Bulk Properties of Solids (AQA AS Physics)

A student was investigating the extension in a long thin metal wire. They suspended the wire from a fixed support, and hung it vertically then hung masses from the lower end.

The load was increased and decreased from zero to the maximum and back again.

The graph shows the force-extension of the wire.

Where on the graph would the elastic limit be found?

A rod is extended with a force so that its length increases. The variation with load L of the extension e of the rod is shown in the graph.

Point P is the elastic limit.

Which shaded area represents the work done during the plastic deformation of the rod?

A student was investigating a rubber band when stretched and relaxed to its original length. The graph shows the force-extension of the rubber band.

As the force is increased, the curve follows the path WXZ to extension x. As the force is reduced, the curve follows the path ZYW to return to zero extension.

The area labelled S is between the curves WXZ and ZYW. The area labelled T is bounded by the curve ZYW and the horizontal axis.

Which statement about the process is correct?

A sample of metal was stretched until it started to go into plastic deformation. The graph below shows the behaviour of the metal. 

When the sample was stretched from 0 to 12.0 mm extension, what is the work done? Assume that the curve SY is a straight line to simplify the calculation

A wire made from a new composite material was loaded with masses and the force-extension curve drawn.

What could be the value of the strain energy stored in the wire when it is stretched elastically to point Z?

A student was investigating a spring with a spring constant k of 3.0 N cm⁻¹, the spring was stretched over a range in which elastic deformation occurred.

Which row, for the stated applied force, gives the correct extension and strain energy?

	force / N	extension / cm	strain energy / mJ
A	24.0	8.0	960
B	12.0	3.0	200
C	6.0	2.0	120
D	3.0	1.0	1.5

A force compresses a mattress spring by 100 mm. The graph shows the effect of the force F on the length l of the spring.

What is the energy stored in the spring when the length is 70 mm?

A spring is extended due to a force. The graph shows the effect of changing force on the extension of the spring.

What is the elastic potential energy of the spring with a force of 8.0 N?

A force of 2.0 N is applied to a spring of unextended length 0.50 m and has a new length of 0.90 m.

A graph shows the variation of its length with tension.

How much strain energy is stored in the spring?

A student carried out an experiment on a ductile material; stretching it with a tensile force beyond its elastic limit. The force is removed.

The graph shows the force-extension of this experiment.

Which area represents the net work done on the sample?

A load of 5.0 N is suspended from the centre of a rod which is suspended from a parallel two-spring system as shown in the diagram.

The spring constant of each spring is 20 N m^–1.

How much elastic energy is stored in the system?

A slingshot ride at a fairground consists of a capsule which is attached to two identical bungee chords, as shown below.

Both bungee chords obey Hooke’s Law and have a spring constant of 150 N m^–1.  When the capsule is lowered and attached to the ground, both bungee chords are extended 25 m.  When the capsule is released from the ground it shoots vertically upwards.

 The mass of the capsule and its passengers is 300 kg.

 Assuming air resistance forces are negligible, what is the maximum height which the capsule can reach?

A 3 kg mass and a 4 kg mass are separated by a short string and attached to a spring.  The two masses hang at rest, as shown in the diagram.

The string separating the masses is then cut through with scissors.

Which row gives the correct accelerations of the two masses as the string is cut?

	Acceleration of 3 kg mass	Acceleration of 4 kg mass
A	g	g
B	3g	4g
C	7g	4g
D	g	g

A cylindrical pressure vessel, with an internal diameter of 200 mm, contains gas at a pressure of 1.5 MPa above atmospheric pressure. 

The gas is contained in the cylinder by placing a circular cover over it and securing the cover with a number of bolts evenly spaced around the cover.  A cross-section of the cylinder is shown in the diagram below.

Each bolt has an effective cross-sectional area of 82 mm².  The maximum stress which each bolt can withstand is 45 MPa.

What is the minimum number of bolts required to contain the gas in the cylinder?

A non-uniform sign is 1.0 m long and has a weight of 20 N.  It is suspended from two vertical springs A and B which are fixed to the ceiling.  The centre of mass of the sign is 65 cm from spring A.  When the sign is attached to the springs it is horizontal and in equilibrium.

Spring A has a spring constant of 140 N m^–1 and has an unstretched length of 10 cm.  Spring B has a spring constant of 520 N m^–1.  Both springs obey Hooke’s law.

What should the unextended length of spring B be before it is attached to the sign?

A block of mass 0.2 kg moves with a velocity of 1.0 m s^–1 on a smooth horizontal table.  Another block, of mass 0.3 kg moves with a velocity of 0.5 m s^–1 in front of block A and in the same direction. 

A spring of negligable mass with a spring constant of 100 N m^–1 is attached to B as shown below. 

What is the maximum compression of the spring?

The diagram below shows an arrangement of three springs, A, B and C.  When a load of F N is applied to the springs the system is in equilibrium.  The spring constants of the springs are k_A, k_B and k_C respectively. 

All of the springs have a negligible mass and are the same length when they are unstretched.

What is the spring constant of a single spring which would produce the same extension as the system above when a force of F N is applied?

A nylon rope of diameter 10 mm is used by a tow truck to tow a car of mass 750 kg.  The tow rope makes an angle of 20^o to the horizontal, as shown below.

A constant frictional force of 200 N acts on the car when it is moving.

If the ultimate tensile stress of the rope is 22.8 MPa,  what is the minimum acceleration of the car which would cause the tow rope to break?

Assume that frictional forces remain constant when the car is moving.

An alloy tube of volume 1.8 x 10^–4 m³ consists aluminium and magnesium.

There is 1.8 times more volume of aluminium compared to magnesium in the alloy

Aluminium has a density of  2700 kg m^–3 and magnesium has a density of 1700 kg m^–3    

What is the density of the alloy?

Two liquids, A and B, which do not mix are poured into an open ended U-tube which has a constant diameter.  The liquids are in equilibrium and are in contact at a distance x above the bottom of the U-tube, as shown below.

What is the ratio  ?