P.3.4.2.2 The Young modulus

A steel wire W has a length l and a circular cross-section of radius r. When W hangs vertically and a load is attached to the bottom end, it extends by e.

Another wire X made from the same material has the same load attached to it.

Which length and radius for X will produce an extension of e/4 ?

• A

• B

• C

• D

What cannot be used as a unit for the Young modulus?

• N m^–2

• Pa

• kg m^–2 s^–2

• kg m^–1 s^–2

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 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

A wire of length L and cross-sectional area A is stretched a distance e by a tensile force. The Young modulus of the material of the wire is E.

Which expression gives the elastic energy stored in the stretched wire?

• 
• 
• 
• 

A steel wire has a cross-sectional area 0.5 mm². The Young modulus of steel is 2.0 × 10¹¹ Pa. Assume the wire obeys Hooke’s law.

What load must be suspended from the wire to produce an extension which is 0.1% of the original length?

• 40 N

• 50 N

• 100 N

• 200 N

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

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