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

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

A load of 4.0 N is suspended from a parallel two-spring system as shown in the diagram.

The spring constant of each spring is 20 N m^–1. The elastic energy, in J, stored in the system is

• 0.1

• 0.2

• 0.4

• 0.8

Which material is the strongest in this image?

• A

• B

• C

• D

Which material has the highest toughness?

• A

• B

• C

• D

Which cannot be units for Young Modulus?

• N m^-2

• Pa

• kg m^-2 s^-2

• kg m^-1 s^-2

A sample of wire has a Young modulus E. A second sample of wire made from an identical material has three times the length and half the diameter of the first sample.

What is the Young modulus of the second sample of wire in terms of E?

• 0.25E

• E

• 6E

• 12E