Force and Pressure

N m

Reason — S.I. Unit of moment of force = S.I. Unit of force x S.I. Unit of distance = N x m

So, the S.I. unit of moment of force is N m.

Applying the force farthest from the pivoted point.

Reason — Larger the perpendicular distance of the point at which the force is applied from the pivoted point, less force is needed to obtain a given moment of force for turning a body.

kgf

Reason — The gravitational unit of thrust is kgf.

N m^-2

Reason —

Unit of Pressure = $\frac{\text{Unit of Force}}{\text{Unit of Area}}$ = $\frac{\text{N}}{\text m^2}$

So, unit of pressure is N m^-2.

Pressure = $\frac{\text{Thrust}}{\text{Area}}$

Reason — Pressure is defined as thrust acting per unit area.

5 kgf

Reason — A body when placed on a surface exerts a thrust on the surface which is equal to its own weight. So thrust = weight of the body = 5 kgf.

suction pads

Reason — Lizards can stay and move on walls because their feet behave like suction pads so they remain pressed against the wall due to atmospheric pressure.

Weight

Reason — Liquids have weight and pressure is weight acting per unit area.

increase in depth

Reason — Pressure of liquid at a point increases with the height of the liquid column above it, so as depth increases pressure inside liquid increases.

100,000 Pa

Reason — At sea level, the atmospheric pressure is 100,000 Pa which is 76 cm of mercury column.

the atmospheric pressure decreases

Reason — At higher altitudes, atmospheric pressure decreases but our body pressure remains the same. So, inside pressure becomes more than atmospheric pressure which causes nose bleeding.

Assertion is false but reason is true

Explanation

Assertion (A) is false because a force does not change the mass of the body on which it is applied.

Reason (R) is true because force is that cause which changes the state of a body (either the state of rest or the state of motion) or changes the size or shape of the body.

Hence, assertion is false but reason is true.

Both A and R are true and R is the correct explanation of A

Explanation

Assertion (A) is true because in heavy container trucks, more number of tyres increases the area of contact and thereby reduces the pressure on the ground and if there are only four tyres in a heavy truck, due to less area the pressure applied by the truck will be more and hence its speed will get affected.

Reason (R) is true because the pressure on a surface depends inversely on the area of the surface on which thrust acts so that smaller the surface area, more is the pressure exerted by the thrust and larger the surface area, lesser is the pressure exerted by the same thrust.

So, here reason justifies the assertion.

Hence, both A and R are true and R is the correct explanation of A.

Assertion is true but reason is false

Explanation
A camel’s broad feet spread its weight over a larger area, so the pressure it exerts on the sand is lower; this prevents its feet from sinking. Hence the Assertion is correct. The Reason, however, is incorrect because the feet decrease, not increase, the pressure on the sand.

Hence, assertion is true but reason is false.

(a) 1 kgf = 10 N (nearly).

(b) Moment of force = force x distance of force from the point of turning.

(c) In a door, handle is provided farthest from the hinges.

(d) The unit of thrust is Newton .

(e) Thrust is the normal force acting on a surface.

(f) Pressure is the thrust acting on a surface of unit area.

(g) The unit of pressure is Pascal.

(h) Pressure is reduced if surface area increases.

(i) Pressure in a liquid increases with the depth.

(j) The atmospheric pressure on earth surface is nearly 10⁵ Pa.

(a) False
Correct Statement — The S.I. unit of force is newton.

(b) False
Correct Statement — A force can produce either linear motion or turning motion.

(c) True

(d) True

(e) False
Correct Statement — Pressure is defined as thrust per unit area. Hence, for a given thrust, pressure is less on a surface of large area.

(f) True

(g) False
Correct Statement — A man exerts more pressure while standing than lying on the ground as area of contact is less in case of standing as compared to lying on the ground.

(h) False
Correct Statement — Incase of blunt nail, the thrust exerted on hammering acts on a larger area so less pressure acts on the piece of wood making it difficult to hammer the nail.

(i) True

(j) False
Correct Statement — Water in a lake exerts pressure in all directions.

(k) True

(l) True

(m) True

(n) False
Correct Statement — Higher we go, lesser is the air pressure.

Force is that cause which changes the state of the body (either the state of rest or the state of motion) or changes the size or shape of the body. The S.I. unit of force is newton (N).

The two effects of a force when applied on a body are —

(i) It can change the shape or size of a body.

(ii) It can stop a moving body or it can move a stationary body.

(a) When a force is applied on a rigid body, it produces only change in motion of the body. The force does not cause any change in the inter-spacing between its constituent particles.

(b) When a force is applied on a non-rigid body, it causes both change in its size or shape and motion in it.

The moment of force is equal to the product of the magnitude of the force and the perpendicular distance of the force from the pivoted point.

The S.I. unit of moment of force is newton x metre (N m).

The two factors which affect moment of force are —

1. Magnitude of force.
2. Perpendicular distance of force from the pivoted point.

The expression for the moment of force about a given axis of rotation is —

Moment of force about a given axis = Force x perpendicular distance of force from the axis of rotation.

The moment of given force about a given axis of rotation is decreased by either decreasing the force or by decreasing the perpendicular distance of force from the axis of rotation.

One way to obtain greater moment of a given force is to increase the distance from the axis of rotation where the force would act.

If the effect on the body is to turn it clockwise, the moment of force is called clockwise moment. If the effect on the body is to turn it anti-clockwise, the moment of force is called anti-clockwise moment.

If a force is applied on a surface in a direction perpendicular to the surface, the force is called thrust. In other words, thrust is the force acting normally on the surface.

The units of thrust are kilogram force(kgf), gram force(gf) and newton(N) (same as that of weight or force).

The effect of thrust depends on the area of the surface on which it acts. Smaller the area of the surface on which a thrust acts larger is its effect and effect of thrust is less on a larger surface area.

Pressure is defined as the thrust acting per unit area.

Pressure = $\frac{\text{Thrust}}{\text{Area}}$

Its unit is pascal (Pa) or $\frac{\text{newton}}{\text{metre}^2}$ (N m^-2).

Pressure is thrust acting per unit area. Thrust is directly proportional to pressure. Greater the thrust, greater is the pressure and smaller the thrust, smaller is the pressure.
Pressure = $\frac{\text{Thrust}}{\text{Area}}$

The two factors on which the pressure on a surface depends are:

1. Area of the surface on which thrust acts.
2. Magnitude of thrust acting on the surface.

The bottom part of the foundation of a building is made wider so that the weight of the building will act on larger surface area exerting less pressure on the ground (as pressure is inversely proportional to surface area). This avoids sinking of buildings into the earth.

A sharp knife has sharp edges that provides less surface area of contact as compared to a blunt knife which has more surface area of contact. So pressure applied by the force is more in sharp knife which makes it easier to cut than a blunt one.

(i) A gum bottle has broader base and narrower neck and when it is placed upside down there will be no change in thrust as thrust is the weight of the body that is exerted on the surface.

(ii) When gum bottle is placed upside down, surface area is less so pressure will be more as pressure is inversely proportional to surface area.

The two factors on which the pressure at a point in a liquid depends are:

1. The height of the liquid column — Liquid pressure increases with the height of the liquid column above the point.
2. The density of the liquid — Liquid pressure increases with the increase in the density of the liquid.

The thrust on unit area of the earth surface due to the column of air is called the atmospheric pressure.

The blood in the veins of our body exerts a pressure which is slightly more than the atmospheric pressure which makes the effect of atmospheric pressure ineffective. So we do not feel uneasy even under the enormous atmospheric pressure.

The atmospheric pressure on the earth surface in pascal is 1.013 x 10⁵ Pa.

A spanner has a long handle to produce a large turning effect by applying a small amount of force at the end of the handle as shown in the figure below:

It is easier to turn the steering wheel of large diameter as larger the diameter, larger is the perpendicular distance from the axis of rotation so less force is applied to generate same amount of turning effect as compared to steering wheel of small diameter.

The hand flour grinder is provided with a handle near the rim which is at a maximum distance from the axis of rotation so that it can easily be rotated at its centre by applying a small force at the handle.

It is easier to open the door by pushing it at its free end because larger the perpendicular distance from the axis of rotation, less is the force required to open it.

A potter's wheel is pivoted at the centre. When the potter applies a force through the stick near the rim of the wheel, the point of application of force is at a maximum distance from the axis of rotation, hence less force is required to rotate the wheel.

(a) Wide wooden sleepers are placed below the railway tracks to increase the surface area of the tracks in contact with the ground. This reduces the pressure exerted by the rails on the ground.

(b) The foundation of a tall building is made wider because the weight of the building will act on larger surface area exerting less pressure on the ground (as pressure is inversely proportional to surface area). This avoids sinking of building into the earth.

The following experiment demonstrates that a liquid exerts pressure at the bottom of the container in which it is kept:

1. Take a glass tube and tie a balloon at its lower end.
2. Hold it vertically straight as shown in the above figure.
3. Pour some water in the tube.

Observations — After sometime we will notice that the balloon bulges out as shown in figure (b) above.

Conclusion — Balloon bulges out because water column exerts pressure at its bottom. The force on the balloon is equal to the weight of the water column known as thrust.

So,

Pressure = $\frac{\text{Thrust}}{\text{Area}}$ = $\frac{\text{W}}{\text{A}}$,

where

• W is weight of the water column (thrust) and
• A is surface area.

The following experiment demonstrates that a liquid exerts pressure sideways also:

1. Take a glass tube closed at one end and having an opening in its side near the bottom.
2. Tie a deflated balloon at the side opening of the tube.
3. Hold the tube vertically straight as shown in the above figure.
4. Pour some water in the tube.

Observations — After sometime we will notice that the balloon bulges out as shown in figure (b) above.

Conclusion — From the above experiment it is concluded that a liquid exerts pressure sideways also.

The experiment is described below:

1. Take a glass tube open at both ends. Hold it vertically.
2. Tie a balloon at its lower end.
3. Pour some water in the tube.
4. Balloon starts bulging out as shown in figure (a) above.
5. Add more water in the tube.
6. Balloon will bulge more as shown in figure (b) above.

Conclusion — From the above experiment it is concluded that when the height of the water column increases, more pressure is exerted on the balloon and it bulges out more. This shows that the liquid pressure at a point increases with the increase in height of the liquid column above that point.

The following experiment demonstrates that at a given depth, a liquid exerts same pressure in all directions:

1. Take a balloon and fill it with water.
2. Tie the mouth of the balloon.
3. Make holes in the balloon by inserting pins at several places in all directions.

Water comes out through each hole which shows that liquid exerts same pressure in all directions.

The following experiment demonstrates that liquid pressure depends on the density of liquid:

1. Take two identical glass tubes open at both the ends. Mark them A and B.
2. Hold both the tubes vertically and tie an inflated balloon to both the tubes at their lower ends.
3. In tube A pour some water.
4. In tube B pour some concentrated sugar solution such that its height is same as that of height of water in tube A.

Observation — It is noticed that the balloon attached to tube B bulges out more as compared to balloon attached to tube A as shown in the above figure.

Conclusion — Density of sugar solution is more than water so it exerts more pressure which shows that liquid pressure depends on the density of liquid.

The following experiment demonstrates that air exerts pressure:

1. Take a glass filled with water up to its brim and place a post card on top of it.
2. Press the palm of your one hand on top of post card and then invert the filled glass upside down.
3. Now gently remove your hand from the post card to release it.

Conclusion — It is observed that post card does not fall from the glass because the atmospheric pressure is acting upwards on the post card from outside the glass which overcomes the pressure on post card due to water in the glass.

Crushing tin can experiment

1. Take a thin walled tin can with airtight stopper. Remove the stopper.
2. Fill the can partially with water. Heat the can over the flame of a burner till water boils.
3. Now the air pressure inside and outside the can is same.
4. When steam comes out of the opening put the stopper.
5. Remove the can from the burner.
6. Place the can in the tub and pour cold water on the can.

It is observed that the can collapses. The reason is that when steam comes out it takes away most of the air from the can. When cold water is poured on the can, steam condenses into water leaving a partial vacuum in the can. The air pressure outside is more than inside which exerts force on the can causing it to collapse.

From this experiment it is concluded that air exerts pressure.

When air is removed from the balloon, the pressure inside it becomes much less than the outside atmospheric pressure and hence the balloon collapses.

There are two forces acting on the water inside the dropper one is liquid pressure from inside and atmospheric pressure from outside. Atmospheric pressure acting from outside balances the liquid pressure from inside so water does not come out from the dropper. When bulb is pressed the liquid pressure increases than atmospheric pressure and water comes out from the dropper.

Two holes are made in a sealed oil tin to take out oil from it because through one hole atmospheric pressure acts due to air entering through it and through another hole the oil comes out easily.

The atmospheric pressure decreases with increase in altitude. So, as we go higher the atmospheric pressure decreases.

A man exerts more pressure on the surface while walking than standing because while walking one foot is in contact with the floor so surface area is less but while standing both foot are in contact with the floor providing a large surface area. Since pressure is inversely proportional to surface area so pressure exerted while walking is more as compared to pressure exerted on standing.

The broad feet of camels and elephants increases the surface of the feet in contact with the ground. This reduces the pressure exerted on the ground as pressure is inversely proportional to surface area.
Thus, this helps camels to walk easily on the desert sand without their feet sinking in it. The large body weight of elephants is supported by their broad feet helping them to move around comfortably.

A sharp pin has less surface area as compared to a blunt pin, so for a given applied force sharp pin exerts more pressure than blunt pin and penetrates a surface like wood or wall easily. So, it works better than a blunt pin.

The diagram demonstrates that liquid pressure at a point increases with the height of the liquid column above it as water flowing out from upper hole falls near the cylinder while water from lower hole falls far from the cylinder.

The pressure at a point due to a liquid increases with the increase in height of the liquid column above it, so to withstand the increasing pressure of water a dam has broader walls at the bottom than at the top.

In the figure given below, the increasing length of arrows in water represents the increasing pressure on the wall of the dam towards the bottom.

Sea divers need to wear specially designed swim-suit because in deep sea, the total pressure exerted on the diver's body is much more than his blood pressure. To withstand it, they need to wear a specially designed swim-suit, made from glass reinforced plastic or cast aluminium. The pressure inside the suit is maintained at one atmosphere. This allows the diver to withstand the enormous external pressure and be safe underwater.

Given,

• Force = 20 N
• Distance = 0.5 m
• Moment of force = ?

Moment of force = Force x Distance
= 20 x 0.5
= 10 N m

So, the moment of force = 10 N m.

Given,

• Force = 25 N
• Moment of force = 2.5 N m
• Perpendicular distance d = ?

$$\begin{aligned}\text{Moment of force} = \text{Force} \times \text{Perpendicular distance} \\[1em] \Rightarrow \text d= \frac{\text{Moment of force}}{\text{F}} \\[1em] = \frac{\text{2.5}}{\text{25}} \\[1em] = 0.1 \text{ m}\end{aligned}$$

So, the perpendicular distance of force from the point = 0.1 m or 10 cm.

Given,

• Force = 5.0 N
• Distance = 10 cm = 0.1 m
• Moment of force = ?

Moment of force = Force x Distance
= 5.0 x 0.1
= 0.5 N m

So, Moment of force = 0.5 N m

Given,

• Moment of force = 2.0 N m
• Diameter = 2 m
• Radius = 1 m
• Force (f) = ?

Therefore

Perpendicular distance = Radius = 1 m

$$\begin{aligned}\text{Moment of force} = \text{Force} \times \text{Perpendicular distance} \\[1em] \text{Force} = \frac{\text{Moment of force}}{\text{Perpendicular distance}} \\[1em] = \frac{\text{2.0}}{\text{1}} \\[1em] = 2 \text{ N}\end{aligned}$$

So, minimum force required is 2 N.

Given,

• Thrust = 200 N
• Area = 0.02 m²
• Pressure = ?

$$\begin{aligned}\text{Pressure} = \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{\text{200}}{\text{0.02}} \\[1em] = 10000 \text{ Pa}\end{aligned}$$

So, the pressure is 10000 Pa.

Given,

• Pressure = 50000 Pa
• Area = 0.05 m²
• Thrust = ?

$$\begin{aligned}\text {Pressure} = \frac{\text{Thrust}}{\text{Area}} \\[1em] \Rightarrow \text {Thrust} = \text {Pressure} \times \text {Area} \\[1em] = 50000 \times 0.05 \\[1em] = 2500\ \text N\end{aligned}$$

So, Thrust = 2500 N

Given,

• Pressure = 50,000 Pa
• Thrust = 100 N
• Area = ?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] \Rightarrow \text{Area}= \frac{\text{Thrust}}{\text{Pressure}} \\[1em] = \frac{100}{50000} \\[1em] = 0.002 \text{ m}^{2}\end{aligned}$$

So, Area of body = 0.002 m² = 2 x 10^-3 m²

Given,

• Thrust = 300 N
• Area = 30 cm² = $\frac{30}{10000}$ = 0.003 m²
• Pressure = ?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{300}{0.003} \\[1em] = 1,00,000 \text{ Pa}\end{aligned}$$

So, Pressure = 1,00,000 Pa = 10⁵ Pa

Given,

• Pressure = 20000 Pa
• Area = 1 cm² = $\frac{\text{1}}{\text{10000}}$ = 0.0001 m² = 10^-4 m²
  Thrust = ?

$$\begin{aligned}\text {Pressure} = \frac{\text{Thrust}}{\text{Area}} \\[1em] \Rightarrow \text {Thrust} = \text {Pressure} \times \text {Area} \\[1em] = 20000 \times 10^{-4} \\[1em] = 2\ \text N\end{aligned}$$

Thrust = 2 N

Given,

• Weight = Thrust = 60 N
• Area = 15 cm x 20 cm = 300 cm² = $\frac{\text{300}}{\text{10000}}$ = 0.03 m²
• Pressure = ?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{\text{60}}{\text{0.03}} \\[1em] = 2000 \text{ Pa}\end{aligned}$$

Pressure = 2000 Pa

Given,

• Thrust = 100 kgf
• Area = 0.5 m²
• Pressure = ?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{\text{100}}{\text{0.5}} \\[1em] = 200 \text{ kgf m}^{-2}\end{aligned}$$

Pressure = 200 kgf m^-2

Given,

• Thrust = Weight = 60 kgf

As

1 kgf = 10 N

∴ 60 kgf = 60 x 10 = 600 N

So,

Thrust = 600 N

• Area = 2.5 cm x 0.5 cm = 1.25 cm² = $\frac{\text{1.25}}{\text{10000}}$ = 0.000125 m²
• Pressure =?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{\text{600}}{\text{0.000125}} \\[1em] = 48,00,000 \text{ Pa}\end{aligned}$$

Pressure = 48,00,000 = 4.8 x 10⁶ Pa

First case :

• Thrust = Weight = 2 kgf
• Area = 20 cm x 10 cm = 200 cm²
• Pressure = ?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{\text{2}}{\text{200}} \\[1em] = 0.01 \text{ kgf cm}^{-2}\end{aligned}$$

So, pressure exerted by brick in first figure is 0.01 kgf cm^-2.

Second case :

• Thrust = Weight = 2 kgf
• Area = 5 cm x 10 cm = 50 cm²
• Pressure = ?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{\text{2}}{\text{50}} \\[1em] = 0.04 \text{ kgf cm}^{-2}\end{aligned}$$

So, pressure exerted by brick in second figure is 0.04 kgf cm^-2.

Third case :

• Thrust = Weight = 2 kgf
• Area = 20 cm x 5 cm = 100 cm²
• Pressure = ?

$$\begin{aligned}\text{Pressure}= \frac{\text{Thrust}}{\text{Area}} \\[1em] = \frac{\text{2}}{\text{100}} \\[1em] = 0.02 \text{ kgf cm}^{-2}\end{aligned}$$

So, pressure exerted by brick in third figure is 0.02 kgf cm^-2.

(i) The turning effect of a force depends on its moment, which is given by:

Moment of force = Force × Perpendicular distance from the pivot

When Samay held the steering wheel close to its centre, the perpendicular distance from the pivot was very small. This made it very difficult to turn the wheel even with greater force.

(ii) When the steering wheel is held at its outer rim, the perpendicular distance from the centre of the wheel is maximum. Therefore, the same force produces a greater moment of force, making the wheel easier to turn.

(iii) The turning effect is maximum when the force is applied perpendicular to the radius of the steering wheel. When the driver applies force at an angle, only the component of the force perpendicular to the radius produces a turning effect. As this component is smaller than the total applied force, the moment of force decreases and turning becomes harder.

(iv) Buses are heavy vehicles and may require a greater turning effect to steer their wheels. A larger steering wheel provides a greater perpendicular distance from the centre. Therefore, the driver can produce the required moment of force by applying a smaller and more comfortable force.