ICSE Class 10 Physics Chapter 01 Force

Chapter 1: Force

Force, Work, Power and Energy

Syllabus

(i) Turning forces concept; moment of a force; forces in equilibrium; centre of gravity, (discussions using simple examples and simple direct problems).

Scope of syllabus - Elementary introduction of translational and rotational motions; moment (turning effect) of a force, also called torque and its C.G.S. and S.I. units; common examples - door, steering wheel, bicycle pedal, etc; clockwise and anticlockwise moments; conditions for a body to be in equilibrium (translational and rotational); principle of moments and its verification using a metre rule suspended by two spring balances with slotted weights hanging from it; simple numerical problems; centre of gravity (qualitative only) with examples of some regular bodies and irregular lamina.

(ii) Uniform circular motion.

Scope of syllabus - As an example of constant speed, though acceleration (force) is present. Difference between centrifugal and centripetal force.

In class IX, we have read that a force when applied on a rigid body can cause only the motion in it, while when applied on a non-rigid body can cause both the change in its size or shape and the motion in it. In mathematical form, force applied on a body is defined as the rate of change in its linear momentum i.e., \(\vec{F} = \frac{d\vec{p}}{dt} = \frac{d(m\vec{v})}{dt}\) or \(\vec{F} = m\vec{a}\) (if mass m is constant). The force is a vector quantity and its S.I. unit is newton (symbol N) or kilogram-force (symbol kgf) where 1 kgf = g N if g is the acceleration due to gravity (= 9.8 m s-2 on average).

Moment Of A Force And Equilibrium

1.1 Translational And Rotational Motions

A rigid body when acted upon by a force, can have two kinds of motion:

(1) linear or translational motion, and

(2) rotational motion.

(1) Linear or translational motion

When a force acts on a stationary rigid body which is free to move, the body starts moving in a straight path in the direction of force. This is called the linear or translational motion. For example in Fig. 1.1, on pushing a ball lying on a floor, it begins to move.

Ball

Push → Direction of motion

Fig. 1.1 Translational motion

(2) Rotational motion

If the body is pivoted at a point and the force is applied on the body at a suitable point, it rotates the body about the axis passing through the pivoted point. This is the turning effect of the force and the motion of body is called the rotational motion. For example, if a wheel is pivoted at its centre and a force is applied tangentially on its rim as shown in Fig. 1.2, the wheel rotates about its centre. Similarly when a force is applied normally on the handle of a door,

Wheel

Pivot

Fig. 1.2 Rotational motion

the door begins to rotate about an axis passing through the hinges on which the door rests.

1.2 Moment (Turning Effect) Of A Force Or Torque

Consider a body which is pivoted at a point O. If a force F is applied horizontally on the body with its line of action in the direction OP as shown in Fig. 1.3, the force is unable to produce linear motion of the body in its direction because the body is not free to move, but this force turns (or rotates) the body about the vertical axis passing through the point O, in the direction shown by the arrow in Fig. 1.3 (i.e., the force rotates the body anticlockwise).

Factors affecting the turning of a body

The turning effect on a body by a force depends on the following two factors:

(1) the magnitude of the force applied, and

(2) the distance of line of action of the force from the axis of rotation (or pivoted point).

Indeed, the turning effect on the body depends on the product of both the above stated factors. This product is called the moment of force (or torque). Thus, the body rotates due to the moment of force (or torque) about the pivoted point. In other words,

The turning effect on the body about an axis is due to the moment of force (or torque) applied on the body.

Measurement of moment of force (or torque)

The moment of a force (or torque) is equal to the product of the magnitude of the force and the perpendicular distance of the line of action of force from the axis of rotation.

In Fig. 1.3, the line of action of force F is shown by the dotted line FP and the perpendicular drawn from the pivoted point O on the line of action of force is OP. Therefore,

Moment of force about the axis passing through the point O

= Force × Perpendicular distance of force from the point O

= F × OP

...(1.1)

Note: For producing maximum turning effect on a body by a given force, the force is applied on the body at a point for which the perpendicular distance of line of action of the force from the axis of rotation is maximum so that the given force may provide the maximum torque to turn the body.

Units of moment of force

Unit of moment of force

= unit of force × unit of distance

The S.I. unit of force is newton and that of distance is metre, so the S.I. unit of moment of force is newton × metre. This is abbreviated as N m.*

The C.G.S. unit of moment of force is dyne × cm.

But if force is measured in gravitational unit, then the unit of moment of force in S.I. system is kgf × m and in C.G.S. system, the unit is gf × cm.

These units are related as follows:

\[ \begin{align} 1 \text{ N m} &= 10^5 \text{ dyne} \times 10^2 \text{ cm}\\ &= 10^7 \text{ dyne cm}\\ 1 \text{ kgf} \times \text{m} &= 9.8 \text{ N m} \end{align} \]

and

\[1 \text{ gf} \times \text{cm} = 980 \text{ dyne cm}\]

...(1.2)

Clockwise and anticlockwise moments:

Conventionally, if the effect on the body is to turn it anticlockwise, the moment of force is called the anticlockwise moment and it is taken positive, while if the effect on the body is to turn it clockwise, the moment of force is called the clockwise moment and it is taken negative.

* The unit N m of moment of force (or torque) is not written joule (J). However the unit N m for work or energy is written joule (J) because torque is a vector, while work or energy is a scalar quantity.

The moment of force is a vector quantity. The direction of anticlockwise moment is along the axis of rotation outwards, while of clockwise moment is along the axis of rotation inwards.

On applying a force on a pivoted body, its direction of rotation depends on (a) the point of application of the force, and (b) the direction of force. Fig. 1.4(a) shows the anticlockwise and clockwise moments produced in a disc pivoted at its centre by changing the point of application of the force F from point A to point B. Fig. 1.4(b) shows the anticlockwise and clockwise moments produced on a pivoted axle by changing the direction of force F at the free end of the axle.

Disc | Disc

Anticlockwise (Positive) | Clockwise (Negative)

(a) By changing the point of application of force

Anticlockwise (Positive) | Clockwise (Negative)

(b) By changing the direction of force

Fig. 1.4 Anticlockwise and clockwise moments

Common examples of moment of force

(1) To open or shut a door, we apply a force (push or pull) F normal to the door at its handle P which is provided at the maximum distance from the hinges as shown in Fig. 1.5.

We can notice that if we apply the force at a point Q (near the hinge R), much greater force is required to open the door and if the force is applied at the hinge R, we will not be able to open the door howsoever large the force may be (because of the force at R, torque will be zero). Thus, the handle P is provided near the free end of the door so that a smaller force at a larger perpendicular distance produce a larger moment of force required to open or shut the door.

Fig. 1.5 Opening of a door

(2) The upper circular stone of a hand flour grinder is provided with a handle near its rim (i.e., at the maximum distance from centre) so that it can easily be rotated about the iron pivot at its centre by applying a small force at the handle.

(3) For turning a steering wheel, a force is applied tangentially on the rim of the wheel (Fig. 1.6). The sense of rotation of wheel is changed by changing the point of application of force without changing the direction of force. In Fig. 1.6 (a), when force F is applied at the point A of the wheel, the wheel rotates anticlockwise; while in Fig. 1.6 (b), the wheel rotates clockwise when the force F in same direction is applied at the point B of the wheel.

Fig. 1.6 Sense of rotation changed by the change of point of application of force

(4) In a bicycle, to turn the wheel anticlockwise, a small force is applied on the foot pedal of a toothed wheel of size bigger than the rear wheel so that the perpendicular distance of

the point of application of force from the axle of wheel is large (Fig. 1.7). The two wheels are joined by a chain through their tooth.

Fig. 1.7 Turning of toothed wheel of a bicycle

(5) A spanner used to tighten or loosen a nut, has a long handle to produce a large moment of force by a small force applied normally at the end of its handle as shown in Fig. 1.8. The spanner is turned anticlockwise to loosen the nut by applying the force in the direction shown in Fig. 1.8, while it is turned clockwise to tighten the nut by applying the force in a direction opposite to that shown in Fig. 1.8.

Fig. 1.8 Spanner (wrench) used to loosen a nut

Conclusion:

From the above examples, we conclude that the turning of a body about an axis depends not only on the magnitude of the force, but it also depends on the perpendicular distance of the line of action of the applied force from the axis of rotation. Larger the perpendicular distance, less is the force needed to turn the body.

1.3 Couple

A single force applied on a pivoted body alone does not cause rotation of the body. Actually the rotation is always produced by a pair of forces. In the above examples, the rotation is due to the force externally applied and the force of reaction produced at the pivoted point. The force of reaction at the pivot is equal in magnitude, but opposite in direction to the applied force. The moment of the force of reaction about the pivot is zero because its distance from the axis of rotation is zero, so the force of reaction at the fixed point (or pivot) is not shown in Fig. 1.3 to Fig. 1.8. Such a pair of forces is called a couple. Thus two equal and opposite parallel forces, not acting along the same line, form a couple. A couple is always needed to produce a rotation. For example, when we open a door, the rotation of the door is produced by a couple

consisting of two forces: (i) the force which we exert at the handle of the door, and (ii) an equal and opposite force of reaction at the hinge.

In case if we require a larger turning effect, the two forces, equal in magnitude and opposite in directions, are applied on the body explicitly such that both the forces turn the body in the same direction.

Example: To open the nut of a car wheel, we apply equal forces, each F, at the two ends of the wrench's arm in opposite directions as shown in Fig. 1.9.

Fig. 1.9 Opening the nut of a car wheel by a wrench

Similarly turning a water tap (Fig. 1.10), tightening the cap of an inkpot (Fig. 1.11), turning the key in the hole of a lock (Fig. 1.12), winding a clock (or a watch) with the key, turning the steering of a motor-car (Fig. 1.13), driving the pedal of a bicycle, etc., are the other examples where a pair of forces (couple) is applied for rotation.

Fig. 1.10 Turning a water tap

Fig. 1.11 Tightening the cap

Fig. 1.12 Turning a key in a lock

Fig. 1.13 Turning a steering wheel

Moment of couple:

Fig. 1.14 illustrates the motion of the body, and (ii) the algebraic sum of moments of all forces about the fixed point is zero, so they do not change the rotational state of the body, then the body is said to be in equilibrium. Thus

When a number of forces acting on a body produce no change in its state of rest or of linear or rotational motion, the body is said to be in equilibrium.

Kinds of equilibrium

The equilibrium is of two kinds: (1) static equilibrium, and (2) dynamic equilibrium.

(1) Static equilibrium: When a body remains in the state of rest under the influence of several forces, the body is in static equilibrium.

Examples: (i) In Fig. 1.15, if a body lying on the table top is pulled by a force F to its left and by an equal force F to its right (along the same line), the body does not move. The reason is that the applied forces are equal and opposite along the same line, so they balance each other (i.e., there is no net horizontal force on the body). Hence the body remains at rest (i.e., in static equilibrium).

Fig. 1.15 A body is static equilibrium

(ii) If a book is lying on a table, the weight of the book exerted on the table vertically downwards is balanced by the equal and opposite force of reaction exerted by the table on the book vertically upwards. Thus, the book is in static equilibrium.

(iii) In a beam balance when the beam is balanced in horizontal position, the clockwise moment of force due to object on its right pan balances the anticlockwise moment of force due to weights on its left pan and the beam has no rotational motion i.e., it is in static equilibrium.

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