24 questions · 24 marks · ≈ 24 min
A student wanted to measure the Young modulus of a wire, to do this they needed to take a number of measurements.
In which row could the measurement not be made directly with the listed apparatus?
| Measurement | Apparatus | |
|---|---|---|
| A | extension of wire | vernier scale |
| B | area of cross-section of wire | micrometer screw gauge |
| C | original length of wire | metre rule |
| D | mass of load applied to a wire | electronic balance |
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What is the unit of the Young modulus?
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N m–2
N m
N m–1
N m2
A material is extended elastically within the limit of proportionality. What is equal to the Young modulus of the material?
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gradient of the stress-strain graph
area under the force-extension graph
area under the stress-strain graph
gradient of the force-extension graph
An experiment was carried out to determine the Young modulus of steel using a steel wire.
The uncertainties in the measurements are given below.
| Measurement | Uncertainty |
|---|---|
| load on wire length of wire diameter of wire extension | ±2% ±0.2% ±1.5% ±1% |
What is the percentage uncertainty in the Young modulus?
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1.3%
1.8%
4.7%
6.2%
A glass rod was put under stress and strain until it broke. The graph of this is shown below.
Which of the following statements is correct about the glass rod?
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the glass shows plastic deformation
when the cross-sectional area of the rod is doubled, the ultimate tensile stress of the rod is halved
Hooke’s law is obeyed for all values of stress up to the breaking point
the glass is ductile
Two wires S and T, with the same initial dimensions, were put under stress and strain, the graph shows the results up to their breaking points.
Which statement is not correct?
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material S has a larger ultimate tensile stress
material S extends elastically
material S extends more than material T when loaded with the same force
material S is brittle
The graphs below show the stress-strain graphs of three materials. The graphs do not have the same scales.
The three materials are copper, rubber and glass.
Which materials are represented by the graphs?
| 1 | 2 | 3 | |
|---|---|---|---|
| A B C D | rubber rubber glass copper | copper glass copper glass | glass copper rubber rubber |
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The stress-strain graph for bone is shown below.
What is the Young modulus of bone?
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2 × 106 N m−2
2 × 108 N m−2
1 × 106 N m−2
1 × 108 N m−2
A student wanted to determine the spring constant of a spring. They did this by using different loads to extend the spring by varying amounts.
To find the spring constant, which quantities are required?
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the elastic limit, extensions and the length of the spring
the loads and the extensions of the spring
the elastic limit and the loads
the loads and the length of the spring
A metal tube with a thin wall thickness w is shown in the diagram. The thickness of the wall is small when compared to the diameter of the tube.
A force T applied parallel to the axis of the tube puts the tube under tension. It is proposed that making the wall thicker would reduce the stress on the tube.
If the tube diameter and the tension remain the same, which wall thickness would half the stress?
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4w
2w
A steel metal wire has the following properties:
diameter = 5.0 × 10–4 m
Young modulus = 2.0 × 1011 Pa
tension = 20 N
The string snaps and contracts elastically.
By what percentage does a length l of a piece of the string contract?
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The Young modulus of a metal wire determines which property?
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spring constant
ductility
ultimate tensile stress
elastic limit
The Young modulus E and the force per unit extension k describes the behaviour of a wire under tensile stress.
For a wire of length L and cross-sectional area A, what is the relationship between E and *k *?
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A steel bar, shown in the diagram, has a circular cross-section that is under tension T.
The diameter of the thinner portion is half the wider portion.
What is the value of ?
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4.0
2.0
0.50
0.25
A student wanted to find the young modulus of a wire. The equation for the young modulus E is:
The student extended the wire with a known force and made a series of measurements.
Which measurement has the largest effect on the uncertainty in the value of the calculated Young modulus?
| Measurement | Symbol | Value | |
|---|---|---|---|
| A | length of wire before force applied | l | 2.043 ± 0.002 m |
| B | force applied | F | 19.62 ± 0.01 N |
| C | extension of wire with force applied | x | 5.2 ± 0.2 mm |
| D | diameter of wire | d | 0.54 ± 0.02 mm |
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A spring was stretched with increasing load. The graph of the results is shown below.
What is the spring constant?
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0.080 N m–1
0.13 N m–1
2.7 N m–1
8.0 N m–1
The graph below shows the stress-strain for a metal.
When the strain on the rod is 0.010, what is the strain energy per unit volume of a rod made from this metal?
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10 kJ m−3
10 MJ m−3
100 kJ m−3
1.0 MJ m−3
A steel spring was stretched to a length of 55 cm when a 25 N weight was hung from it. The spring has a spring constant of 150 N m–1.
What was the original length of the spring?
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0.61 m
0.72 m
0.38 m
0.49 m
A steel cable used in a construction crane has a Young's modulus of . The cable has a cross-sectional area of and is subjected to a tensile force of . The cable obeys Hooke's law.
What is the stress in the steel cable?
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A child with a mass of 40 kg was standing on a diving board. The diving board has a length of 5.0 m and is hinged at one end then supported by a spring 2.0 m from the hinged end. The spring has a spring constant of 10 kN m–1
What is the extra compression of the spring caused by the child standing on the end of the board?
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16 cm
9.8 cm
1.6 cm
1.0 cm
The diagram shows a metal cube is placed between two board and compressed elastically by two opposing forces F. The cube has a length of each side of
How will ∆l, the amount of compression, relate to l ?
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A metal wire that is supported vertically from a fixed point has a load of 84 N applied to the lower end. The wire has a cross-sectional area of 0.02 mm2 and obeys Hooke’s law. The length of the wire increases by 0.30 %.
What is the Young modulus of the metal wire?
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Two wires S and T is joined, S has a length of 3.0 m and T a length of 1.0 m, both wires have a uniform cross-sectional area.
When a load was hung from the wires S stretched by 1.5 mm and T by 1.0 mm.
The same load is then hung from a second wire of the same cross-section and same Young modulus, consisting of 1.0 m of metal S and 3.0 m of metal T.
What is the total extension of this second wire?
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3.5 mm
2.5 mm
5.0 mm
4.8 mm
Two steel wires X and Y that both obey Hooke’s law were used in an experiment. Wire X has a length and a cross-sectional area A. Wire Y has a length of and cross-sectional area of .
What is the ratio when both wires are stretched to the same extension?
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