Force Class 10 ICSE Notes
ICSE Class 10 Physics Chapter 10 Force Notes, Summary, Definition, Diagram. Force Notes.
A) Moment of force and equilibrium
1.1 Translational Motion and Rotational motion:
When we are applying a force on a rigid body then two motions will occur
- Linear or translational Motion
- Rotational motion
1.) Linear or translational Motion:
Suppose, we are applying an external force on a rigid body which is at rest and easy to move then because of that force the body starts to move along a straight line path in the direction in which force is applied. Such type of motion is called as linear or translational Motion.
For example:
If we applied a push to a ball which is placed on the floor after applying push it starts to move along a straight line path as shown in figure. Such motion of an object or body is called as linear or translational Motion.
2.) Rotational motion:
If we are hanging a body from a fixed point and we applied a suitable force at point on body then body starts to rotate only about an axis which is passing through the point at which we hanged the body. Such type of force is responsible for turning effect of body and the resultant motion of the body is called as rotational motion of the body.
For example:
If we hanged a circular wheel from its centre point and we are applying force tangentially along its edge as shown in figure then wheel starts to rotate about an axis which is passing through the centre point where we hanged the wheel. So such motion is called as rotational motion of the body.
1.2 Moment (Turning effect) of a force or torque:
- To explain the moment of force or torque consider the following activity. Let us consider the body is hanged from a point O as shown in figure. If we are applying a horizontal force F on the body so that the line of action of force is AP as shown in figure. Now in this case the force does not responsible for linear motion of the body as it is not free to move. But the body starts to rotate about a vertical axis passing through the point O because of the force applied in the direction shown in figure by the arrow. In this case, the force applied is responsible for rotating the body in anticlockwise direction.
- There are some factors which affects the turning effect of the body which are discussed as given below:
- The magnitude of the force we are applying on the body
- The perpendicular distance between line of action of force and the axis of rotation where we hanged that body.
- And the product of magnitude of force and the perpendicular distance between line of action of force and the pivoted point is called as moment of force or torque. Thus, we can conclude that the rotational motion of body is due to the moment of force or torque.
How to measure the moment of force or torque:
- We already know that, the moment of force or torque is the product of magnitude of force and the perpendicular distance between line of action of force and the axis of rotation.
- From figure given above OP is the perpendicular distance between line of action of force and the axis of rotation.
Thus,
Moment of force about an axis passing through point O = force*perpendicular distance of force from point O
= F*OP
Unit of moment of force or torque:
Unit of moment of force = unit of force*unit of distance
= newton*meter
= Nm
- Thus, the SI unit of moment of force or torque is Nm.
- And the CGS unit of moment of force or torque is dyne cm.
Now we can memorise the units shortly as given below:
1 N m = 105dyne*102cm
= 107 dyne cm
1 kgf *m = 9.8 Nm
1gf*cm = 980 dyne cm
Clockwise and anticlockwise moments:
- If the applied force on the body is responsible for rotating the body in anticlockwise direction then the moment of force is called as anticlockwise moment and which is taken as positive.
- If the applied force on the body is responsible for rotating the body in clockwise direction then the moment of force is called as clockwise moment and it is considered as negative.
- Also, the moment of force is a vector quantity. In case of anticlockwise moment the direction of moment is along the axis of rotation but in outward direction.
- In case of clockwise moment, the direction of moment is along the axis of rotation but in inward direction.
Examples of moment of force:
- When we are shutting or opening the door we applying a force F in the form of push or pull which is perpendicular to the door at its handle P as shown in figure.
- Now if we are applying force at a point Q near the hinge R, then we need much greater force to open the door and hence the force applied at point R is not able to open the door because for the force applied at point R the torque produced is zero.
- And hence for doors, the handles are provided at the near end of the door like point P so that small force applied at a larger perpendicular distance from the hinge helps in producing maximum moment of force and so that door can be easily opened or shut down.
2.) In case of hand flour grinder the upper circular stone is provided to handle near the it’s rim and hence it is easily rotated around the iron pivot which is at its centre only by applying a force of small magnitude at the handle.
3.)
- Also, the spanner which is used for tightening of loosing the nut is having a long handle in order to produce a large moment of force by applying only small magnitude force at its end as shown in figure.
- While loosing the nut, the spanner is turned in anticlockwise direction by applying the force.
- While tightening the nut, the spanner is turned in click direction by applying the force in the direction opposite.
4.)
- Also, the jack screw which are used in lifting heavy load like vehicle, are having a long arm so that less force applied is sufficient to rotate it and in order to raise or lower the load table.
- So from all above examples we conclude that, the moment of force not only depends on the magnitude of force applied but also on the perpendicular distance between line of action of force and the axis of rotation. Hence, larger is the perpendicular distance less is the force required to produce the same turning effect and vice versa.
- And couple is always necessary to produce a rotation.
1.3 Couple:
- A pivoted body is rotating not only because of a single force but actually the rotation of the body is due to a pair of forces. The examples above explained in that the rotation is possible as we are applying a force externally and reaction s producing at the pivoted point. Since, the force of reaction produced at the point of pivot is equal in magnitude but opposite in direction to the applied force.
- And hence the moment of force of reaction about he pivot is zero because the distance of that pivot point from the axis of rotation is zero. So no action will occur there.
- Thus, the pair of force formed due to external force and the force of reaction produced is called as couple. Hence, two equal and opposite parallel forces which are not acting along the same line are responsible for the formation of couple.
- And couple is always necessary to produce a rotation.
For example:
When we are opening the door the rotation of door is produced due to the couple which consist of two forces:
i) the force which we are exerting at the handle of the door.
ii) an equal and opposite force of reaction produced at the hinge.
For example:
- While opening the nut of car wheel we have to apply the equal forces F at the two ends of the wrenches arm in the opposite direction.
- Similar thing will happen while turning a water tap, tightening the cap of inkpot, turning the key in the hole of key lock, winding a clock with a key, turning the steering wheel of a truck, pushing pedals of bicycle etc. All are the examples of a pair of forces which produces rotation effect.
Moment of couple:
- To explain the effect produced by couple let us consider a bar AB which is pivoted at point O as shown in figure. Now, if at the two ends A and B we applied force of equal magnitude F and in opposite directions. The perpendicular distance between these two forces is AB = d and which is called as couple arm.
- If the sum of two forces is zero which are applied in any direction cannot produces the translational Motion of the object as the resultant force is zero but each force produces turning effect on the bar in the same direction.
- In this way, two forces together are responsible for producing couple which helps in rotating the bar about the point O as shown in figure.
- In the figure given below two forces rotate the bar in anticlockwise direction.
Now moment of force at end A = F*OA
Moment of force at end B = F*OB
Total moment of couple = F*OA + F*OB
= F*(OA + OB)
= F*AB
= F*d
Thus, we can define a moment of couple as,
Moment of couple= either force* perpendicular distance between two forces
1.4 Equilibrium of bodies:
- We all know that, when a single force is applied on a body which is free to move produced translational Motion of the body. And if such a single force is applied on a body which is pivoted or fixed at a point then it produces rotational motion.
- But, in some cases if we are applying forces from many directions and the resultant of such all forces is zero then the body does change either the state of rest or the state of linear motion of the body also.
- Also, if the algebraic sum of all the forces about a certain fixed point is zero then the body do not change the rotational state of the body also.
- Thus, when a body is preserving its state in the presence of two or more forces then only such body is said to be in equilibrium.
- In this way, we can define ” when a number of forces are not responsible for changing the state of rest of body or linear or rotational motion of the body then only the body is said to be in the state of equilibrium.
Types of equilibrium:
There are two kinds of equilibrium
1.) Static equilibrium
2.) Dynamic equilibrium
Static equilibrium:
When we are applying number of forces on a body and the resultant force is responsible for making the body in a state of rest then such equilibrium is called as static equilibrium.
For example:
If a body placed in the top of the table as shown in figure is pulled by a force F in left direction and if by force F’ to its right direction along the same line then body does not moves. Because both the forces are equal in magnitude and opposite in direction and acting along the same line and hence they balances each other. And hence no resultant horizontal force is on the body and due to which body is in the state of rest called as in static equilibrium.
If a book is placed on the table, then weigh of the book exerted on the table in vertically downward direction is balanced by the equal and opposite force if reaction exerted by the table on the book vertically in upward direction.
And hence book is in the static equilibrium.
2.) Dynamic equilibrium:
If we are applying several forces on a body then also the body is in its state of motion i.e. the motion may be translational or rotational then such equilibrium is called as dynamic equilibrium.
For example:
- When a rain drop falling reaches the earth’s surface with a constant velocity then the weight of the drop falling is balanced by the sum of buoyant force and the force due friction or viscosity of air. And hence the net force on the drop is zero because of that the raindrop is falling with constant velocity.
- When a string is whirled in a circular path to that string a stone is tied at one end moves with uniform speed is the example of dynamic equilibrium because the tension produced in the string is balanced by the centripetal force required for circular motion.
- In similar manner, the motion of a planet around the sun, the motion of satellite around the planet or the motion of an electron around the nucleus of an atom all are the examples of dynamic equilibrium. Since , in each case the force of attraction on the moving body is providing necessary centripetal force required for circular motion.
Conditions for equilibrium:
- So, from above examples we can say that body is said to be in equilibrium only when it satisfies the following conditions:
- The resultant force of all the forces acting on the body should be zero.
- Also, the algebraic sum of moments of all forces acting on the body about the point of rotation should be zero. That means, the sum of anticlockwise moments about the axis of rotation should be equal to the sum of clockwise moments about the same axis of rotation.
1.5 Principal of moments:
- When we are applying number of forces on a body which is pivoted at a point then that forces are responsible for the rotation of body about the pivot point. And the resultant moment of all the forces about the pivoted point is found by taking the algebraic sum of moment of each force about that point. While finding the moment the anticlockwise moment is taken as positive while the clockwise moment is taken as negative.
- Thus, according to the principal of moments, the body is said to be in equilibrium only when the algebraic sum of moments of all forces acting on a body about the axis of rotation is zero.
Hence,
Sum of anticlockwise moments = sum of clockwise moments
The best example is the physical balance or beam balance which works on the principal of moments.
Verification of principal of moments:
- To verify the principal of moments suspend a meter rule horizontally at a fixed point O with the help of strong thread as shown in figure.
- Now, suspend two spring balances A and B on the meter rule on the either side of the thread as shown in figure. Now, take slotted weights W1 and W2 in spring balances A and B respectively. Now, meter rule starts to tilt in any one side. Now adjust the weights in the spring balances or the position of the spring balances on the either side of the thread so that the meter rule becomes horizontal again.
- Let us consider spring balance A carries weight W1 at a distance OA=L1.
- And spring balance B carries weight W2 at a distance OB = L2.
- Now here, the weight W1 is tending the meter rule in clockwise direction while the weight W2 tends the meter rule in anticlockwise direction.
- Clockwise moment = W1*L1
- Anticlockwise moment = W2*L2
- But in equilibrium condition the meter rule is in the horizontal direction and hence
- W1*L1 = W2*L2
That means,
Clockwise moment = Anticlockwise moment
Hence, the principal of moments is verified here.
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