MaterialsAQA A-Level Physics: Topic test

20 questions, 54 marks

AQA A-Level Physics

Materials topic test

Total 54 marks

Name

Class

Date

1
A solid aluminium cylinder has a radius of 1.5 cm and a length of 8.0 cm. Its mass is 153 g.
(a)
What is the volume of the cylinder?
[1 mark]
A2.26×10⁻⁴ m³
B5.65×10⁻² m³
C5.65×10⁻⁵ m³
D5.65×10⁻⁶ m³
(b)
What is the density of the aluminium?
[1 mark]
A2.7×10³ kg m⁻³
B2.7 kg m⁻³
C2.7×10⁶ kg m⁻³
D3.7×10⁻⁴ kg m⁻³
(c)
The cylinder is melted and recast as a solid cube of the same aluminium. Calculate the length of one side of the cube.
[2 marks]
Total for question 1: 4 marks
2
A spring has an unstretched length of 0.250 m. When a mass of 0.60 kg is hung from it, the length of the spring becomes 0.310 m. The spring obeys Hooke's law for all loads up to 15 N. Take g = 9.81 N kg⁻¹.
(a)
What is the extension of the spring when the 0.60 kg mass is hanging from it?
[1 mark]
A0.310 m
B0.060 m
C0.250 m
D0.560 m
(b)
What is the spring constant of the spring?
[1 mark]
A24 N m⁻¹
B19 N m⁻¹
C10 N m⁻¹
D98 N m⁻¹
(c)
A 1.0 kg mass is hung from the same spring. Calculate the length of the spring.
[2 marks]
Total for question 2: 4 marks
3
A cylindrical titanium rod of unstretched length 0.80 m and diameter 12 mm hangs from a fixed support and carries a load that produces a tension of 1.5×10⁴ N in the rod. The Young modulus of titanium is 1.1×10¹¹ Pa and the rod obeys Hooke's law.
(a)
Calculate the stress in the rod and the strain of the rod.
[3 marks]
(b)
Calculate the elastic strain energy stored in the rod. Explain why this is half of the product of the tension and the extension.
[4 marks]
Total for question 3: 7 marks
4
A metal wire of length 2.0 m and diameter 0.40 mm is loaded gradually until it breaks. Over the first part of the loading the stress–strain relationship is a straight line through the origin, reaching a stress of 2.4×10⁸ Pa at a strain of 1.2×10⁻³. Beyond that point the wire stretches much more for each small increase in stress. A glass rod is tested in the same way and breaks without any such change.
(a)
Describe and explain the behaviour of the metal wire as the load is increased until it breaks. State how the behaviour of the glass rod differs.
[6 marks]
(b)
Use the data for the straight part of the graph to calculate the Young modulus of the metal, the tension in the wire and the extension at a stress of 2.4×10⁸ Pa. Calculate the elastic strain energy stored in the wire at this stress.
[6 marks]
Total for question 4: 12 marks
5
A steel guitar string has an unstretched length of 0.65 m and a diameter of 0.25 mm. It is tightened until the tension is 80 N. The Young modulus of the steel is 2.0×10¹¹ Pa and the string obeys Hooke's law.
(a)
What is the cross-sectional area of the string?
[1 mark]
A1.96×10⁻⁷ m²
B4.91×10⁻² m²
C7.85×10⁻⁴ m²
D4.91×10⁻⁸ m²
(b)
What is the extension of the string?
[1 mark]
A1.3 mm
B53 mm
C5.3 mm
D8.2 mm
(c)
A thinner string made of the same steel is tightened to the same tension. Explain why its strain is greater.
[2 marks]
Total for question 5: 4 marks
6
A spring of spring constant 60 N m⁻¹ is attached to a trolley of mass 0.50 kg on a horizontal, frictionless track. The trolley is pulled 0.25 m from its equilibrium position and released from rest. The spring obeys Hooke's law and its mass is negligible.
(a)
What is the elastic strain energy stored in the spring when the trolley is released?
[1 mark]
A1.9 J
B3.8 J
C15 J
D0.94 J
(b)
What is the speed of the trolley as it passes through the equilibrium position?
[1 mark]
A3.9 m s⁻¹
B2.7 m s⁻¹
C7.5 m s⁻¹
D1.9 m s⁻¹
(c)
Explain why the energy stored in the spring is given by $\frac{1}{2}Fx$ and not $Fx$ .
[2 marks]
Total for question 6: 4 marks
7
A nylon thread of diameter 0.80 mm and unstretched length 3.0 m breaks when the tension reaches 120 N. The Young modulus of the nylon is 3.0×10⁹ Pa. Assume that the thread obeys Hooke's law right up to the point where it breaks.
(a)
Calculate the breaking stress of the nylon.
[3 marks]
(b)
Calculate the extension of the thread just before it breaks and the elastic strain energy stored in it at this point.
[4 marks]
Total for question 7: 7 marks
8
A student makes a catapult from an elastic cord of unstretched length 0.40 m and cross-sectional area 2.0×10⁻⁵ m². The cord obeys Hooke's law up to an extension of 0.50 m and has a Young modulus of 5.0×10⁶ Pa. The student stretches the cord by 0.30 m to launch a stone of mass 0.050 kg vertically upwards. Take g = 9.81 m s⁻².
(a)
Show that the spring constant of the cord is 250 N m⁻¹. Calculate the stress in the cord and the strain of the cord when it is stretched by 0.30 m.
[6 marks]
(b)
The catapult transfers 80% of the elastic strain energy to the stone as kinetic energy. Calculate the elastic strain energy stored, the speed of the stone as it leaves the catapult and the maximum height it reaches above the point of release. State one assumption you have made.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).