P.3.4.2.1 Bulk properties of solids

The table contains information on four wires. It shows the stiffness of each wire and the maximum strain energy stored in the wire when extended to the breaking point.

Assume each wire has the same initial dimensions and obeys Hooke’s law.

Which wire extends the least before reaching the breaking point?

• A

• B

• C

• D

A non-uniform sign is 0.80 m long and has a weight of 18 N

It is suspended from two vertical springs P and Q. The springs obey Hooke’s law and the spring constant of each spring is 240 N m^–1

The top end of spring P is fixed and the top end of spring Q is adjusted until the sign is horizontal and in equilibrium.

What is the extension of spring Q?

• 0.014 m

• 0.038 m

• 0.049 m

• 0.061 m

What is the name given to a material that breaks without deformation when a force is applied to it?

• Plastic

• Brittle

• Stiff

• Elastic

Two separate wires X and Y have the same original length and cross-sectional area.

The graph shows the extension ∆L produced in X and Y when the tensile force F applied to the wires is increased up to the point where they break.

Which statement is incorrect?

• For a given extension more energy is stored in X than in Y.

• The Young modulus of the material of wire Y is greater than that of wire X.

• Both wire X and wire Y obey Hooke’s law.

• Wire X has a greater breaking stress than wire Y.

A load of 3.0 N is attached to a spring of negligible mass and spring constant 15 N m^–1.

What is the energy stored in the spring?

• 0.3 J

• 0.6 J

• 0.9 J

• 1.2 J

The diagram shows how the stress varies with strain for metal specimens X and Y which are different. Both specimens were stretched until they broke.

Which of the following is incorrect?

• X is stiffer than Y

• X has a higher value of the Young modulus

• X is more brittle than Y

• Y has a lower maximum tensile stress than X

Two vertical copper wires X and Y of equal length are joined as shown. Y has a greater diameter than X. A weight W is hung from the lower end of Y.

Which of the following is correct?

• The strain in X is the same as that in Y.

• The stress in Y is greater than that in X.

• The tension in Y is the same as that in X.

• The elastic energy stored in X is less than that stored in Y.

Two masses hang at rest from a spring, as shown in the diagram. The string separating the masses is burned through.

Which of the following gives the accelerations of the two masses as the string breaks?

acceleration of free fall = g

• A

• B

• C

• D

The overhead cables used to transmit electrical power by the National Grid usually consist of a central core of steel cables surrounded by a sheath of cables of low resistivity material, such as aluminium.

What is the main purpose of the steel core?

• To force more current into the outer sheath.

• To provide additional current paths through the cables.

• To reduce the power lost from the cables.

• To increase the mechanical strength of the cables.

Answer explanation

The synoptic (or “common sense”) element in answering this question makes the question more difficult than it really should be.

When studying power transmission, students should know that it is essential to minimise I²R losses from the cables. This is done by using high voltage (to reduce the current for a given amount of power) and by employing cables of low resistance. However, the cables also need to be mechanically strong so that they will help to support their own weight. The electrical good conductors such as copper and aluminium tend to be mechanically weak, so in practice the cables are reinforced by incorporating a stronger material.

The four bars A, B, C and D have diameters, lengths and loads as shown. They are all made of the same material.

Which bar has the greatest extension?

• A

• B

• C

• D