Unit 6: Mechanical Properties of Matter — Short Questions

Mathematically P = F/A

Large area of feet to spread their weight over a bigger area, reduce air pressure on ground.

Thus, heavy animals like elephant have a large area of the foot to reduce pressure on ground.

Deer have small feet to run faster by reduce air fraction with ground. This helps the deer escape predation easily.

P = F/A

When we walk on bare footed, the small contact area with high pressure, cause in pain. A large contact area would spread the force, reduce in pressure and discomfort.

Pascal's Law

When pressure is applied at one point in an enclosed fluid, it is transmitted equally to all parts of liquid without loss.

Applications (i) Hydraulic press
(ii) Car lift at service station
(iii) Hydraulic brakes of vehicles

The property of an object to re-gain its original size and shape after removal of applied force is called elasticity.

Hooke's law states that extension or compression is directly proportional to force applied.

No. an object does not remain elastic beyond its elastic limit. Once the elastic limit is exceeded, the object undergoes plastic deformation and does not return to its original shape.

Force An agent which produces or tends to produce motion, stops or tends to stop the motion or deforms or tends to deform an object.

Pressure The normal force per unit area is called pressure.

Mathematically P = F/A

The pressure of liquid given by relation

P = ρgh

It is clear that pressure is directly proportional to depth of liquid (P ∝ h).

The basic principle is hydrostatic pressure utilizing a liquid column in a barometer.

See QNo.4.

In steel more effort is required to change the shape as compared to rubber because the steel molecules retain their shape quickly as the deforming force ceases to act. That is why steel is more elastic than rubber.

Some materials such as clay dough or plasticine do not return to their original shape after the removal of the deforming force. They are known as inelastic materials.

Sports boots for football and hockey have studs on their soles. They reduce the area in contact between your feet and the ground. This increases the pressure and your feet grip the surface more firmly.

Atmospheric pressure extends up to a height of about 100 kilometers. The density of air is not the same in the atmosphere. It decreases continuously with altitude and hence atmospheric pressure decreases with altitude.

We have studied that pressure in a liquid increases with depth. At depth h, the pressure of liquid is given by P = ρgh

This formula is applicable to all the fluids. As the gases of the atmosphere are also fluid, therefore, the atmospheric pressure should be more and more on the ground at sea level. As we go'up in the air, atmospheric pressure decreases. At a height of about 5km it falls to 55 kPa and at a height of 30 km it to 1 kPa.

The atmospheric pressure does not always remain uniform but fluctuates. By observing the variation, the meteorologists can forecast the weather condition. Atmospheric pressure depends upon the density of air. At height altitudes, where the air is less dense, the atmospheric pressure falls down. Similarly, increase in the quantity of water vapours also decreases the density. Thus, atmospheric pressure becomes low in cloudy region. Weather casters use this knowledge to predict rains. A fall in pressure often means that rain clouds are on the way and the rain is to follow.

Pressure is given by

P = F/A = constant/A => P ∝ 1/A

For a constant force, pressure is inversely proportional to the area, i.e., if area is less then pressure is more and vice versa. In case of heels, the pressure is concentrated on a very small area thus pressure exerted by it is more and hence leaves a deeper marks on the carpet.

We know that the pressure is given by,

P = F/A

Equation (1) shows that pressure is inversely proportional to the area. That is greater the area, smaller will be the pressure and vice versa. Now the cutting edge of the knife is made very thin for getting smaller area and maximum pressure by increasing pressure, we can cut various objects with knife very easily.

We know that the pressure of liquid in terms of height is given by,

P = ρgh-----(1)

Equation (1) shows that the pressure of water pipe system increases with height.

Thus for the easy flow of water in a pipe system, the water tanks are constructed at the highest level in our houses.

At the top of mountains, the air pressure is lower as compared to plane area. So low pressure air will be filled in a balloon at the top of mountains.

Now when moves from mountains towards plane areas, the air pressure increases. Thus the outside air pressure becomes higher than air pressure inside the balloon. The high atmospheric pressure stress the walls of the balloon inwards, due to which the balloon contracts and its volume decreases.

We know that,

P = F/A-----(1)

Equation (1) shows that pressure is inversely proportional to the contact area, i.e. larger the contact area smaller will be pressure exerted and vice versa. Since camels have feet with comparatively large surface area, therefore they exert little pressure. As a result of less pressure, their feet does not insert deep in the sand and remain on upper surface of the sand. Thus they can walk in desert easily due to less pressure exerted by their feet on sand surface.

Pressure exerted by liquid is given by:

P = ρgh => P = (constant) h

=> P ∝ h

Since pressure in liquid is directly proportional to the height of the liquid, i.e., depth of the dam. Thus, as the depth increases, more and more pressure is exerted by water on the walls of the dam. A thicker wall can withstand greater pressure, therefore, the thickness of the dam increases towards the bottom.

Water is not suitable in barometer because of its lower density. The density of mercury is 13.6 times than water. So the height of water column at sea-level in barometer will be

(0.76m) (13.6) = 10.335m. (760mm = 0.76m)

A glass tube with this length is not practicable, that's why water is not suitable use in barometer.

Barometer is a device used for measuring atmospheric pressure. Atmospheric pressure decreases as we travel to high altitude areas. When atmospheric pressure decreases, the pressure on the mercury inside barometer also decreases. This decrease in pressure on the mercury leads to a decrease in the mercury level in column.

The level of mercury in the column depends upon the atmospheric pressure, i.e. greater the atmospheric pressure, high will be the level of mercury in the column and vice versa.

Now we know that the atmospheric pressure decreases at the top of mountains, so the level of mercury in glass tube of the barometer will fall down i.e. decreases.

Elastic Limit It is a limit with in which a body recovers its original length, volume or shape after the deforming force is removed. When a stress crosses this limit, a body is permanently deformed and is unable to restore its original state after the stress is removed.

Hooke's Law "The strain produced in a body by the stress applied to it is directly proportional to the stress within the elastic limit of the body".

Young's modulus The ratio of stress to tensile strain is called young's modulus"

Y = Stress / TensileStrain

Some identical springs, each with spring constant k, are arranged as shown below:

For each arrangement, complete the table by determining:
i. The total extension in terms of x.
ii. The spring constant in terms of k.

Ans

Arrangement [Series diagram]
Total Extension x: For springs in series, the extensions add up. If one spring extends x, then the total extension is: X_total = 2x
Spring constant ) of the arrangement: In this case the two springs are in series. The equivalent spring constant k_eq for springs in series is given by: k_eq = k/2

Arrangement [Parallel diagram]
Total Extension x: For springs in parallel, the extensions of each spring is the same as if only one spring were used: X_total = x
Spring constant: In this case the two springs are in parallel. The equivalent spring constant k_eq for springs in parallel is given by: k_eq = k+k = 2k

For spring in sovier, the total extension is the sum of extension of each spring.

i. Steel is more durable and can with stand higher pressure without deforming.
ii. Steel has greater strength and corrosion resistance.

(a) Iron is more elastic than rubber because iron returns to its original shape more completely after the deforming forces are removed.

Rubber, on the other hand, undergoes more permanent deformation.

(b) Air is more elastic than water because air can be compressed and expanded more easily than water, returning to its original volume and shape.

The water pressure 1 meter below the surface is the same in both a swimming pool and a large lake, assuming both are freshwater. The pressure is given by formula:

P = ρgh

Where P is the pressure, ρ is the water density, g is gravity and h is depth. At 1 meter the pressure is the same in both environment because depth and density environment because depth and density

According to Pascal's Principle, if pressure is increased in one part of a confined liquid, the pressure will increase equally in all other parts of the liquid.

Example from daily life Hydraulic Brake System in vehicles.

When you press the brake pedal, it increases the pressure in the master cylinder, which is filled with brake fluid (a confined liquid). This increased pressure is transmitted equally to all parts of the brake system, including the brake calipers, which then apply the pressure to the brake pads to stop the vehicle.

The trapped air in the barometer adds pressure, which lower the Hg height by opposing atmospheric pressure.

The long neck of giraffe is not a problem when raised suddenly due to a special value called the "rete mirabile" which regulates blood pressure and flow to the brain.

It causes the reading lower than actual atmospheric pressure.

ρ = m/v

It depends upon type of material and is constant for a given material regardless of size or shape of object.

An engineer estimates a large structure's load by calculating the weight of materials, occupants and external forces like wind, snow and earthquakes.

See QNo.10

See QNo.8+9

See QNo.6

See QNo.5

See QNo.6