newtons Laws

Work, Force and Energy

Conservation of Energy

Linear Momentum and Collisions

Rotational Motion

Energy and Momentum in Rotating Systems

Gravity

Special Relativity

Fluid Statics

Fluid Dynamics

Oscillatory Motion

Wave Motion

Superposition and Interference

Heat and Temperature

Energy Transfer Processes and Thermodynamics

The Kinetic Theory of Gases

The Second Law of Thermodynamics, Heat Engines and Entropy

Filters

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.

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)