CBSE Class 10 Physics Thrust and Pressure Notes Set 18

Thrust and Pressure

Thrust is the force acting perpendicular to a surface. Pressure is the thrust acting on each unit area: \( P = \dfrac{F}{A} \). It is a scalar. The SI unit is the pascal (1 Pa = 1 N/m\( ^2 \)). Other units: 1 bar = 10\( ^5 \) Pa, 1 atm = 1.013 \( \times \) 10\( ^5 \) Pa, 1 mbar = 100 Pa, 1 torr = 1 mm of Hg.

For a given thrust, pressure is inversely proportional to area. This is why knives and nails have sharp points, while school bags have broad straps, tractors have wide tyres and buildings have broad foundations.

Density and Relative Density

Density \( \rho = \dfrac{m}{V} \). SI unit kg/m\( ^3 \); CGS unit g/cm\( ^3 \); 1 g/cm\( ^3 \) = 1000 kg/m\( ^3 \). Water has density 1000 kg/m\( ^3 \). Relative density (specific gravity) = density of substance / density of water. It is a pure number with no unit. The density of a gas changes with temperature and pressure, while that of a solid or liquid is nearly constant.

Pressure in Fluids

1. A fluid is a liquid or a gas. It presses on the base and the walls of its container, and this pressure at a point acts equally in all directions.
2. Pascal's law: pressure applied to an enclosed fluid is transmitted equally to every part of the fluid and to the walls. Hydraulic lifts, presses and brakes use this law, so a small force on a small piston gives a large force on a large piston: \( \dfrac{F_1}{A_1} = \dfrac{F_2}{A_2} \).
3. Pressure due to a liquid column: \( P = h\rho g \). It depends only on the depth h, the density of the liquid and g, and not on the shape of the vessel or the area of the base.
4. At the same level in a liquid at rest the pressure is the same. Pressure increases with depth.
5. Total (absolute) pressure at depth h = atmospheric pressure + \( h\rho g \).

Atmospheric Pressure

The weight of the air column above a surface causes atmospheric pressure, about 10\( ^5 \) Pa at sea level. It decreases as altitude increases. We do not feel it because the pressure inside our body balances it.

1. Absolute pressure = atmospheric pressure + gauge pressure.
2. Vacuum pressure is the amount by which a pressure is below atmospheric: absolute pressure = atmospheric - vacuum pressure.
3. A mercury barometer measures atmospheric pressure. The mercury column is about 76 cm (760 mm) high at sea level. Mercury is used because its high density keeps the column short; a water barometer would need about 10.3 m.
4. A manometer measures the pressure of a gas using a liquid column.
5. Two immiscible liquids in a U-tube balance when \( h_1\rho_1 = h_2\rho_2 \): the denser liquid stands lower.

Buoyancy and Archimedes' Principle

A fluid pushes up on a body immersed in it because pressure increases with depth, so the push on the bottom is greater than that on the top. This upward force is the buoyant force (upthrust). Archimedes' principle states that when a body is immersed wholly or partly in a fluid, the upthrust equals the weight of the fluid displaced: \( F_B = \rho_L V_L g \).

1. Apparent weight = weight in air - upthrust. This loss of weight equals the weight of the displaced fluid.
2. The upthrust on a fully submerged body does not change with depth.
3. Relative density of a sinking solid = weight in air / loss of weight in water.
4. Relative density of a liquid = loss of weight of a solid in the liquid / loss of weight of the same solid in water.
5. Applications: ships, submarines, hydrometers and lactometers.

Floating and Sinking

Law of floatation: a floating body displaces liquid whose weight equals the weight of the body. The fraction of a floating body immersed is \( \dfrac{V_{in}}{V} = \dfrac{\rho_s}{\rho_L} \) and the fraction outside is \( 1 - \dfrac{\rho_s}{\rho_L} \). A floating body has zero apparent weight. A floating body is lifted higher in a denser liquid. A sheet of metal floats if it is shaped into a bowl, since it then displaces more liquid. Ice floating in water does not change the water level on melting.

Worked Examples

Example 1. A force of 600 N acts on an area of 0.02 m\( ^2 \). Pressure = 600/0.02 = 30000 Pa.

Example 2. Pressure at the bottom of a 5 m deep lake (g = 10 m/s\( ^2 \)) = 1000 \( \times \) 10 \( \times \) 5 = 5 \( \times \) 10\( ^4 \) Pa above atmospheric pressure.

Example 3. A solid weighs 60 gf in air and 50 gf in water. Loss = 10 gf, so relative density = 60/10 = 6.