Study Material by ICSEHUB

1 :Force

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Definitions

1.       Force  Force is a physical cause that changes of tend to change the shape or the state of rest or state of motion of the body.

2.       Rigid Body  Rigid body is a body that does not get deformed under the action of force.

3.       Translational motion/ linear motion - In translational motion body moves along a straight line-path in the direction of force applied.

4.       Rotational Motion  This motion occurs when force is applied on a body that is pivoted or fixed at a point.

5.       Torque/Moment of force  It is the turning effect of force acting on a body about the point or axis of rotation. It is the product of the magnitude of force applied and perpendicular distance between the line of action of force and axis of rotation.  SI unit is Newton-meter and CGS unit is dyne-centimeter.  1 Nm = 107 dyne-cm. It is a vector quantity.

6.       Gravitational unit of force is Kgf and gf

a)      1 N = 105 dyne

b)      1 Kgf = 9.8 N  [newton  nine]

c)       1 gf = 980 dyne

d)      1 Kgf m = 9.8 Nm

e)      1 gf cm = 980 dyne cm

7.       Couple  Pair of equal and opposite parallel forces whose line of action are not the same. Its magnitude is equal to either of two forces and perpendicular distance between the line of action of two forces. Examples : Door , Car steering and Bicycle pedal

8.       Equilibrium  A body is said to be in a state of equilibrium when the resultant of number of forces acting on a body is zero (0) such that state of the body (whether rest or motion)  remains unchanged .

a)      Static equilibrium  A body is said to be in state of static equailibrium if it remains in state of rest under the influence of applied forces. (Resting body , Beam Balance)

b)      Dynamic equilibrium  A body is said to be in state of dynamic equilibrium if it remains in state of motion under the influence of applied forces. (Raindrop , Planets around the sun , electrons revolving around nucleus).

9.       Principle of Moments  According to principle of moments the algebraic sum of clockwise moments is equal to the sum of anti-clockwise moments when number of forces acting on a rigid body is in equilibrim.

10.   Centre of Gravity  Centre of gravity is defined as a point where the entire weight of the body acts. The algebraic sum of moments of weight of the particles constituting the body is zero about this point.

11.   Uniform circular motion  A body is said to be in a uniform circular motion if it moves with a constant speed in a circular path.

1.       Centripetal Force  A force acting on a body moving in circular path and is directed towards the center around which the body is moving. It is a real force.

2.       Centrifugal Force  A force that appears to act on a body moving in a circular path and is directed away from the center around which the body is moving.  It is a fictitious/virtual  force. [appears is used as it is a imaginary/virtual force]

Important Points

1.       Anticlockwise moment is positive (+) and Clock-wise is negative (-)

2.       Torque / Moment of force is 0 when :

·         Force applied is zero i.e. f=0

·         Perpendicular distance between line of action of force and axis of body is zero i.e. d=0

·         Line of action of force is passing through the axis of body

3.       Equilibrium is of two type  Static (object lying on table, beam balance)and Dynamic ( Earth rotating around the sun , electron around nucleus , rain drop)

4.       Conditions needed for equilibrium :

·         The resultant of number of external forces acting on a rigid body must be 0

·         The resultant of all the external moment of force or torque acting about the point of rotation of body must be 0

5.

 Shape Center of Gravity Uniform Straight wire Midpoint Uniform beam , cylinder or rod Midpoint of the axis Circular ring Geometric centre , where is no matter Solid Cone At a height , 1/4th  from its base on the axis Hollow Cone At a height , 1/3rd from its base on its axis Triangle , Trangular Lamina Centroid (Intersection of midpoints) Sphere Geometric centre Rectangular Lamina , Square , Rhombus , Parallelogram Point of intersection of diagonals Cube , Cuboid Midpoint of line joining the center of opposite sides

6.       In a uniform circular motion :

·         Speed is uniform/constant

·         Acceleration and velocity is non-uniform due to change in direction

·         Work is 0 (as displacement becomes 0) after one rotation.

Question Bank

QI. Define moment of force and state its S.I. unit.

Moment of force or torque is the turing effect of force acting on a body about its point or axis of rotation. It is the product of the force applied and the perpendicular distance between the line of action of force and axis of rotation. Its SI unit is Newton metre

Q2. State two factors affecting the turning effect of a force.

·         Magnitude of the force applied

·         Perpendicular distance between the line of action of force and point or axis of rotation.

Q3. Why is it easier to open a door by applying the force at the free end of it?

It is easier to open a door by applying the force at the free end of it because perpendicular distance of the line of action of force from the point (or axis) of rotation is maximum. Therefore less force is used to generate the required torque.

Q4. Moment of force is scalar or vector quantity?

Moment of force is vector quantity.

Q5. State the gravitational units of torque.

Gravitational units of torque are Kilogramforce metre ( Kgf m) and gramforce centimeter (gf cm).  1Kgf m = 9.8 N & 1 gf cm = 980 dyne cm.

Q6. State two conditions for a body, acted upon by several forces, to be in equilibrium.

·         Resultant of all the external forces acting on the body is zero .

·         Resultant of all the external moment of forces or torque acting on the body is zero.

Q7. A uniform meter rule can be balanced at the 70 cm mark when a mass 50g is hung from the 94 cm mark. Find mass of ruler.

Sum of clockwise moments = Sum of anti clockwise moments

Therefore, (94 - 70) x 50 = (70-50) x W

24 x 50=20 x W

24x50 /20 = W

W = 60 grams

Q8. Define the term centre of gravity ofa body.

Center of gravity is the point at which the entire weight of the body acts and the algebraic sum of  moment of weights of the particles constituting the body is zero about this point.

Q9. At which point is the centre of gravity situated in:

(i)  Triangular lamina : Centroid ; point of intersection og medians

(ii)  Circular lamina : Geometric centere

(iii)  Hollow cone : At a height 1/3rd from the base on the axis

(iv) Solid or hollow sphere : Geometric center

(v) Uniform ring : Geometric center where there is no material

Q10. On which factors Center of Gravity of a body depends upon?

·         Shape of the body

·         Distribution of its mass

Q11. Name the force required for uniform circular motion. State its direction.

Centripetal force. Towards the center around which the body moves

Q12. On which principle does beam balance work?

Principle of moments

Q13. Write direction of torque with its sign.

Anti-clockwise à Positive (+)

Clockwise à Negative (-)

Q14. Why does a wrench handle is long? [same for Steering wheel /Hand flour grinder / chakki ]

Wrench handle is long because when the line of action of force from the point (or axis) of rotation increases then required force to be applied decreases.

Q15. Name a body in which center of gravity does not lie in the geometric center.

Hollow cone or  solid cone

Formula

 FORCE Concept Formula S.I. CGS Force m x a Newton (N) dyne (10-5 N) Torque F x ( ⊥ distance between Point of action and axis) Newton-meter dyne-cm

2 :Work , Power and Energy

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Definitions

1.       Work  Work is said to be done only when the force applied to the body causes a displacment in the direction of the applied force.

2.       Power  Power is defined as rate of doing work. It is a scalar quantity, so it will never be negative.

3.       Horse power  It is equals to 746 Watts

4.       1 Watthour  Amount of energy spent or produced by a source of power 1 Watt in 1 hour.

5.       Energy  Capacity of a body to do work. It is a scalar quantity, so it will never be negative.

6.       Calorie  Heat required to raise the temperature of 1 gram of water by 1 C (14.5C to 15.5C)

7.       ElectronVolt  Unit used for the energy of atomic paricles. 1eV = 1.6 x 10-9Joule

8.       Mechanical Energy  Energy possesed by a body by virtue of its position or motion

·         Kinetic Energy  Energy possesed by a body by virtue of its state of motion

o   Translational K.E. - Energy possesed by a body due to its motion in straight line path / linear motion.

o   Rotational K.E. - Energy possesed by a body due to its motion in circular path.

o   Vibrational K.E. - Energy possesed by a body due to its to and fro motion about its mean position.

·         Potential Energy  Energy possesed by a body by virtue of its position or configuration.

o   Elastic P.E.  Energy possesed by a body due to its changed configuration or deformed state

o   Gravitaional P.E.  Energy possesed by a body due to its position with respect to the centre of the earth.

9.       Law of conservation of Energy  Energy can neither  be created nor be destroyed. It may be transformed from one form to another in a system , but total energy in a system remains constant. Mechanical energy *(constant)* = Kinetic Energy + Potential Energy

10.   Work Energy Theorem  Work done by the force on a body is equals to the increase in kinetic energy.

11.   Radiant energy  Light received from solar energy is called Radiant energy

Important Points

1.       Work done by a body can be à Positive , Negative or Zero

2.       Zero Work  When there is no force or no displacement or angle between action of force and displacement is 90 degree.

·         Coolie carrying a load

·         Oscillating Pendulum , Earth/Planets revolving around Sun or other circular motions [Reason : Displacement is along the tangent whereas centripetal force is towards center thereby making angle of 90 degree; also in circular motion displacement after one rotation is zero]

3.       In Negative work angle is 180 therefore displacement is at opposite direction as that of force applied. (Cos180 = -1)

·         Gravitational work on ball thrown upwards

·         Work done by Cricketer (palm) while catching a ball.

4.       Work done is minimun when Zero work is done (not negative work)

5. Force v/s Displacement Graph  Work done can be calculated by calculating the Area enclosed under the graph.

Work done = Area = (100 x 20) + ( ½ x 10 x 100 ) = 2000 + 500 = 2500

6.       Work done by Gravity

·         mgh [when work done by gravity is positive +]

·         -mgh [when work done is against the force of gravity]

7.       Work = F.S.Cos θ

8.       1 J = 107erg

9.       Momentum = √2mK     [ Relation between Momentum and Kinetic Energy]

10.   Kinetic energy is of three(3) types  Transitional , Rotational and Vibrational and Potential is of two(2) types  elastic and gravitational

11.   Gravitational potential energy on the surface of the Earth is considered Zero (0)

12.   Heat energy is also called thermal energy

13.   At microscopic level light energy is due to small energy particle  photons

14.   A thermocouple converts Heat Energy into Electrical Energy. It consist of two metals kept at different temperature. Temperature difference develops a potential difference and current flows.

15.    kWh  and Wh (Watt hour) are units of energy

16.   Convert units in SI unit unless other unit is specified.

17.   V2 = u2 + 2aS

18.   Work done is Change in kinetic energy à W = KE1  KE2

Question Bank

State the condition when the work done by a force is (a) positive (b) negative. Explain with the help of examples.

Work done is positive when the displacement is caused in the direction of force applied.  Ex Man pushing a trolley/cart or Feely falling body under the action of gravity

Work done is negative when the displacement is caused opposite to the direction of force applied.Ex- Man trying to stop a moving car.

A satellite revolves around the earth in a circular orbit, What is the work done by the satellite? Give reason.

Work done by satellite is zero. Centripetal force acts towards the center and displacment at a point is along the tangent to the orbt. Therefore, angle between the force applied and displacement is 90 degree and work is zero.  ( F x S x cos90 = FxSx0 = 0)

What is SI and CGS unit of work and how are they related?

SI unit of work is Joule and its CGS unit is erg.  1 joule = 107 erg

Define the term energy and state its S.I. unit.

Capacity of the body to do work is called its energy. Its SI unit is Joule.

Define one kilowatt hour. How is it related to joule?

Energy consumed or produced by a source of power 1 kiloWatt in 1 hour is defined as 1 kilowatt hour. 1KWh = 1000Wh = 1000W x 3600 sec = 3600000 Joule = 3.6 x 106 Joule.

Differentiate between energy and power?

 Energy Power It is the capacity of a body to do work It the rate of doing work. Do not depend upon time Depends upon time SI unit is Joule SI unit is Watt

[Write SI unit at last or avoid writing it as it is not considered in many cases]

A machine raises a load of 750 N through a height of 16 m in 5 s. Calculate:

(i) the energy spent by the machine.  12000 Joules

(ii) the power of the machine if it is 100% efficient.  2400 Watt

Work is a scalar or vector quantity?

Work is a scalar quantity

A pump is used to lift 500 kg of water from a depth of 80 m in 10 s, Calculate:

(i)  Work done by the pump.  400000 Joules  or 400 kJ(assuming g=10m/s)                   [hint: find force using f=mg or  f=ma where g or a is acceleration due to gravity.  Then apply W= FxS]

(ii)  Power at which the pump works. 40000 Watt  or 40 KiloWatt            [hint : P = W/t]

(iii)  Power rating of the pump if its efficiency is 80%.

Name different types of Kinetic and Potential Energy.

Kinetic Energy  Translational Kinetic Energy , Rotational Kinetic Energy and Vibrational Kinetic Energy

Potential Energy  Eleastic Potential Energy , Gravitational Potential Energy

State the energy conversion in the following cases:

(i) Loudspeaker when in use  : Electrical energy to Sound energy

(ii) While charging a battery  : Electrical energy to Chemical Energy

(iii) Photoelectric cell : Light energy to Electrical energy

(iv) Burning of wood, coal, etc.  : Chemical energy to Ligth and Heat energy

(v) When water falls from a height. : Potential Energy to Kinetic energy

(vi) Microphone when in use  : Sound energy to Electrical energy

(vii) Thermocouple : Heat energy to Electrical energy

(viii) Electromagnet  : Electrical energy to Magnetic energy

(ix) Thunderstorm  : Electrical energy to Ligth and Sound energy

(x) Petrol or Diesel engine car  : Chemical energy to Mechanical energy

(xi) Dam  : Mechanical energy to Electric energy

Give relation between Kinetic energy and momentum

Momentum = √2mK     (where m= mass and K =kinetic energy)

A body of mass 60 kg has momentum 3000 kg ms-l- Calculate:

(i) Kinetic energy : 75000 Joules                  [never forget units , remember p=mv and p =√2mK ]

(ii) Speed of the body : 50 m/s

What is law of conservation of energy ?

Energy can neither be created nor be destroyed. It may be converted from one form to another in a system. But total energy in a system remains constant.

[  Energy can neither be created nor be destroyed

It may be converted from one form to another in a system

But total energy in a system remains constant.] 3 points

A ball of mass 10 g falls from a height of 5 m. It rebounds from the ground to a height of 4 m. (take g=10 m/s)  Find:

(i) the initial potential energy of the ball. 0.5 Joule

(ii) the kinetic energy of the ball just before striking the ground.  0.5 Joule

(iii) the kinetic energy of the ball after striking the ground.  0.4 Joule

(iv) the loss in kinetic energy of the ball on striking the ground.   0.1 Joule

Definitions

1.       Machine  Machine is a device that helps us to overcome resistance due to large force or gain speed by appling a small force in a convenient point and in a desired direction.

2.       Ideal Machine  Machine in which there is no loss of energy. Its efficiency is 100%

3.       Actual Machine  Machine in which there is loss of energy. Its efficiency is less than 100%

4.       Lever  Lever is rigid,straight or bent bar that is capable of rotating around a fixed point.

5.       Pulley  Pulley is a metallic or wooden disc with a grooved edge.

Important Points

1.       Loss of energy occur due to following

·         Parts of machines are not weightless

·         Parts of machine are not frictionless

·         Parts do not have perfect rigidity

2.       Mechanical Advantage (MA) and Velocity Ratio (VR) are ratios therefore have no unit.

3.       Lever works on  Principle of moments

4.       Law of Levers = Effort Arm / Load Arm

5.       VR depends upon the design or dimension of the machine.

6.       VR of a given machine remains constant for a given machine

7.       Levers are of 3 types : - FLE

 Class I Class II Class III Fulcrum is between Load and Effort Load is between Effort and Fulcrum Effort is between Load and Fulcrum MA may be greater , equal or smaller than 1 =MA or MA MA  > 1 Bcz. Load is in between, so Effort arm is always greater than Load Arm MA < 1 Bcz. Fulcrum is in between and always smaller than Load Arm Force multiplier or Velocity Multiplier Force Multiplier Velocity Multiplier Ex: See-Saw , Scissors , long handle oar , crowbar , shears , claw hammer , Handle of pump , spade turning the soil , Rowing a boat (simple) Ex : Nut cracker , lemon squeezer , vegetable cutter , hinges of door , wheel barrow , bottle opener , bar to lift load Ex : Broomstick , Tongs , Stapler remover , fishing rod , foot treadle , knife , spade lifting a load , Rowing a boat (Race)

8.       MA = Efficiency x VR

In  a  single  movable  pulley,  if the weight  of  the  load  is  L  and  the  weight  of  the movable pulleyis W, find the expression forits mechanical advantage.

According to the question,

L + W = 2 T & E = T

Therefore,  L = 2 T  W

Mechanical advantage= L/E = (2T  W) / T

= 2T/T  W/T = 2 W/E