Units and Standards
In making a measurement of any physical quantity, some definite and convenient quantity of the same kind is taken as the standard, in terms of which the quantity as a whole is expressed. The conventional quantity used as the standard of measurement is called a unit. The unit of area is the area of a square each side of which is of unit length. Two Important Systems of Fundamental Units are there. They are
(1) The C. G. S. System (Metric System)
(2) The F.P.S. System (British System)
In the C.G.S. system C stands for 'Centimetre (cm.)' as the unit of length, G for 'Gram (gm.) as the unit of mass, and S for "Second (sec.) as the unit of time.
In the F. P.S. system, F stands for 'Foot (ft.)' as the unit of length, P for 'Pound (lb.)' as the unit of mass, and S for 'Second (sec.) as the unit of time.
In MKS System M stands for meter, K stands for kilogram, S stands for second.
SI: In this system there are seven fundamental quantities which are as shown below:-
Ser
No
Physical quantity
Name
symbol
1.
Length
Meter
M
2.
Mass
Kilogram
Kg
3.
Time
Second
Sec
4.
Temperature
Kelvin
K
5.
Luminous Intensity
Candle
Cd
6.
Electric current
Ampere
A
7.
Amount of substance
Mole
mol
Speed
The rate of change of position a body irrespective of direction is called Speed.
Speed = Distance traveled = s meters
Time taken t seconds
= s/t m/sec
Speed is a scalar quantity i.e., it has magnitude only.
Velocity
The rate of change of position of a body in a particular direction is called velocity. It is measured by the distance covered in a particular direction per unit time measures it.
Velocity = Distance covered (in particular direction)
Time
\V = s meters = s m/s
T seconds t
Velocity is a vector quantity i.e., it posses both magnitude and direction.
Uniform Velocity
If a body covers equal distances, in a particular direction, in equal intervals of time, however small, it is said to move with uniform velocity.
Consider a truck moving along Delhi Road. This truck is covering equal distances (5 meters) in equal intervals of time (sys, 1 second) in the same direction. Therefore truck is moving with a uniform velocity. In this case, velocity of truck. = 5m/1s = 5ms-1
Variable Velocity
If a body covers unequal distances in a particular direction, in equal intervals of time however small, it is said to move with a variable velocity.
It should be noted that even if a body covers equal distances in equal intervals of time, but changes its direction, it is said to possess variable velocity.
Average Velocity
The average velocity of moving body during a given interval of time is measured by the total distance traveled divided by total time taken.
Average velocity = Total distance traveled
Total time taken
Acceleration
The rate of change of velocity is called acceleration. change of velocity per unit time.
Acceleration = Change in velocity (OR) a = v - u
Time t
Where a = Acceleration of body
u = Initial velocity
v = Final velocity
t = Time taken for the velocity to change from u to v.
Acceleration has magnitude as well as direction; therefore it is a vector quantity.
Newton's First Law of Motion.
" If a body is at rest, it will continue to remain at rest until it is acted upon by some external agency. "
Force.
It is defined as that external agency that changes or tends to change the state of rest or of uniform motion of a body in a straight line.
The first law of motion is also called the "Law of Inertia" inertia is the inability of a material body to change by itself its state of rest or of uniform motion in a straight line.
Newton's Second Law of Motion.
According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force.
Momentum.
It is the quantity of motion of a body. It is the product of mass and velocity. It is a vector quantity.
Momentum = mass x velocity. The units of momentum are:(1) In C.G.S. units, g-cm/s (2) In rationalized units, kg-m/s.
Newton's Third Law of Motion.
According to Newton's third law of motion, to every action there is always an equal and opposite reaction.
Centrifugal Force.
Centrifugal force. When a body is rotating on a circular path, it has a tendency to move along a tangent. If a body A leaves the circular; path at any instant, for an observer B who is not sharing the motion along the circular path (i.e., a body B standing outside the reference circle), the body A appears to fly off tangentially at the point of release. For an observer C, who is sharing the same circular motion as that of the body A, the body A appears to be at rest before it is released. According to C, when A is released, it appears to fly off radically away from the center. It appears to the body C as if the body A has been thrown off along the radius away from the center by some force. This inertia force is known as centrifugal force'. Its magnitude is mv2/r. It is not a force of reaction. Centrifugal force is a fictitious force and holds good in rotating frame of reference.
When a car is turning round a corner, the persons sitting inside the car experience an outward force. This is due to the fact that the passengers provide no centripetal force.
Applications
1.Sugar crystals are separated from molasses with the help of a centrifuge.
2.ln cream separators, when the vessel containing the milk is rotated at high speed, the lighter cream particles collect around the axis of rotation while the skimmed milk moves away from the axis.
3. In drying machines, the wet clothes are rotated at high speed. The water particles fly off tangentially through the holes in the wall of the outer vessel.
4.Honey is also separated from bees wax with the help of a centrifuge.
5. Analysis of blood samples.
Centripetal Force
It is defined as the force, which acts towards the center along the radius of a circular path on which the body is moving with a uniform velocity.
Work
The term 'work' by itself does not convey any meaning in physics. Work is either done on a body or by a body. Therefore the complete term is
(I) Work done on a body
(II) Work done by a body.
In everyday life the term work is attributed to numerous acts eg: lifting a load, going up a hill, coming down the hill, stopping a moving ball, bullet hitting a target etc.
Work done is equal to the product of the force and distance moved by the body along the direction of the force.
W=F x S
Units of Work
W = F x S = Force x distance,
MKS. UNITS Work is Joule
CGS .UNITS Work is ergs.
Power
Power is defined as the rate of doing work.
Power = work done I Time
Units of power = watt in MKS
= ergs/s in CGS , =HP in FPS.
Energy
Energy of a body is defined as its capacity to do work. In physics there are many forms of energy e.g. heat, light, sound, magnetic, electric, potential etc, In mechanics we are mainly concerned with the two forms of energy of a body viz. Kinetic energy and potential energy.
Kinetic Energy
It is energy possessed by a moving body
Magnitude of Kinetic Energy
Consider a body of mass M moving with a velocity v. A retarding force F is applied on the body to bring it to rest. Let the body move a distance S before coming to rest and the retardation be a.
o –V2 = 2(-a)S
\ a = v2
2s
Retardation force = Ma = Mv2
2s
Kinetic energy = ½ M v2
Potential Energy
It is the mechanical energy possessed by a body due to its position or distortion. At the ground level, the potential energy of a body is zero. Suppose there is a body of mass M at a height h above the ground.
This body can do work = Mg x h when allowed to fall freely. Therefore its capacity to do work = Mgh and its potential energy = Mgh.
A compressed spring and stretched wire have potential energy spring in a watch after winding possesses potential energy. Any body subjected to deforming forces possesses potential energy.
Unit of Energy
Energy has the same units as that of work.
Law of Conservation of Energy
The total energy of a body remains constant. Only one form of energy changes into another form.
Potential Energy + kinetic Energy = Constant.
Simple Machines
In modern age, in every instrument or mechanism, we come across some simple devices. These devices are levers, pulleys, screw jack, wedge, inclined plane etc. These devices are called simple machines. If a tyre of a car is to be replaced, the screw jack is used to lift the car. Loading of trucks and goods wagons is done. with a plank serving as an inclined plane. Scissors, pair of tongs, forceps, punching machine etc., work on the principle of levers. Knife works on the principle of a wedge.
Simple machines are those where the effort is applied at a more convenient point in a more convenient direction.
Principle of Work
Whenever effort is applied on a machine and the point of application moves through a certain distance, work is said to be done on the machine. This work done on the machine is called input. The load or resistance overcome is moved through a certain distance and the machine does this work. Work done by the machine is called output. In an actual machine, there is always some loss of energy due to friction etc. Therefore the output is always less than the input. According to the principle of work, in a perfect machine.
Output = Input
Mechanical advantage
It is defined as the rate of resistance overcome to the effort applied.
MA = w = Resistance overcome
p Effort applied
Velocity ratio:
It is defined as the ratio of the distance moved by the effort applied to the distance moved by the resistance overcome,
VR = D/d = Distance moved by the effort
Distance moved by the resistance overcome
Efficiency It is defined as the ratio of output to input.
Output = W x d
Input = p x D
Efficiency h = Output = W x d = W/P = MA
Input P x D/d VR
\Efficiency = Mechanical Advantage
Velocity Ration
Mechanical advantage = efficiency x velocity ratio,
MA is a ratio of two forces,
VR is a ratio of two distances,
"h" is a ratio of two works done by the machine and on the machine.
In a perfect machine,
Output = Input and h = 1
\ Mechanical advantage = Velocity ratio
Lever
Lever is a rigid bar, which is capable of rotating about a fixed point called the fulcrum. The perpendicular distance between the fulcrum and the direction in which the effort is applied is called the power arm or effort arm. The perpendicular distance between the fulcrum and the direction of the load or resistance overcome or weight overcome is called the weight arm or the resistance arm.
Consider a lever AB, capable of a rotating about the fulcrum F . effort applied. If the lever is in equilibrium, p x BF = W x AF (OR)
Effort x effort arm = Load x arm
There are three types of levers. They are
(1) Class I Levers Here the fulcrum F is in between load Wand effort P.
According to the principle of lever,
P x a = w x b
W/P = a/b
(1) a>b, p will be less than W, Mechanical advantage is greater than 1.
(2) If a = b, p = W Mechanical advantage is equal to 1.
(3) If a
(2) Class II Levers
Here load W is in between the fulcrum F and the effort p, p
AF = a and BF = b
According to the principle of lever,
P x a = w x b
W/P = a/b
Here a is always greater than b. Therefore, less effort is applied to overcome a heavy load. The Mechanical advantage is always greater than 1.
(3) Class III Lever
Here effort p is in between the fulcrum F and the load W.
AF = a and BF = b
According to the principle of lever ,
W/P =a/b
Here a is always less than b. Therefore, more effort has to be applied to overcome a small load the mechanical advantage is always less than 1.
Ex:- Fire tongs, fore arm used for lifting load on the palm, forceps in the weight box and fishing rod.
Note:- The three types of levers can be remembered as follows:
FWP in levers three Must each in turn, the center be.
It means that, in class I levers F is in the middle, in class II levers, W is in the middle and in class III levers, p is in the middle.
Eg.1. A stone is thrown vertically upwards with a velocity of 24.5 m/s (1) calculate the highest height which it rises. (2)Calculate also the time it takes to reach the highest point.
u = 24.5 m/s. v=o, h=? , g=-9.8 m/s2.
V2-U2 = 2as. 0- 24.52=2.(-9.81 ).h, h= 30.625 m.
(2), v= u + at, t = 24.5/9.8 = 2.5 sec.
Eg.2. A body is thrown vertically upwards and rises to a height of 10 meters Calculate (1 ) the velocity with which the body was thrown upward and (2) the time it takes to reach the highest point.
u =?, v= 0, h =10 m,
g= -9.8 m/s2. V2-U2 = 2as, 0- (u)2=2.(-9.81 ).10,
u = 14 m/sec. 2.v= u- gt, t= 14/9.8 =1.43 sec.
Eg.3. A projectile weight 45 kg is fired from a gun weight 8000 kg with velocity of 500m/s . Find the velocity of recoil of the gun?
Here m=200 kg, M=8000 kg, u=500 m/sec,
v=? MV = m v, V = m v/M = 12.5 m/sec,
Eg.4. A motor car of mass 25 quintals is moving with a velocity of 36 kmph. By application of breaks it is brought to rest in a distance of 25 mtrs. Find the average force of resistance in newton.
M =25 quintals = 2500 kg,
u= 36 kmph, u= 10 m/sec, s= 25 mtr,
v=o, F= ? V2-U2 = 2as.
0 – 102=2.(a).h, a= -2 m/sec2, Force of resistance,
F= ma. = 2500 x 2 = 5000N.
Eg.5 Physical quantities, formulas and units.
Sr.No
Physical quantity
Formula
Units
1.
Velocity
Displacement
m/sec.
2.
Acceleration
Velocity/time
m/sec2,
3.
Force
Mass x acceleration
kg or Newton
4.
Work
Force x distance
kg-m
5.
Power
Work / time
kg-m/sec.
6.
Pressure
Force/ area
kg/m2.
7.
Stress
Force/ area
kg/m2
8.
Moment
Force x distance
kg-m.
9.
Torque
Force x distance
kg-m.
10.
Couple
Force x distance
kg-m.
11.
Effort
Force
kg.
12.
Energy
Capacity to do work
kg-m
Eg.6. What is the work done by a man in carrying a suitcase weight 30 kg over head when he travels a distance of 1 in (1) vertically and (2). Horizontal direction.
(1) Distance moved in vertical direction = 10 m.
Work done = mgh = 30 x 9.8 x 10 = 2940 Joules.
(2). Since a force has no component at right angles to it, therefore, component of mgh in the horizontal direction = F = mg cos90°=0,
Eg. 7 .A man whose mass is 60 kg walks up to the top of building whose height is 15 m above the street level?
(1) How many joules of work has he done.
(2) What is the increase in his potential energy,
m= 60 kg, g= -9.8 m/.sec2.
(1) work done = 60 x 9.8 x 15 joules.
(2). Increase in p .E = work done = 60 x 9.8 x 15 =8820 Joules.
Eg.8. The value of "g" is maximum at (HMT 1993)
(a) At earth's surface (b), At earth center (c) At hill top (d) At hill top
Eg.9. If a ball thrown up, the highest point will be______________
Eg.10.0ne HP is equal to _______________ watts
Eg.11. Length, mass, time, are ________________
Eg.12. Static friction is always less than the dynamic friction (T/F)
No comments:
Post a Comment