HKAL Exercise : Part 2 Matters
Chapter 7Properties of Matter
7.1Solids
Energy stored in a spring
1.A wire, of force constant k, has an extension e when it is supporting a weight W. If the elastic limit is not exceeded, the energy stored in the wire is equal to
(1)×k×e.
(2)×W×e.
(3)×stress ×strain.
A.(1) only
B.(2) only
C.(1) and (2) only
D.(2) and (3) only
Young Modulus
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HKAL Exercise Chapter 7Properties of Matter
2.In an experiment to measure the Young modulus for steel in the form of a long wire, each measurement is made with the same percentage error. Which of the following measurements contributes the greatest error to the final result ?
A.the applied force
B.the length of the wire
C.the extension of the wire
D.The above 3 measurements will make an equal contribution.
3.Two copper wires, X and Y, are suspended vertically, and the same downward vertical force F is applied to the lower end of each wire. The extension of X is twice the extension of Y. Which of the following may account for this difference?
(1)X is twice as long as Y, but their diameters are equal.
(2)The diameter of X is half the diameter of Y, but their lengths are equals.
(3)Y is half as long as X, and its diameter is half that of X.
A.(1) onlyB.(2) only
C.(1) and (3) onlyD.(2) and (3) only
4.In an experiment to determine the Young modulus for a steel wire, a student obtained the following data :
length of steel wire= 1.74 m
diameter of steel wire= 0.79 mm
mass of the load = 11.00 kg
extension = 2.1 mm
acceleration of free fall= 9.8 m s-2
Which of the following leads to the greatest uncertainty in the calculated value of the Young modulus ?
A.measurement of length
B.measurement of diameter
C.measurement of extension
D.assumed value of the acceleration of free fall
5.A uniform wire is stretched under tension. The strain in the wire depends on
(1)the Young modulus of the wire.
(2)the unstretched length of the wire.
(3)the cross-sectional area of the wire.
A.(2) only
B.(3) only
C.(1) and (3) only
D.(1), (2) and (3)
6.Two wires X and Y of the same length and of the same elastic metal are each stretched to the same tension. The diameter of wire X is twice that of wire Y. The ratio of the elastic potential energy stored in wire X to that stored in wire Y is
A.1 : 1.
B.1 : 4.
C.2 : 1.
D.4 : 1.
7.A uniform wire of force constant k and Young modulus E is cut into four shorter wires of equal length. If they are arranged side by side and treated as a single wire combination, what are the force constant and the Young modulus for this combination ?
Force constantYoung modulus
A.2kE
B.4k 4E
C.16kE
D.16k 4E
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HKAL Exercise Chapter 7Properties of Matter
8.Figure 1 shows the force-extension graph for a length of steel wire A. The wire obeys Hooke’s law over the range of extensions considered.
Figure 1
(a)If the wire has a diameter of 0.50 mm and its unstretched length is 1.5 m, calculate the Young modulus of the steel. (2 marks)
(b)A second wire B is made of the same steel. It has the same unstretched length as A, but half the diameter. Draw accurately on the axes of Figure 1 the force-extension graph for this wire. Label your graph B. (1 mark)
(c)A student discovers that for a given force within the range considered above, the elastic energy stored by wire A is one fourth to that stored by wire B. Use the two graphs, or some other theoretical argument, to explain this fact. (1 mark)
(d)If the breaking stress of the steel is 4.0 ×108 N/m2, calculate the maximum force which can be applied longitudinally to wire A. (2 marks)
9.
Figure 2
In Figure 2, a 1.5 m long rigid rod of negligible mass is suspended from the ceiling by two 1.2 m long vertical wires attached to its ends A and B. The wire attached to the end A is an aluminium wire of diameter 1.5 ×10-3 m; and that attached to the other end B is a steel wire of diameter 0.9 ×10-3 m. Initially, the rod is precisely horizontal. The Young modulus and breaking stress of aluminium and brass are as follows (Assume that the change in cross-sectional area of the wires under stress is negligible.) :
Material / Young modulus / Pa / Breaking stress / Paaluminium
steel / 6.9 ×1010
20.8 ×1010 / 2.2 ×108
1.6 ×108
(a)A 5-kg mass is hung from the midpoint, C, of the rod. Assume that the elastic limits of both wires are not exceeded.
(i)Calculate the extensions of the two wires.(4 marks)
(ii)Find the angle that the rod makes with the horizontal.(2 marks)
(iii)In what direction should the 5-kg mass be shifted so that the two wires have equal extension ? State which wire is in a greater tension. (1 mark)
(b)The 5-kg mass is replaced with another mass hung at a distance, d, from end A. For a certain optimum value of d, the rod can support the maximum amount of mass without breaking either wire. (The angle between the rod and the horizontal is very small and therefore can be neglected.)
Calculate
(i)the maximum mass the rod can support,(3 marks)
(ii)the optimum value of d.(2 marks)
10.
Figure 3
In a typical solid model, layers of atoms are arranged in a cubic square lattice array with each atom at an equilibrium distance x from its nearest neighbours, both in its own layer and in the layers above or below. Suppose a long steel wire, with many layers, is stretched a little so that each layer is now x + Δx from those above or below it, as illustrated in Figure 3.
(a)What is the elastic strain produced ?(1 mark)
(b)Assume that the deformation is elastic, and that the binding force holding the pair of atom Ai and Bi (i = 1, 2,…) together when the wire is stretched can be considered as acting like a spring.
(i)If this ‘spring constant’ is k, what is the force between the Ai and Bi ?(1 mark)
(ii)If each layer contains N atoms, what is the total force between pairs of atoms in adjacent planes ? (1 mark)
(iii)Determine the elastic stress acting between the two layers of atoms.(3 marks)
(c)Use the information in (a) and (b) to determine an expression for the Young modulus of the solid. (2 marks)
(d)It is known that for brass, Young modulus is 1.2×1011 N/m2 and that the interatomic spacing is 0.35 nm.
(i)Estimate a value for k.(1 mark)
(ii)Suppose that a brass wire breaks at a tensile stress of 4×109 N/m2, estimate the increase in distance, Δx, between layers of atoms before breaking occurs. (2 marks)
Interpretation of stress-strain curve
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HKAL Exercise Chapter 7Properties of Matter
11.
Three wires of different material, but of the same length and cross-sectional area are stretched until they break. Their stress-strain curves are shown in the figure above. If E1, E2 and E3 represent the energy required to break wire 1, wire 2 and wire 3 respectively, which of the following is correct ?
A.E1E2E3
B.E2E1E3
C.E3E1E2
D.E3E2E1
12.
The graph above shows the tensile stress – tensile strain curves for three materials X, Y and Z up to their breaking points. Which of the following statements is/are correct ?
(1)X can be stretched to twice its original length without breaking.
(2)X is stiffer than Y.
(3)Z is stronger than Y.
A.(1) onlyB.(3) only
C.(1) and (2) only
D.(1), (2) and (3)
13.
A suspended fibre was stretched by an increasing load attached to the bottom end. Then it was allowed to contract by slowly reducing the load. A stress-strain graph was obtained as shown. Which one of the following conclusions may be deduced from the graph ?
(1)All the work done in stretching the fibre is converted into internal energy.
(2)The temperature of the fibre rises after it has been stretched and allowed to contract for a few times.
(3)Less work is done in stretching than is recovered in contracting.
A.(2) onlyB.(3) only
C.(1) and (2) onlyD.(2) and (3) only
14.A metal wire is gradually loaded until the elastic limit is exceeded, and then gradually unloaded. Which of the following graphs best represents the variation of stress with strain ?
A.B.
C.D.
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HKAL Exercise Chapter 7Properties of Matter
Properties of materials
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HKAL Exercise Chapter 7Properties of Matter
15.Equal and steadily increasing forces are applied to each of the following three wires: a carbon fibre, a steel wire and a brass wire. Numerical values for the Young modulus E, the ultimate tensile stress S, and the area of cross-section A of the wires are:
E/1010N/m2 / S/108
N/m2 / A/10-6
m2
carbon
fibre / 40 / 17 / 0.10
steel wire / 21 / 10 / 0.30
brass wire / 12 / 40 / 0.05
Which of the wires is the strongest and which of the wires will break first? Choose the combination satisfying both criteria.
StrongestWire which
wirewill break first
A.steel wirecarbon fibre
B.carbon wiresteel wire
C.brass fibrecarbon fibre
D.brass wirebrass wire
16.The breaking stress of a steel wire is 6.0 ×108 N/m2. If the steel wire is replaced by a similar piece which is twice as long, which of the following statements is/are true ?
(1)The work done in stretching the longer wire to the breaking point is the same as for the shorter wire.
(2)The extension when the longer wire breaks is twice as for the shorter wire.
(3)The stress needed to break the longer wire is 6.0 ×108 N/m2.
A.(1) only
B.(3) only
C.(2) and (3) only
D.(1), (2) and (3)
17.Which of the following materials satisfies the description : brittle, strong, stiff ?
A.steel
B.glass
C.concrete
D.wood
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HKAL Exercise Chapter 7Properties of Matter
18.Glass is a strong, stiff and brittle material. Sketch the stress-strain graph for glass and briefly explain why it is so described. (3 marks)
7.2Model of a Solid
Intermolecular Forces
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HKAL Exercise Chapter 7Properties of Matter
19.
The graph shows how the force F between two atoms in a solid varies with the distance r between them. Which of the following statements about the distances a and b marked on the graph is/are correct?
(1)The stiffness of the solid depends on the slope of the curve near a.
(2)b is the smallest possible separation of the atoms.
(3)a is the equilibrium separation of the two atoms.
A.(2) only
B.(3) only
C.(1) and (2) only
D.(1) and (3) only
20.
Two neighbouring molecules with separation r experience a force F between them. The graph shows how F varies with r. Which of the following statements is/are correct ?
(1)εis the equilibrium separation of the molecules.
(2)Hooke’s law follows from the linearity of the region LMN.
(3)Thermal expansion can be explained by the fact that the curve NPQ is not symmetrical about P.
A.(2) only
B.(3) only
C.(1) and (2) only
D.(2) and (3) only
21.Of the three common materials, copper, glass and rubber, which two best illustrate the properties described in the following statements when each is stretched under room temperature ?
(1)It obeys Hooke’s law almost up to its breaking point.
(2)It tolerates a large strain when exhibiting elastic behaviour.
(1)(2)
A.glasscopper
B.glassrubber
C.rubberglass
D.copperrubber
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HKAL Exercise Chapter 7Properties of Matter
Intermolecular Potential Energy
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HKAL Exercise Chapter 7Properties of Matter
22.
The figure above shows the variation of the potential energy V between two atoms with the distance r separating them. Which of the following statements is/are correct?
(1)The atoms will experience an attractive force when ra.
(2)The atoms will experience a repulsive force when ra.
(3)The atoms can be in equilibrium when r = b.
A.(1) onlyB.(3) only
C.(1) and (2) only
D.(2) and (3) only
23.
The graph above shows how the potential energy between molecules of a substance varies with their separation. Which of the following is an INCORRECT inference from the graph ?
A.The energy required to separate two molecules completely is E.
B.The larger the value of E, the higher is the melting point of the substance.
C.No resultant force acts on each molecule when r = r0.
D.The force between molecules is repulsive when rr0.
24.
The diagram above shows the variation of the potential energy U between neighbouring atoms in a solid with the separation r between them. Which of the following features of the curves best explains why the solid expands on heating ?
A.YZXYB.OHXZ
C.KYYWD.HKXY
25.
The potential energy, U, of a pair of atoms as a function of their separation, r, is shown for two crystalline solids P and Q. From these curves alone, one may conclude that
(1)the equilibrium separation of the atoms in P is greater than that in Q.
(2)the energy required to separate two atoms of P in equilibrium is less than that for Q.
(3)P is stiffer than Q.
A.(1) only
B.(1) and (3) only
C.(2) and (3) only
D.(1), (2) and (3)
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HKAL Exercise Chapter 7Properties of Matter
26.Let r be the separation of two molecules in a solid and U be the intermolecular potential energy of these two molecules. When r = ro, the attractive force between the two molecules is equal to their repulsive force. Let U = 0 when r = ro. Which of the following statement is INCORRECT ?
A.When rro, U decreases as r increases.
B.When r is very small, U is close to infinite.
C.When U is very large, the force between the two molecules is repulsive.
D.U is non-negative for all values of r.
Phases of matter
27.When the temperature of a solid is increased, what will happen to the average kinetic energy and the average potential energy of the molecules ?
average kineticaverage potential
energyenergy
A.increases no change
B.no change increases
C.increases increases
D.no change decreases
Young Modulus (from solid model)
28.
In an idealized atomic model of the material of a wire, each atom is in equilibrium at a distance x from its nearest neighbours, both in its own later and in the later above or below. There are n atoms per unit area within each layer. If the force required to increase the separation between two atoms from x to (x + Δx) is (kΔx), what is the longitudinal strain in the wire.
A.k/x
B.Δx/x
C.kΔx
D.nkΔx/x2
7.3Liquid
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HKAL Exercise Chapter 7Properties of Matter
Density
29.Which of the following are reasonable estimates of the density and volume of an adult human ?
Density / kg m-3 Volume / m3
A. 1 000 0.1
B. 1 000 0.01
C. 10 000 0.01
D. 10 000 0.001
Archimedes’Principle
30.
A wooden block of density 750 kg/m3 and volume 1.5 m3 is fastened to the bottom of a fresh-water pond as shown above. If the string suddenly breaks, the initial acceleration of the block will be close to
A.0.33 m/s2
B.3.33 m/s2
C.10 m/s2
D.13.33 m/s2
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HKAL Exercise Chapter 7Properties of Matter
Long Question
31.
Figure 4
A uniform cylindrical object of length 0.40 m and cross-sectional area 20 ×10-4 m2 is made of a material of density 750 kg/m3. It is held vertically with its upper surface protruding from water in a wide container as shown in Figure 4 (not drawn to scale). It is released at time t = 0 and sinks into the water, but it does not completely submerge.
(a)For this part of the question, i.e. part (a), you may assume that there is no loss of energy due to viscosity and that the cylinder remains upright.
(i)Find the equilibrium position of the object.
(Hint : When an object is partially immersed in a liquid, it experiences an upward force equal to the weight of the liquid displaced.) (1 mark)
(ii)Find the resultant force acting on the object in terms of the vertical displacement x from the equilibrium position. (3 marks)
(iii)Draw a sketch graph showing the force experienced by the object as a function of time t. (2 marks)
(iv)At what time will the object first return to its original position at t = 0 ?(2 marks)
(v)What is the maximum possible amplitude of this motion ? Explain your answer.
(2 marks)
(vi)Indicate how energy is conserved in this process.(2 marks)
(b)In practice, the assumptions of part (a) might not apply and the object would behave differently.
(i)Assuming that it remained upright, briefly describe the motion which would be observed in practice and explain how energy is conserved in this case. (2 marks)
(ii)For larger amplitudes of oscillation, the cylinder would not remain upright. Describe what you would expect to happen and explain briefly why this would be so.(2 marks)
7.4Fluid Dynamics
Equation of Continuity
32.
A pipe X of cross-sectional area 36 cm2 branches into two smaller pipes, Y of area 18 cm2 and Z of area 6 cm2. An incompressible liquid flows through the pipes and travels at a speed of 0.2 m/s in X and 0.1 m/s at Y. What is the speed of the fluid in Z?
A.0.1 m/sB.0.3 m/s
C.0.9 m/sD.1.2 m/s
Bernoulli’s Principle (Bernoulli’s equation)
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HKAL Exercise Chapter 7Properties of Matter
33.In fluid dynamics, which of the following assumptions is/are used in deriving Bernoulli’s equation?
(1)The fluid undergoes streamline flow.
(2)The fluid is compressible.
(3)No viscous force act on the fluid.
A.(1) only
B.(3) only
C.(1) and (2) only
D.(1) and (3) only
34.A liquid of density 1.00 ×103 kg m-3 flows along a horizontal pipe whose cross-sectional area changes from 15 ×10-6 m2 to 30 ×10-6 m2. Manometers (using the same liquid) are attached to the two sections of the pipe and the vertical difference between the levels of liquid in them is 15 mm. The rate of flow of the liquid mass in the pipe must be
(g may be taken to be 10 m/s2)
A.0.95 ×10-2 kg/s.
B.1.91 ×10-2 kg/s.
C.1.50 ×10-2 kg/s.
D.3.00 ×10-2 kg/s.
35.
The above diagram shows the steady flow of water through a horizontal uniform pipe with a central narrow section near Y. The water levels in manometers at X, Y and Z indicate the pressure in each section. The levels in Y and Z are NOT shown. Which of the following statements is/are correct ?
(1)The water speed in the narrow section is greater smaller than the speeds in other sections.
(2)The water speed in section Z is equal to that in section X.
(3)The water level in manometer Y is the lowest.
A.(1) only
B.(3) only
C.(1) and (2) only
D.(1), (2) and (3)
36.
The figure above shows part of a pipe having circular cross-sections. The area of the cross-section at B is double triple that at A and the centre of the cross-section at B is 0.6 m higher than that at A. If an ideal liquid flows steadily through the pipe with speed 2 m s-1 at A, what is the difference in static pressure between A and B ? (Given : density of the liquid is 1 000 kg m-3)
A.4 500 N m-2
B.6 000 N m-2
C.7 500 N m-2
D.10 000 N m-2
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HKAL Exercise Chapter 7Properties of Matter
Long Question
37.When a jet aeroplane is just taking off from the runway, the speed of the air stream over the top surface of its wings is 80 m/s, while the speed under the bottom surface is 30 m/s. Calculate the mass of the jet plane if the wings have an area of 220 m2.
(Density of air = 1.29 kg/m3, acceleration of free fall = 10 m/s2)(3 marks)
38.Figure 5 shows a petrol pump in a garage. The pump delivers petrol with a density of 800 kg/m3 at a rate of 1.5×10-2 m3/s. The input to the pump is from a pipe with a cross-sectional area A1 of 5×10-3 m2 at a suction pressure P1 of 2×104 Pa. The discharge of the pump is at a gauge pressure P2 of 3.5×105 Pa into a pipe with a cross-sectional area A2 of 15×10-4 m2. The pipes at the entrance and exit are at the same horizontal level and the temperature of the petrol remains constant throughout the flow.