Showing posts with label Mechanics of Solids. Show all posts
Showing posts with label Mechanics of Solids. Show all posts

Saturday 24 October 2015

Different types of forces

There are different types of forces that act in different ways on structures such as bridges, chairs, buildings, in fact any structure. The main examples of forces are shown below. Study the diagram and text and then draw a diagram/ pictogram to represent each of these forces. 







A Static Load : A good example of this is a person seen on the left. He is holding a stack of books on his back but he is not moving. The force downwards is STATIC.
A Dynamic Load : A good example of a dynamic load is the person on the right. He is carrying a
weight of books but walking. The force is moving or DYNAMIC.

DYNAMIC LOAD (moving)                                     STATIC LOAD (standing still)

 

Internal Resistance : The person in the diagram is sat on the mono-bicycle and the air filled tyre is under great pressure. The air pressure inside it pushes back against his/her weight. 

INTERNAL RESISTANCE

Tension : The rope is in "tension" as the two people
pull on it. This stretching puts the rope in tension. 
TENSION



Compression : The weight lifter finds that his body
is compressed by the weights he is holding above
his head.

COMPRESSION

 

 Shear Force : A good example of shear force is
seen with a simple scissors. The two handles put
force in different directions on the pin that holds the
two parts together. The force applied to the pin is
called shear force.
                                                                                 SHEAR FORCE




 Torsion : The plastic ruler is twisted between both hands. The ruler is said to be in a state of torsion.
                                                              TORSION




Saturday 2 May 2015

Strength of Materials Multiple Choice Questions and Answers

Strength of Materials
Multiple Choice Questions and
Answers

1. The unit of force in S.I. units is
(a) kilogram
(b) newton
(c) watt
(d) dyne
(e) joule.
Ans: b
2. The unit of work or energy in S.I. units is
(a) newton
(b) pascal
(c) kilogram meter
(d) watt
(e) joule.
Ans: e
3. The unit of power in S.I. units is
(a) newton meter
(b) watt
(c) joule
(d) kilogram meter/sec.
(e) pascal per sec.
Ans: b
4. Forces are called concurrent when their lines of
action meet in
(a) one point
(b) two points
(c) plane
(d) perpendicular planes
(e) different planes.
Ans: a
5. Forces are called coplanar when all of them
acting on body lie in
(a) one point
(b) one plane
(c) different planes
(d) perpendicular planes
(e) different points.
Ans: b
6. A force acting on a body may
(a) introduce internal stresses
(b) balance the other forces acting on it
(c) retard its motion
(d) change its motion
(e) all of the above.
Ans: e
7. Which is the correct statement about law of
polygon of forces ?
(a) if any number of forces acting at a point can be
represented by the sides
of a polygon taken in order, then the forces are in
equilibrium
(b) if any number of forces acting at a point can be
represented in direction and magnitude by the sides
of a polygon, then the forces are in equilibrium
(c) if a polygon representing forces acting at a point
is closed then forces are in equilibrium
(d) if any number of forces acting at a point can be
represented in direction and magnitude by the sides
of a polygon taken in order, then the forces are in
equilibrium
(e) none of the above.
Ans: d
8. Effect of a force on a body depends upon
(a) magnitude
(b) direction
(c) position or line of action
(d) all of the above
(e) none of the above.
Ans: d
9. If a number of forces act simultaneously on
a particle, it is possible
(a) not a replace them by a single force
(b) to replace them by a single force
(c) to replace them by a single force through C.G.
(d) to replace them by a couple
(e) to replace them by a couple and a force.
Ans: b
11. A force is completely defined when we specify
(a) magnitude
(b) direction
(c) point of application
(d) all of the above
(e) none of the above.
Ans: d
12. If two equal forces of magnitude P act at an
angle 9°, their resultant will be
(a) P/2 cos 9/2
(b) IP sin 9/2
(c) 2P tan 9/2
(d) IP cos 9/2
(e) Psin 9/2.
Ans: d
13. The algebraic sum of the resolved parts of a
number of forces in a given direction is equal to the
resolved part of their resultant in the same
direction. This is as per the principle of
(a) forces
(b) independence of forces
(c) dependence of forces
(d) balance of force
(e) resolution of forces.
Ans: e
14. The resolved part of the resultant of two forces
inclined at an angle 9 in a given direction is equal to
(a) the algebraic sum of the resolved parts of the
forces in the given direction
(b) the sum of the resolved parts of the forces in
the given direction
(c) the difference of the forces multiplied by the
cosine of 9
(d) the sum of the forces multiplied by the sine of 9
(e) the sum of the forces multiplied by the tangent of
9.
Ans: a
15. Which of the following do not have identical
dimensions ?
(a) Momentum and impulse
(b) Torque and energy
(c) Torque and work
(d) Kinetic energy and potential energy
(e) Moment of a force and angular momentum.
Ans: e
16. Which of the following is not the unit of
distance ?
(a) angstrom
(b) light year
(c) micron
(d) millimeter
(e) milestone.
Ans: e
17. Which of the following is not the unit of power ?
(a) kW (kilowatt)
(b) hp (horse power)
(c) kcal/sec
(d) kg m/sec
(e) kcal/kg sec.
Ans: e
18. Which of the following is not the unit of work,
energy and heat ?
(a) kcal
(b) kg m
(c) kWhr
(d) hp
(e) hp hr.
Ans: d
19. Which of the following is not the unit of
pressure ?
(a) kg/cm
(b) ata
(c) atmosphere
(d) mm of wcl
(e) newton.
Ans: e
20. The weight of a body is due to
(a) centripetal force of earth
(b) gravitational pull exerted by the earth
(c) forces experienced by body in atmos-phere
(d) force of attraction experienced by par-ticles
(e) gravitational force of attraction towards the
centre of the earth.
Ans: e
21. The forces, which meet at one point, but their
lines of action do not lie in a plane, are called
(a) coplanar non-concurrent forces
(b) non-coplanar concurrent forces
(c) non-coplanar non-concurrent forces
(d) intersecting forces
(e) none of the above.
Ans: b
22. When trying to turn a key into a lock, following is
applied
(a) coplanar force
(b) non-coplanar forces
(c) lever
(d) moment
(e) couple.
Ans: e
23. Which of the following is not a scalar quantity
(a) time
(b) mass
(c) volume
(d) density
(e) acceleration.
Ans: e
24. According to principle of transmissibility of
forces, the effect of a force upon a body is
(a) maximum when it acts at the center of gravity of
a body
(b) different at different points in its line of action
(c) the same at every point in its line of action
(d) minimum when it acts at the C.G. of the body
(e) none of the above.
Ans: c
25. Which of the following is a vector quantity
(a) energy
(b) mass
(c) momentum
(d) angle
(e) speed.
Ans: c
26. The magnitude of two forces, which when acting
at right angle produce resultant force of VlOkg and
when acting at 60° produce resultant of Vl3 kg.
These forces are
(a) 2 and V6
(b) 3 and 1 kg
(c) V5andV5
(d) 2 and 5
(e) none of the above.
Ans: c
27. A number of forces acting at a point will be in
equilibrium if
(a) their total sum is zero
(b) two resolved parts in two directions at right
angles are equal
(c) sum of resolved parts in any two per-pendicular
directions are both zero
(d) all of them are inclined equally
(e) none of the above.
Ans: c
28. Two non-collinear parallel equal forces acting in
opposite direction
(a) balance each other
(b) constitute a moment
(c) constitute a couple
(d) constitute a moment of couple
(e) constitute a resultant couple.
Ans: c
29. According to principle of moments
(a) if a system of coplanar forces is in equilibrium,
then their algebraic sum is zero
(b) if a system of coplanar forces is in equilibrium,
then the algebraic sum of their moments about any
point in their plane is zero
(c) the algebraic sum of the moments of any two
forces about any point is equal to moment of
theiwesultant about the same point
(d) positive and negative couples can be balanced
(e) none of the above.
Ans: b
30. Which of the following is not a vector quantity
(a) weight
(b) velocity
(c) acceleration
(d) force
(e) moment.
Ans: a
31. According to law of triangle of forces
(a) three forces acting at a point will be in
equilibrium
(b) three forces acting at a point can be represented
by a triangle, each side being proportional to force
(c) if three forces acting upon a patticle are
represented in magnitude and direction by the sides
of a triangle, taken in order, they will be in
equilibrium
(d) if three forces acting at a point are in
equilibrium, each force is proportional to the sine of
the angle between the other two
(e) none of the above.
Ans: c
1033. If a rigid body is in equilibrium under the
action of three forces, then
(a) these forces are equal
(b) the lines of action of these forces meet in a point
(c) the lines of action of these forces are parallel
(d) (b) and (c) above
(e) none of the above.
Ans: d
1036. D' Alembert's principle is used for
(a) reducing the problem of kinetics to equivalent
statics problem
(b) determining stresses in the truss
(c) stability of floating bodies
(d) designing safe structures
(e) solving kinematic problems.
Ans: a
37. A heavy ladder resting on floor and against a
vertical wall may not be in equilibrium, if
(a) the floor is smooth, the wall is rough
(b) the floor is rough, the wall is smooth
(c) the floor and wall both are smooth surfaces
(d) the floor and wall both are rough sur-faces
(e) will be in equilibrium under all condi-tions.
Ans: c
38. According to Lami's theorem
(a) three forces acting at a point will be in
equilibrium
(b) three forces acting at a point can be represented
by a triangle, each side being proportional to force
(c) if three forces acting upon a particle are
represented in magnitude and
direction by the sides of a triangle, taken in order,
they will be in equilibrium
(d) if three forces acting at a point are in
equilibrium, each force is proportional to the sine of
the angle between the other two
(e) none of the above.
Ans: d
39. Two coplanar couples having equal and op-
posite moments
(a) balance each other
(b) produce a couple and an unbalanced force
(c) are equivalent
(d) produce a moment of couple
(e) can not balance each other.
Ans: e
40. A framed structure is perfect if it contains
members equal to
(a) 2n-3
(b) n-l
(c) '2n-l
(d) n - 2
(e) 3n-2.
where n = number of joints in a frame
Ans: a
42. The product of either force of couple with the
arm of the couple is called
(a) resultant couple
(b) moment of the forces
(c) resulting couple
(d) moment of the couple
(e) none of the above.
Ans: d
43. In detennining stresses in frames by methods of
sections, the frame is divided into two parts by an
imaginary section drawn in such a way as not to cut
more than
(a) two members with unknown forces of the frame
(b) three members with unknown forces of the
frame
(c) four members with unknown forces of the frame
(d) three members with known forces of the frame
(e) four members with two known forces.
Ans: b
44. The center of gravity of a uniform lamina lies at
(a) the center of heavy portion
(b) the bottom surface
(c) the mid point of its axis
(d) all of the above
(e) none of the above.
Ans: c
45. Center of gravity of a solid cone lies on the axis
at the height
(a) one-fourth of the total height above base
(b) one-third of the total height above base
(c) one-half of the total height above base
(d) three-eighth of the total height above the base
(e) none of the above.
Ans: a
46. Center of percussion is
(a) the point of C.G.
(b) the point of metacentre
(c) the point of application of the resultant of all the
forces tending to cause a body to rotate about a
certain axis
(d) point of suspension
(e) the point in a body about which it can rotate
horizontally and oscillate under the influence of
gravity.
Ans: c
47. Center of gravity of a thin hollow cone lies on
the axis at a height of
(a) one-fourth of the total height above base
(b) one-third of the total height above base
(c) one-half of the total height above base
(d) three-eighth of the total height above the base
(e) none of the above.
Ans: b
48. The units of moment of inertia of an area are
(a) kg m2
(b) m4
(c) kg/m2
(d) m3
(e) kg/m4.
Ans: b
49. The center of percussion of the homogeneous
rod of length L suspended at the top will be
(a) L/2
(b) L/3
(c) 3L/4
(d) 2L/3
(e) 3L/8.
Ans: d
50. The center of gravity of a triangle lies at the
point of
(a) concurrence of the medians
(b) intersection of its altitudes
(c) intersection of bisector of angles
(d) intersection of diagonals
(e) all of the above.
Ans: a
51. The units of moment of inertia of mass are
(a) kg m2
(b) m4
(c) kg/m2
(d) kg/m
(e) m2/kg.
Ans: a
52. The possible loading in various members of
framed structures are
(a) compression or tension
(b) buckling or shear
(c) shear or tension
(d) all of the above
(e) bending.
Ans: a
53. A heavy string attached at two ends at same
horizontal level and when central dip is very small
approaches the following curve
(a) catenary
(b) parabola
(c) hyperbola
(d) elliptical
(e) circular arc.
Ans: b
54. A trolley wire weighs 1.2 kg per meter length.
The ends of the wire are attached to two poles 20
meters apart. If the horizontal tension is 1500 kg
find the dip in the middle of the span
(a) 2.5 cm
(b) 3.0 cm
(c) 4.0 cm
(d) 5.0 cm
(e) 2.0 cm.
Ans: c
55. From a circular plate of diameter 6 cm is cut out
a circle whose diameter is a radius of the plate.
Find the e.g. of the remainder from the center of
circular plate
(a) 0.5 cm
(b) 1.0 cm
(c) 1.5 cm
(d) 2.5 cm
(e) 0.25 cm.
Ans: a
58. Pick up the incorrect statement from the
following :
(a) The C.G. of a circle is at its center
(b) The C.G. of a triangle is at the intersection of its
medians
(c) The C.G. of a rectangle is at the inter-section of
its diagonals
(d) The C.G. of a semicircle is at a distance of r/2
from the center
(e) The C-G. of an ellipse is at its center.
Ans: d
59. The centre of percussion of a solid cylinder of
radius r resting on a horizontal plane will be
(a) r/2
(b) 2r/3
(c) r/A
(d) 3r/2
(e) 3r/A.
Ans: d
62. In the equation of virtual work, following force is
neglected
(a) reaction of any smooth surface with which the
body is in contact
(b) reaction of a rough surface of a body which rolls
on it without slipping
(c) reaction at a point or an axis, fixed in space,
around which a body is con-strained to turn
(d) all of the above
(e) none of the above.
Ans: d
63. If a suspended body is struck at the centre of
percussion, then the pressure on die axis passing
through the point of suspension will be
(a) maximum
(b) minimum
(c) zero
(d) infinity
(e) same as the force applied.
Ans: c
65. The resultant of the following three couples 20
kg force, 0.5 m arm, $ ve sense 30 kg force, 1 m
arm, - ve sense 40 kg force, 0.25 m arm, + ve
sense having arm of 0.5 m will be
(a) 20 kg, - ve sense
(b) 20 kg, + ve sense
(c) 10 kg, + ve sense
(d) 10 kg, - ve sense
(e) 45 kg, + ve sense.
Ans: a
68. Angle oT friction is the
(a) angle between normal reaction and the resultant
of normal reaction and the limiting friction
(b) ratio of limiting friction and normal reaction
(c) the ratio of minimum friction force to the friction
force acting when the body is just about to move
(d) the ratio of minimum friction force to friction
force acting when the body is in motion
(e) ratio of static and dynamic friction.
Ans: a
69. The coefficient of friction depends on
(a) area of contact
(b) shape of surfaces
(c) strength of surfaces
(d) nature of surface
(e) all of the above.
Ans: d
70. Least force required to draw a body up the
inclined plane is W sin (plane inclination + friction
angle) applied in the direction
(a) along the plane
(b) horizontally
(c) vertically
(d) at an angle equal to the angle of friction to the
inclined plane
(e) unpredictable.
Ans: d
71. The ratio of limiting friction and normal reaction
is known as
(a) coefficient of friction
(b) angle of friction
(c) angle of repose
(d) sliding friction
(e) friction resistance.
Ans: a
72. Which one of the following statements is not
correct
(a) the tangent of the angle of friction is equal to
coefficient of friction
(b) the angle of repose is equal to angle of friction
(c) the tangent of the angle of repose is equal to
coefficient of friction
(d) the sine of the angle of repose is equal to
coefficient to friction
(e) none of the above.
Ans: d
73. On a ladder resting on smooth ground and
leaning against vertical wall, the force of friction will
be
(a) towards the wall at its upper end
(b) away from the wall at its upper end
(c) upwards at its upper end
(d) downwards at its upper end
(e) none of the above.
Ans: c
74. On the ladder resting on the ground and leaning
against a smooth vertical wall, the force of friction
will be
(a) downwards at its upper end
(b) upwards at its upper end
(c) perpendicular to the wall at its upper end
(d) zero at its upper end
(e) none of the above.
Ans: d
76. Frictional force encountered after
commencement of motion is called
(a) post friction
(b) limiting friction
(c) kinematic friction
(d) frictional resistance
(e) dynamic friction.
Ans: e
77. Coefficient of friction is the
(a) angle between normal reaction and the resultant
of normal reaction and the limiting friction
(b) ratio of limiting friction and normal reaction
(c) the friction force acting when the body is just
about to move
(d) the friction force acting when the body is in
motion
(e) tangent of angle of repose.
Ans: b
78. Pick up wrong statement about friction force for
dry surfaces. Friction force is
(a) proportional to normal load between the
surfaces
(b) dependent on the materials of contact surface
(c) proportional to velocity of sliding
(d) independent of the area of contact surfaces
(e) none of the above is wrong statement.
Ans: c
79. A body of weight W on inclined plane of a being
pulled up by a horizontal force P will be on the point
of motion up the plane when P is equal to
(a) W
(b) W sin (a + $)
(c) Wtan(a + <|))
(d) W\an(a-<t>)
(e) Wtana.
Ans: c
80. A particle moves along a straight line such that
distance (x) traversed in t seconds is given by x =
t2 (t - 4), the acceleration of the particle will be
given by the equation
(a) 3t2-lt
(b) 3t2+2t
(c) 6f-8
(d) 6f-4
(e) 6t2-8t.
Ans: c
81. If rain is falling in the opposite direction of the
movement of a pedestrain, he has to hold his
umbrella
(a) more inclined when moving
(b) less inclined when moving
(c) more inclined when standing
(d) less inclined when standing
(e) none of the above.
Ans: d
86. A projectile is fired at an angle 9 to the vertical.
Its horizontal range will be maximum when 9 is
(a) 0°
(b) 30°
(c) 45°
(d) 60°
(e) 90°.
Ans: c
88. Limiting force of friction is the
(a) tangent of angle between normal-reaction and
the resultant of normal reaction and limiting friction
(b) ratio of limiting friction and normal reaction
(c) the friction force acting when the body is just
about to move
(d) the friction force acting when the body is in
motion
(e) minimum force of friction.
Ans: c
89. Coulomb friction is the friction between
(a) bodies having relative motion
(b) two dry surfaces
(c) two lubricated surfaces
(d) solids and liquids
(e) electrically charged particles.
Ans: a
90. Dynamic friction as compared to static friction
is
(a) same
(b) more
(c) less
(d) may be less of more depending on nature of
surfaces and velocity
(e) has no correlation.
Ans: c
92. Tangent of angle of friction is equal to
(a) kinetic friction
(b) limiting friction
(c) angle of repose
(d) coefficient of friction
(e) friction force.
Ans: d
93. Kinetic friction is the
(a) tangent of angle between normal reac-tion and
the resultant of normal reac-tion and the limiting
friction
(b) ratio of limiting friction and normal reaction
(c) the friction force acting when the body is just
about to move
(d) the friction force acting when the body is in
motion
(e) dynamic friction.
Ans: d
95. The effort required to lift a load W on a screw
jack with helix angle a and angle of friction <j) is
equal to
(a) Wtan(a + <)>)
(b) Wtan(a-<)>)
(c) Wcos(a + <t>)
(d) Wsin(a + <(>)
(e) W (sin a + cos <j>).
Ans: a
96. A semi-circular disc rests on a horizontal
surface with its top flat surface horizontal and
circular portion touching down. The coefficient of
friction between semi-cricular disc and horizontal
surface is \i. This disc is to be pulled by a horizontal
force applied at one edge and it always remains
horizontal. When the disc is about to start moving,
its top horizontal force will
(a) remain horizontal
(b) slant up towards direction of pull
(c) slant down towards direction of pull
(d) unpredictable
(e) none of the above.
Ans: c
97. A particle inside a hollow sphere of radius r,
having coefficient of friction -rr can rest upto height
of
(a) r/2
(b) r/A
(c) r/%
(d) 0.134 r
(e) 3r/8.
Ans: d
98. The algebraic sum of moments of the forces
forming couple about any point in their plane is
(a) equal to the moment of the couple
(b) constant
(c) both of above are correct
(d) both of above are wrong
(e) none of the above.
Ans: a
99. A single force and a couple acting in the
same plane upon a rigid body
(a) balance each other
(b) cannot balance each other
(c) produce moment of a couple
(d) are equivalent
(e) none of the above.
Ans: b
100. If three forces acting in one plane upon a rigid
body, keep it in equilibrium, then they must either
(a) meet in a point
(b) be all parallel
(c) at least two of them must meet
(d) all the above are correct
(e) none of the above.
Ans: d
101. The maximum frictional force which comes
into play when a body just begins to slide over
another surface is called
(a) limiting friction
(b) sliding friction
(c) rolling friction
(d) kinematic friction
(e) dynamic friction.
Ans: a
102. The co-efficient of friction depends upon
(a) nature of surfaces
(b), area of contact
(c) shape of the surfaces
(d) ail of the above.
(e) (a) and (b) above.
Ans: a
104. The necessary condition for forces to be in
equilibrium is that these should be
(a) coplanar
(b) meet at one point ;
(c) both (a) and (b) above
(d) all be equal
(e) something else.
Ans: c
105. If three forces acting in different planes can be
represented by a triangle, these will be in
(a) non-equilibrium
(b) partial equilibrium
(c) full equilibrium
(d) unpredictable
(e) none of the above.
Ans: a
106. If n = number of members andy = number of
joints, then for a perfect frame, n =
(a) j-2
(b)2j-l
(c) 2/-3
(d)3/-2
(e) 2/ -4.
Ans: c
107. A body moves, from rest with a constant
acceleration of 5 m per sec. The distance covered
in 5 sec is most nearly
(a) 38 m
(b) 62.5 m
(C) 96 m
(d) 124 m
(e) 240 m.
Ans: b
108. A flywheel on a motor goes from rest to 1000
rpm in 6 sec. The number of revolutions made is
nearly equal to
(a) 25
(b) 50
(c) 100
(d) 250
(e) 500.
Ans: b
109 Which of the following is the locus of a point
that moves in such a manner that its distance from
a fixed point is equal to its distance from a fixed line
multiplied by a constant greater than one
(a) ellipse
(b) hyperbola
(c) parabola
(d) circle
(e) none of the above.
Ans: b
111. Which of the following is not the unit of energy
(a) kg m
(b) kcal
(c) wattr
(d) watt hours
(e) kg m x (m/sec)2.
Ans: c
112. A sample of metal weighs 219 gms in air, 180
gms in water, 120 gms in an unknown fluid. Then
which is correct statement about density of metal
(a) density of metal can't be determined
(b) metal is twice as dense as water
(c) metal will float in water
(d) metal is twice as dense as unknown fluid
(e) none of the above.
Ans: a
113. The C.G. of a solid hemisphere lies on the
central radius 3r
(a) at distance — from the plane base 3r
(b) at distance — from the plane base 3r
(c) at distance — from the plane base 3r
(d) at distance — from the plane base or
(e) at distance — from the plane base.
Ans: d
117. The C.G. of a plane lamina will not be at its
geometrical centre in the case of a
(a) right angled triangle
(b) equilateral triangle
(c) square
(d) circle
(e) rectangle.
Ans: a
119. The C.G. of a right circular solid cone of height
h lies at the following distance from the base
(a) h/2
(b) J/3
(c) h/6
(d) h/4
(e) 3/i/5.
Ans: d
122. The M.I. of hollow circular section about a
central axis perpendicular to section as compared
to its M.I. about horizontal axis is
(a) same
(b) double
(c) half
(d) four times
(e) one fourth.
Ans: b
126. Which of the following is the example of lever
of first order
(a) arm of man
(b) pair of scissors
(c) pair of clinical tongs
(d) all of the above
(e) none of the above.
Ans: d
127. A pair of smith's tongs is an example of the
lever of
(a) zeioth order
(b) first order
(c) second order
(d) third order
(e) fourth order.
Ans: c
128. In the lever of third order, load W, effort P and
fulcrum F are oriented as follows
(a) W between P and F
(b) F between W and P
(c) P between W and F
(d) W, P and F all on one side
(e) none of the above.
Ans: a
129. The angle which an inclined plane makes with
the horizontal when a body placed on it is about to
move down is known as angle of
(a) friction
(b) limiting friction
(c) repose
(d) kinematic friction
(e) static friction.
Ans: c
130. In actual machines
(a) mechanical advantage is greater than velocity
ratio
(b) mechanical advantage is equal to velocity
ratio
(c) mechanical advantage is less than velocity ratio
(d) mechanical advantage is unity
(e) none of the above.
Ans: c
131. In ideal machines
(a) mechanical advantage is greater than velocity
ratio
(b) mechanical advantage is equal to velocity
ratio
(c) mechanical advantage is less than velocity ratio
(d) mechanical advantage is unity
(e) none of the above.
Ans: b
132. A cable with a uniformly distributed load per
horizontal metre run will take the following shape
(a) straight line
(b) parabola
(c) hyperbola
(d) elliptical
(e) part of a circle.
Ans: b

Friday 18 July 2014

Thermodynamics vs. kinetics in chemical reactions

Thermodynamics vs. kinetics in chemical reactions
Thermodynamics dictates equilibrium (which says whether
this reaction will take place).
Says nothing about what rate (how fast) the reaction will
be.
In a spontaneous reaction, ΔG is negative. When ΔG is
negative, reaction is spontaneous.
ΔG (Gibbs free energy) follows this fomula : ΔG=ΔH - TΔS.
It is largely dependent on two concepts :
Enthalpy : ΔH. Negative values of this (i.e. exothermic)
decrease ΔG, making the reaction more favorable.
Entropy : - TΔS. The T represents temperature. The S
represents entropy, or a measurement of disorder. This
term in the equation is negative and temperature is
always positive. Therefore, increasing the change in
entropy (positive ΔS) makes the reaction more favorable.
The endothermic or exothermic qualities of a reaction are
indicated by ΔH (enthalpy).
Negative enthalpy indicates exothermic reaction
Positive enthalpy indicates endothermic reaction
Note that because ΔG is dependent on both enthalpy and
entropy, it is possible for endothermic reactions to proceed
spontaneously.
Thermodynamics is independent of reaction mechanism
(concerned with original and final states only).
Thermodynamics concerns the equilibrium constant K
(upper-case).
Kinetics involves the rate of the reaction
Kinetics is affected by catalysts. The rate of the reaction
involves the activation energy. Catalysts lower the
activation energy, which causes the reaction to speed up.
Kinetics concerns the rate constant k (lower-case).
Examples of thermodynamics-kinetics feuds :
Combustion (aka burning) of my physical chemistry book
is thermodynamically favored. Unfortunately, it is not
favored kinetically because the activation energy for the
combustion reaction is too high for the present conditions.
One could always invest a little energy in the form of a
flame and start the reaction. The energy produced from the
combustion would supply the activation energy of the next
reaction.
The conversion of diamond into graphite is
thermodynamically favored (negative ΔG.) The speed of
this reaction is just too darn incredibly slow for a diamond
to turn into graphite.
Thermodynamics
Kinetics
Determines
Equilibrium (product vs. reactant)
Speed of reaction
Constant
K (uppercase) = equilibrium constant
k (lowercase) = rate constant
Determined by
ΔG (enthalpy and entropy)
activation energy
Buzzwords
Entropy, enthalpy, Gibbs free energy, spontaneous, endo-
and exothermic, equilibrium
Rate, speed, time, catalyst, enzyme, activation energy,
reaction order, first-order, second-order, rate-limiting step,
bottleneck

Kinetics vs Thermodynamics

Kinetics vs Thermodynamics
Table of Contents
1. Introduction
2. Kinetics Overview
3. Thermodynamics Overview
4. Thermodynamics vs. Kinetics
5. Outside links
6. References
7. Problems
8. Answers
9. Contributors
Kinetics and thermodynamics are related to each other in
ways that can be explained by using chemical reactions. A
discussion of kinetics and thermodynamics requires an
explanation of the underlying relationships between the
two, through application to chemical reactions and several
examples from natural processes.
Introduction
It is important to mention that a chemical reaction has
kinetic and thermodynamic aspects. The quantity related
to kinetics is the rate constant k; this constant is
associated with the activation energy required for the
reaction to proceed, that is, the reactivity of the reactants.
The thermodynamic quantity is the energy difference
resulting from the free energy (ΔG) given off during a
chemical reaction—the stability of the products relative to
the reactants. Although kinetics describes the rates of
reactions and how fast equilibrium is reached, it gives no
information about conditions once the reaction equilibrates.
In the same measure, thermodynamics only gives
information regarding the equilibrium conditions of products
after the reaction takes place, but does not explain the rate
of reaction.
Kinetics Overview
The rate constant, k, measures how fast a chemical
reaction reaches equilibrium assuming the reactants were
supplied with enough activation energy to enable the
reaction to proceed in the forward direction—reactants to
products. This requirement for input of energy symbolizes
the fact that the reactants are unreactive under certain
conditions The reaction must have some sort of energy
input before it can proceed; otherwise, the reactants
cannot cross the activation energy threshold and convert
to products. The reaction is activated by energy supplied
to the reactants by different energy sources. The rate of
reaction , the rate constant, and the kinetic energy required
for activation of reaction indicate how fast the reaction
reaches equilibrium. See Diagram #1.
Diagram #1: Depicted in the graph below are the main
points discussed in the previous paragraph. The transition
state represents a threshold the reactants must pass
before the reaction can proceed in the forward direction.
The activation energy is the energy required to reach the
transition state. Once this threshold is reached, the
reaction proceed in the favorable "downhill" direction. It is
important to remember that each reaction has a different
transition state threshold, with different activation
energies, and determined by the reactants and the
conditions in which the reaction is taking place. The value
of k is affected by these two factors, and can be increased
in the presence of a catalyst (such as an enzyme), which
increases reaction rate. In chemical reactions, specifically,
the catalyst can both provide more energy to the reactants
and lower the transition state energy. The provider of
activation energy can also be a spark, heat, or anything
else that gives off energy. Regardless of what provides the
activation energy, a kinetic or nonspontaneous reaction is
one in which the most stable state is that of the
reactants. The change in energy between the reactants
and products, also known as ΔG, relates to
thermodynamics and will be discussed shortly.
Diagram #1 link: http://www4.nau.edu/meteorite/
Meteorite/Images/EnergyDiagram.jpg
Example 1: Fuel
The gas in a fuel tank is not "wasted" or burnt away while
the car is sitting in the parking lot. Fuel is unreactive
under standard conditions; the spark created while turning
on the engine is what provides the activation energy to the
reactants, beginning the process of fuel-burning that
powers the car. For more information about the way fuel-
burning reactions are driven, visit 'outside link' number 1.
For a video that shows why two elements do not
spontaneously combust (as fuel would, had it not needed
activation energy), go to 'outside link' number 5.
Thermodynamics Overview
Thermodynamics can be considered in terms of the energy
stored within a reaction, a reactant, or a product. Most
often, thermodynamics is thought of as the different forms
of energy that are converted every time a reaction emits
energy or is initiated by energy. With respect to Gibbs free
energy (ΔG), thermodynamics refers to either (1) the
energy released during a reaction, in which case ΔG will be
negative and the reaction exergonic or spontaneous, or (2)
the energy consumed during a reaction, in which case ΔG
will be positive and the reaction endergonic or
nonspontaneous. A thermodynamic reaction favors the
products, resulting in a spontaneous reaction that occurs
without the need to constantly supply energy. This
indicates that the reactions' most stable state is that of
the products.
Thus, going back to Diagram #1, thermodynamics is what
describes the free energy between the reactants and the
products. Because thermodynamic values apply only after
the reactants have turned into products, they are said to
describe the equilibrium state. The relationship between
free energy (aka, Gibbs free energy) and other
thermodynamic quantities is expressed mathematically in
the following equation:
Because "U" is the variable representing the internal
energy of a system, it is closely correlated with the free
energy. Changes in internal energy change the value of the
free energy, in turn affecting chemical reactions in several
ways: the rate of reaction, whether the reaction is
spontaneous or non-spontaneous, and even whether or not
activation energy will be needed to initiate the reaction.
Example 2: Systems
The best way to understand thermodynamics is by
realizing that anything that transfers, receives, or contains
heat can be described as a system. Heat can enter or
leave a system, which affects the amount of thermal
energy it contains. Consider a kettle of water sitting on a
stove. As it is heated, thermal energy is added to the
system (the kettle with the water). As the stove is turned
off, the kettle cools down as the heat diffuses back to the
room; the kettle slowly equilibrates to room temperature.
This is an example of the system losing thermal energy.
To view an animated diagram of a thermodynamic system,
click on 'Outside Link' number 2.
Thermodynamics vs. Kinetics
As mentioned above, the most stable states of a kinetic
reaction are those of the reactants, in which an input of
energy is required to move the reaction from a state of
stability, to that of reacting and converting itself to
products. Kinetics is related to reactivity. In contrast, the
most stable state of a thermodynamically favorable
reaction is the products, because the reaction occurs
spontaneously, without the need for energy to be added.
Thermodynamics is related to stability .
Therefore, something that is unreactive will desire to stay
in the form of reactants, which will require an input of
energy to cause the reaction to go forward, converting
reactants into products. This is illustrated in example #3
below. A reactive species does not require an input of
energy to be converted from reactants to products,
because its most stable and preferred state is that of the
products. Instead, a thermodynamically favorable reaction
requires energy to be converted from products back to
reactants.An energy source moves the reaction forward
(kinetics corresponds to movement). The same is for
thermodynamically favorable reactions, except that the
reaction must be stimulated backward from products to
reactants.
Example 3: ATP
Adenosine triphosphate, also known as ATP, provides the
energy cells require in order to maintain metabolic
pathways, DNA synthesis and repair, and any other cellular
function necessary for survival. ATP itself is a reactive
molecule that has three phosphate groups. Molecules tend
toward stable states, converting to states of lower
energies. Thus, ATP, a high-energy molecule, tends to lose
a phosphate group and become adenosine diphosphate,
ADP. In order for this to happen, an enzyme strips one
phosphate group off of ATP, converting it to the more
stable molecule ADP. This enzyme provides the energy of
activation that enables ATP to become ADP, indicating
that ATP is kinetically stable.
Example 4: Water and Sugar
The following example involves solvents and polarity:
consider a simple situation, a spoonful of sugar is added to
a cup of water. If the two are left to react, over time the
sugar dissolves in the water, becoming the product of
sugar+water. The natural charges and polarity of water
causes the sugar molecules to react with it, eventually
dissolving within the water. There is no required input of
energy, indicating that this reaction is thermodynamically
favorable, and therefore spontaneous. Clearly, the two
reactants prefer to react and maintain stability as
products.
Note: although this is a thermodynamically favorable or
spontaneous reaction and does not require energy input,
the use of kinetic energy will force this reaction to happen
faster. If sugar is added to the cup of water and the
system is heated, the kinetic energy of the reactants is
increased by the thermal energy of the heat, which causes
the molecules to react with one another at a much faster
rate than if they been left alone at room temperature. This
is an example of how thermodynamics and kinetics are
closely related.
Outside links
1. Fuel Reactions and Kinetics: http://
www.explainthatstuff.com/fuelcells.html
2. Thermodynamic System: http://
upload.wikimedia.org/wikipedia/commons/8/8a/
Triple_expansion_engine_animation.gif
3. Nonspontaneous Reaction (compare with Diagram #
1): http://www.biology.arizona.edu/biochemistry/
problem_sets/energy_enzymes_catalysis/
graphics/16t.gif
4. Thermodynamics: http://en.wikipedia.org/wiki/
Thermodynamics#Thermodynamic_systems
5. Demonstration of two kinetically-stable elements in
a mixture, after given enough energy of activation:
http://www.metacafe.com/watch/908325/solid_
rocket_fuel_ignition/
References
1. Journal of Coordination Chemistry, Volume 62, Issue
1 Oct. 2009, pages 108-109
2. Thermodynamic stability and crystal structure of
lanthanide complexes with di-2-pyridyl ketone. S.
Dom iacute nguez a; J. Torres b; J. Gonz aacute lez-
Platas c; M. Hummert d; H. Schumann - e; C.
Kremer b
3. Role of Solvation Barriers in Protein Kinetic Stability.
RODRIGUEZ-LARREA David ; MINNING Stefan ;
BORCHERT Torben V. ; SANCHEZ-RUIZ Jose M.
Problems
1. Is it possible that graphite is thermodynamically
stable and diamond is less reactive under standard
conditions?
2. Explain how kinetics relate to thermodynamics. Use
the terms 'energy of motion', 'energy of heat', and an
example from the module in your answer.
3. Why would it be beneficial for a thermodynamically-
stable reaction to use an energy input in the form of
an enzyme or a catalyst even if it does not require
energy to proceed?
4. How come gas does not spontaneously combust
inside a fuel tank?
5. How is the rate constant k related to equilibrium?
How does the rate constant change if heat is added
to the reaction?
6. If the difference in energy between the reactants and
products is negative, is the reaction spontaneous or
nonspontaneous?
Answers
1. Yes. Their different structures will differentiate their
polarity and charge, and will cause the two
compounds to act differently. Thus, one can be
thermodynamically stable, while the other can be
less reactive.
2. The energy of motion is related to kinetics, which
determines how fast the reaction will reach
equilibrium, related to thermodynamics. The energy
of motion (kinetics) added to a reaction causes the
reaction to happen faster, using energy of heat as a
way by which to accelerate the reaction. An example
of this is the cup of water with the sugar while it is
being heated. The heat energy converts into kinetic
energy (energy of motion), accelerating the reaction
between the water molecules and the sugar crystals.
3. A catalyst or enzyme will still be beneficial in a
thermodynamically-favorable reaction because it will
simply accelerate it.
4. Fuel is unreactive to standard conditions and regular
atmosphere, which means it'll require an energy input
in order to react. The energy input is the spark
caused by the ignition of the car.
5. The rate constant k is related to equilibrium in that
it tells us about how fast the reaction reaches
equilibrium. If heat is added to a reaction, its rate
will increase due to increased kinetic energy.
6. The reaction will be spontaneous, thermodynamically
favorable. This is because the energy is given-off,
not consumed by the reaction.

Tuesday 8 July 2014

Newton’s Third Law of Motion

Newton’s Third Law of Motion


Newton's third law of motion was discovered and formulated, during the investigation of the fact that in all experiments it appeared that "whenever a body exerts a force on a second appeared that "whenever a body exerts a force on a second body, the second body always exerts a force on the first one".
        Let us visualize and understand this phenomena with an experiment:
        Suppose, we throw a stone on a surface of good strength; and the surface is made of glass, one finds it broken (the surface). From here one concludes that a force was exerted by stone on the surface and consequently it was broken.
        Now, the question is, did that surface also exert a force on the stone. Just to know about it let us change our throwing object from stone to an egg of almost equal mass. Now, one throws this egg on the same surface of good strength with the same throwing force which he used for the stone. What happens? Obviously with your daily experience you know that the egg will be broken (And the damage to the surface will not be visible due to egg's spoiling the observation).
        This is only possible if there was a force acting on the egg at the time it hit the surface. In fact we can now conclude that there is mutual force acting on the contact point of the surface and the object thrown. The breaking of either one (or may be both) depends on their ability to absorb forces without getting damaged (that is their strength) so in precise words:-
        To every action there is always opposite and equal reaction, it is equivalent to say that mutual actions of two bodies upon each other are always equal and directed to contrary parts.

Note: The most important fact to notice here is that these oppositely directed equal action and reaction can never balance or cancel each other because they always act, on two different point (broadly on two different objects) For balancing any two forces the first requirement is that they should act one one and the same object. (or point, if object can be treated as a point mass, which is a common practice).
 
Illustration of Newton's Third Law:
Some of the examples of Newton's third law of motion are given below:
 1.      Book kept on a table: A book lying on a table exerts a force on the table which is equal to the weight of the book. This is the force of action. The table supports the book, by exerting an equal force on the book. This is the force of reaction, as shown in the figure. As the system is at rest, net force on it is zero. Therefore, forces of action and reaction must be equal and opposite.
forces-of-action-and-reaction

Sunday 15 December 2013

Whitworth quick return mechanism

Whitworth quick return mechanism :
The Whitworth quick return mechanism converts rotary
motion into reciprocating motion, but unlike the crank and
slider, the forward reciprocating motion is at a different rate
than the backward stroke. At the bottom of the drive arm,
the peg only has to move through a few degrees to sweep
the arm from left to right, but it takes the remainder of the
revolution to bring the arm back. This mechanism is most
commonly seen as the drive for a shaping machine.

Wednesday 11 December 2013

CANTILEVER BEAM

CANTILEVER BEAM-
A cantilever is a beam anchored at only one end. The beam
carries the load to the support where it is resisted by
moment and shear stress.Cantilever construction allows for
overhanging structures without external bracing. Cantilevers
can also be constructed with trusses or slabs.
Cantilevers are widely found in construction, notably in
cantilever bridges and balconies. In cantilever bridges the
cantilevers are usually built as pairs, with each cantilever
used to support one end of a central section. The Forth
Bridge in Scotland is an example of a cantilever truss
bridge.

Sunday 17 November 2013

difference between Moment and Couple

What is the difference between Moment and Couple?
• Moment of force is the measure of turning effect of
a force about a point. A couple consists of two equal
and opposite forces acting with two different but
parallel lines of action. Each force has its own
moment.
• Moment of a force is dependent on the distance
from the pivot and the magnitude of the force while
the moment of a couple is the net effect of the two
moments of the forces. Moment of a couple is
independent of the location of the point considered. It
is constant throughout the plane. The resultant
moment of a couple is called a torque.
• Torque, also called moment or moment of force, is
the tendency of a force to rotate an object about an
axis, fulcrum, or pivot. Just as a force is a push or a
pull, a torque can be thought of as a twist.
Couple - Two equal but opposite forces
Torque - Moment of a couple