(d) A student noticed that when a mass of 10.0 kg suspended from a wire identical to that described above was pushed down- wards and released, it executed vertical : oscillations of small amplitude. Use the graph to explain briefly why you would expect the oscillations to be simple harmonic. (b) () A force is required to cause an extension of a spring. Explain why this causes energy to be stored in the spring. (i) A spring of spring constant k under- goes an elastic change resulting in an extension x. Deduce that W, its strain energy, is given by w = kx? B60 (a) When materials áre stretched their beha- viour may be either elastic or plastic. Distinguish carefully between these (e) Atoy train, mass m, travels along a trackat speed v and is brought to rest by two spring buffers which are shown below. terms. (b) Whilst stretching a length of thin copper wire it is noticed that () at first a fairly strong pull is needed to stretch it by a small amount and that it stretches uniformly, (ii) beyond a certain point the wire extends by a very much larger amount for no farther increase in the pull, (ii) finally the wire breaks. Sketch a force-extension graph to ilus- trate the behaviour of this wire. Mark on it the region where the behaviour is elastic and the region where it is plastic. (L) Spring buffer Each buifer has spring constant k. (i) By considering the energy transfer, derive an expression to show how the maximum compression of the buffers varies with the initial speed of the train. B61 The force constan kofa spring is the constant of proportionality in the Hooke's law relation T = ke between tension T and extensicn e. (ii) Calculate the maximum compres- sion of the buffers for a train of mass m = 1.2 kg travelling with an initial speed v = 0.45 ms when the spring constant k of each buffer is 4.8 x 10'Nm . ll SNm 3Nm State and explain a reason why, in practice, spring buffers of this design [C, '92] A spring A of force constant 6Nm ' is connected in series with a spring B of force constant 3Nm ', as shown in the diagram. One end of the combination is securely anchored and a force of 0.6N is applied to the other end. are not used. FLUID FLOW (Chapter 12) (a) By how much does cach spring extend? (b) What is the force constant of the combi- nation? B63 (a) Explain the terms lines of flow and siream- [C) B62 (a) (i) Distinguish between clastic and plastic deformation of a material. (i) Šketch a graph to show how the extension x of a copper wire varies with F, the applied load. Mark on your sketch the region where the wire obeys Hooke's law. tines when applied to fluid flow and deduce the relationship between them in laminar flow. (b) State Bernoulli's equation, define the physical quantities which appear in it and the conditions required for its validity. (c) The depth of water in a tank oflarge tass sectional area is maintained at 20 cm anl
(d) A student noticed that when a mass of 10.0 kg suspended from a wire identical to that described above was pushed down- wards and released, it executed vertical : oscillations of small amplitude. Use the graph to explain briefly why you would expect the oscillations to be simple harmonic. (b) () A force is required to cause an extension of a spring. Explain why this causes energy to be stored in the spring. (i) A spring of spring constant k under- goes an elastic change resulting in an extension x. Deduce that W, its strain energy, is given by w = kx? B60 (a) When materials áre stretched their beha- viour may be either elastic or plastic. Distinguish carefully between these (e) Atoy train, mass m, travels along a trackat speed v and is brought to rest by two spring buffers which are shown below. terms. (b) Whilst stretching a length of thin copper wire it is noticed that () at first a fairly strong pull is needed to stretch it by a small amount and that it stretches uniformly, (ii) beyond a certain point the wire extends by a very much larger amount for no farther increase in the pull, (ii) finally the wire breaks. Sketch a force-extension graph to ilus- trate the behaviour of this wire. Mark on it the region where the behaviour is elastic and the region where it is plastic. (L) Spring buffer Each buifer has spring constant k. (i) By considering the energy transfer, derive an expression to show how the maximum compression of the buffers varies with the initial speed of the train. B61 The force constan kofa spring is the constant of proportionality in the Hooke's law relation T = ke between tension T and extensicn e. (ii) Calculate the maximum compres- sion of the buffers for a train of mass m = 1.2 kg travelling with an initial speed v = 0.45 ms when the spring constant k of each buffer is 4.8 x 10'Nm . ll SNm 3Nm State and explain a reason why, in practice, spring buffers of this design [C, '92] A spring A of force constant 6Nm ' is connected in series with a spring B of force constant 3Nm ', as shown in the diagram. One end of the combination is securely anchored and a force of 0.6N is applied to the other end. are not used. FLUID FLOW (Chapter 12) (a) By how much does cach spring extend? (b) What is the force constant of the combi- nation? B63 (a) Explain the terms lines of flow and siream- [C) B62 (a) (i) Distinguish between clastic and plastic deformation of a material. (i) Šketch a graph to show how the extension x of a copper wire varies with F, the applied load. Mark on your sketch the region where the wire obeys Hooke's law. tines when applied to fluid flow and deduce the relationship between them in laminar flow. (b) State Bernoulli's equation, define the physical quantities which appear in it and the conditions required for its validity. (c) The depth of water in a tank oflarge tass sectional area is maintained at 20 cm anl
Related questions
Question
Question B62
![218
SECTION B STRUCTURAL PROPERTIES OF MATTER
QUESTIONS ON SECTION B
219
•The force F, in N, of attraction between two
particles in a given solid varies with their
separation d, in m, according to the relation
B58 The end X of a uniform cylindrical.rod XY is
clamped in a fixed horizontal position. The
free end Y is depressed under the action of the
weight of the rod by a small amount d. The rod
projects a distance /from the point of clamping
X. The depression d is found to be directly
proportional to the ratio g/A where 'g is the
acceieration due to gravity and A the cross-
sectional area of the rod. Also, d depends on /
and the densityp and the Young modulus E of
the material cf the rod. Use the method of
dimensions to deternmine how d might depend
on !, p and E.
(d) A student noticed that when a mass of
10.0 kg suspended from a wire identical to
that described above was pushed down-
wards and released, it executed vertical
oscillations of small amplitude. Use the
graph to explain briefly why you would
expect the osciilations to be simple
harmonic.
(b) (i) A force is required to cause an
extension of a spring. Explain why
this causes energy to be stored in the
spring.
(ii) A spring of spring constant k under-
goes an elastic change resulting in an
extension x. Deduce that W, its strain
energy, is given by
7.8 x 10 20
3.0 x 10 96
d?
State, giving a reason, the resultant force
between the two particles at their equilibrium
separation. Calculate a value for this equili-
brium separation.
[J]
W = kx?
The graph (p. 217) displays a load against
extension plot for a metal wire of diameter
1.5 mm and original length 1.0 mm. When the
load reached the value at A the wire broke.
B60 (a) When materials åre stretched their beha-
viour may be cither elastic or plastic.
Distinguish carefully between these
(c) A toy train, mass m, travels along a track at
speed v and is brought to rest by two
spring buffers which are shown below.
terms.
(b) Whilst stretching a length of thin copper
wire it is noticed that
From the graph deduce values of
(a) the stress in the wire when it broke,
(b) the work done in breaking the wire,
(c) the Young modulus for the metal of the
wire.
Define elastic deformation. A wire of the same
metal as the above is required to support a load
of 1.0 kN without exceeding its elastic limit.
Calculate the minimum dianmeter of such a
Spring buffer
(i) at first a fairly strong pull is needed
to stretch it by a small amount and
that it stretches uniformly
(ii) beyond a certain point the wire
extends by a very much larger
amount for no further increase in
the pull,
(iii) finally the wire breaks.
Sketch a force-extension graph to illus-
trate the behaviour of this wire. Mark on it
the region where the behaviour is elastic
and the region where it is plastic.
How would you show experimentally the way
in which d varies with the length and radius of
the rod?
wire,
(O & C]
[0 & C*}
Each buffer has spring constant k.
(i) By considering the energy transfer,
derive an expression to show how the
maximum compression of the buffers
varies with the initial speed of the
(a) (i) Define stress and strain as related to
B59 (a) In order to determine Young's modulus for
(L)
the material of a wire in a school
laboratory, it is usual to apply a tensile
stress to the wire and to measure the tensile
strain produced. Explain the meanings of
the terms in italics and state the relation-
ship between them.
(b)
the extension of a wire.
(ii) A rubber cord and a steel wire are
each subjected to linear stress. Draw
sketch graphs showing how the
resultant strain of each sample
depends on the applied stress, and
point out any important differences
between the graphs.
(iii) Forsome materials, the strain-stress
curve obtained when the tension
applied to the specimen is being
increased may differ significantly
from that when the tension is being
decreased, even though no perma-
B61 The force constant kof a spring is the constant of
proportionality in the Hooke's law relation
T = ke between tension T and extension e.
train.
(ii) Calculate the maximum compres-
sion of the buffers for a train of mass
m = 1.2 kg travelling with an initial
speed v = 0.45 ms- when the
spring constant k of each buffer is
4.8 x 10 Nm '.
Additional
Scale
load/kg
reading mm
0.6N-
6Nm
3Nm
2.8
2,0
3.8
State and explain a reason why, in
practice, spring buffers of this design
are not used.
4.0
4.5
A spring A of force constant 6 Nm is
connected in series with a spring B of force
constant 3 N m', as shown in the diagram.
One end of the combination is securely
anchored and a force of 0.6 N is applied to
the other end.
6,0
5.1
[C, '92}
8.0
5.7
10.0
6.3
12.0
6.9
nent extension has been caused.
How may this phenomenon be
interpreted?
14.0
7.5
16.0
8.1
FLUID FLOW (Chapter 12)
(a) By how much does each spring extend?
(b) What is the force constant of the combi-
The tabie shows readings obtained when
stretching a wire supported at its upper
end by suspending masses from its lower
end. The unstretched length of the wire
was 2.23 m and its diameter 0.71 mm.
Using a graphical method, determine a
value for Young's modulus for the mate-
rial of the wire.
(c) Describe suitable apparatus for obtaining
the readings shown and explain the
important features of the design.
i ) Describe the important features of
the structure of a polymeric solid,
B63 (a) Explain the terms lines of flow and stream-
nation?
[C]
lines when applied to fluid flow and
deduce the relationship between them in
laminar flow.
such as rubber.
(i) Making reference to the curve you
have drawn for rubber in (a)(ii)
above, account for the behaviour of
rubber under linear stress in terms of
changes which may occur in the
internal structure of the polymer.
[I*]
B62 (a) (i) Distinguish between elastic and
plastic deformation of a material.
(ii) Sketch a graph to show how the
extension x of a copper wire varies
with F, the applied load. Mark on
your sketch the region where the wire
obeys Hooke's law.
(b) State Bernoulli's equation, define the
physical quantities which appear in it
and the conditions required for its
validity.
(c) The depth ofwater in a tank of large cros
sectional area is maintained at 20 cm and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ba1df1b-a579-4ec2-a934-74c558332424%2Ffa331696-2067-411f-9438-796c6948ec37%2Fnllgd4g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:218
SECTION B STRUCTURAL PROPERTIES OF MATTER
QUESTIONS ON SECTION B
219
•The force F, in N, of attraction between two
particles in a given solid varies with their
separation d, in m, according to the relation
B58 The end X of a uniform cylindrical.rod XY is
clamped in a fixed horizontal position. The
free end Y is depressed under the action of the
weight of the rod by a small amount d. The rod
projects a distance /from the point of clamping
X. The depression d is found to be directly
proportional to the ratio g/A where 'g is the
acceieration due to gravity and A the cross-
sectional area of the rod. Also, d depends on /
and the densityp and the Young modulus E of
the material cf the rod. Use the method of
dimensions to deternmine how d might depend
on !, p and E.
(d) A student noticed that when a mass of
10.0 kg suspended from a wire identical to
that described above was pushed down-
wards and released, it executed vertical
oscillations of small amplitude. Use the
graph to explain briefly why you would
expect the osciilations to be simple
harmonic.
(b) (i) A force is required to cause an
extension of a spring. Explain why
this causes energy to be stored in the
spring.
(ii) A spring of spring constant k under-
goes an elastic change resulting in an
extension x. Deduce that W, its strain
energy, is given by
7.8 x 10 20
3.0 x 10 96
d?
State, giving a reason, the resultant force
between the two particles at their equilibrium
separation. Calculate a value for this equili-
brium separation.
[J]
W = kx?
The graph (p. 217) displays a load against
extension plot for a metal wire of diameter
1.5 mm and original length 1.0 mm. When the
load reached the value at A the wire broke.
B60 (a) When materials åre stretched their beha-
viour may be cither elastic or plastic.
Distinguish carefully between these
(c) A toy train, mass m, travels along a track at
speed v and is brought to rest by two
spring buffers which are shown below.
terms.
(b) Whilst stretching a length of thin copper
wire it is noticed that
From the graph deduce values of
(a) the stress in the wire when it broke,
(b) the work done in breaking the wire,
(c) the Young modulus for the metal of the
wire.
Define elastic deformation. A wire of the same
metal as the above is required to support a load
of 1.0 kN without exceeding its elastic limit.
Calculate the minimum dianmeter of such a
Spring buffer
(i) at first a fairly strong pull is needed
to stretch it by a small amount and
that it stretches uniformly
(ii) beyond a certain point the wire
extends by a very much larger
amount for no further increase in
the pull,
(iii) finally the wire breaks.
Sketch a force-extension graph to illus-
trate the behaviour of this wire. Mark on it
the region where the behaviour is elastic
and the region where it is plastic.
How would you show experimentally the way
in which d varies with the length and radius of
the rod?
wire,
(O & C]
[0 & C*}
Each buffer has spring constant k.
(i) By considering the energy transfer,
derive an expression to show how the
maximum compression of the buffers
varies with the initial speed of the
(a) (i) Define stress and strain as related to
B59 (a) In order to determine Young's modulus for
(L)
the material of a wire in a school
laboratory, it is usual to apply a tensile
stress to the wire and to measure the tensile
strain produced. Explain the meanings of
the terms in italics and state the relation-
ship between them.
(b)
the extension of a wire.
(ii) A rubber cord and a steel wire are
each subjected to linear stress. Draw
sketch graphs showing how the
resultant strain of each sample
depends on the applied stress, and
point out any important differences
between the graphs.
(iii) Forsome materials, the strain-stress
curve obtained when the tension
applied to the specimen is being
increased may differ significantly
from that when the tension is being
decreased, even though no perma-
B61 The force constant kof a spring is the constant of
proportionality in the Hooke's law relation
T = ke between tension T and extension e.
train.
(ii) Calculate the maximum compres-
sion of the buffers for a train of mass
m = 1.2 kg travelling with an initial
speed v = 0.45 ms- when the
spring constant k of each buffer is
4.8 x 10 Nm '.
Additional
Scale
load/kg
reading mm
0.6N-
6Nm
3Nm
2.8
2,0
3.8
State and explain a reason why, in
practice, spring buffers of this design
are not used.
4.0
4.5
A spring A of force constant 6 Nm is
connected in series with a spring B of force
constant 3 N m', as shown in the diagram.
One end of the combination is securely
anchored and a force of 0.6 N is applied to
the other end.
6,0
5.1
[C, '92}
8.0
5.7
10.0
6.3
12.0
6.9
nent extension has been caused.
How may this phenomenon be
interpreted?
14.0
7.5
16.0
8.1
FLUID FLOW (Chapter 12)
(a) By how much does each spring extend?
(b) What is the force constant of the combi-
The tabie shows readings obtained when
stretching a wire supported at its upper
end by suspending masses from its lower
end. The unstretched length of the wire
was 2.23 m and its diameter 0.71 mm.
Using a graphical method, determine a
value for Young's modulus for the mate-
rial of the wire.
(c) Describe suitable apparatus for obtaining
the readings shown and explain the
important features of the design.
i ) Describe the important features of
the structure of a polymeric solid,
B63 (a) Explain the terms lines of flow and stream-
nation?
[C]
lines when applied to fluid flow and
deduce the relationship between them in
laminar flow.
such as rubber.
(i) Making reference to the curve you
have drawn for rubber in (a)(ii)
above, account for the behaviour of
rubber under linear stress in terms of
changes which may occur in the
internal structure of the polymer.
[I*]
B62 (a) (i) Distinguish between elastic and
plastic deformation of a material.
(ii) Sketch a graph to show how the
extension x of a copper wire varies
with F, the applied load. Mark on
your sketch the region where the wire
obeys Hooke's law.
(b) State Bernoulli's equation, define the
physical quantities which appear in it
and the conditions required for its
validity.
(c) The depth ofwater in a tank of large cros
sectional area is maintained at 20 cm and
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps with 10 images
