Notes
Force : Force is a physical quantity that changes the state of rest or of uniform motion of a body in a straight line.
Newton's first law of motion : A stationary object on which no force is acting, remains stationary. An object in motion continues to move with the same speed and direction when no force is acting on the object.
A force acts on two bodies through an interaction between them.
Contact force : A force that acts through a direct contact of two objects or via one more object, is called a contact force.
Non-contact force : A force that acts between two objects even if the two objects are not in contact, is called a non contact force.
Balanced forces : if a body is acted upon by two forces, equal in magnitude, opposite in direction and having the same line of action, the forces are called balanced forces. Here, the net force acting on the body is zero.
Unbalanced force : If two or more forces act on a body such that their resultant is not zero, the resultant is an unbalanced force. It produces acceleration in the body.
- If several forces are applied on an object in the same direction, a force equal to their addition acts on that object.
- If two forces are applied on one object in directions opposite to each other, a force equal to their difference acts on the object.
- A force is expressed in magnitude and direction. Force is a vector quantity.
Inertia : The tendency of an object to remain in its existing state is called Its inertia.
Types of inertia : 1. Inertia of the state of rest : An object in the state of rest can not change its state of rest due to its inherent property. This property is called the inertia of the state of rest. Examples : (1) When we dust a carpet, the carpet moves but the dust particles in it remain at rest due to inertia and hence get separated from the carpet. Hence, the carpet becomes clean. 2) When a bus starts suddenly, the passengers experience a backward jerk due to inertia. 2. Inertia of motion : The inherent property of an object due to which its state of motion can not change, is called its inertia of motion. For exmaple a revolving electric fan continues to revolve even after it is switched off, passengers sitting in the running bus get a jerk in the forward direction if the bus suddenly stops. 3. Directional inertia : The inherent property of an object due to which the object can not change the direction of its motion, is called directional inertia. For example, if a vehicle in motion along a straight line suddenly turns, the passengers sitting in it are thrown opposite to the direction of turning.
The effects of a force acting on a body :
Pressure : The force exerted perpendicularly on a unit area is called pressure.
The effect of a given force varies inversely as the area of the surface on which the force is applied. The less the surface area, the greater is the effect of the force.
OR
For a given force, pressure is inversely proportional to the area of the surface on which the force acts.
Example: (1) The cutting edge of a sharp knife has less cross sectional area relative to that of a blunt knife. Hence, it is easy to cut vegetables, fruits with a sharp knife, rather than with a blunt knife. (2) The tip of a pointed nail has an extremely small area, while that of a blunt nail has a comparatively large area. A given force creates a large pressure on the pointed nail and it can be easily hammered into the wood, while a very less pressure is created on the blunt nail and it cannot be easily hammered into the wood. This shows that pressure varies inversely as the area of the surface on which the force is applied, if the force remains constant. If the same force is applied to surfaces having different areas the pressure is more on the surface having a smaller area. (3) Load carrying heavy vehicles have large number of wheels so that the load (weight, force) is distributed over large surface area of the wheels in contact with the road. Hence, the pressure decreases and the tyres do not burst.
Atmospheric Pressure : Air, due to its weight, exerts pressure on the surface of the earth. The pressure exerted by air or the atmosphere surrounding the earth is known as the atmospheric pressure. It is the ratio of the weight of the air to the area of the surface of the earth. It decreases with altitude as the density of air decreases with altitude and also the weight of the air column above a given place. Its density is high up to about 16 km from the earth’s surface. Beyond that, up to about 400 km, its density is very low.
The SI unit of pressure is N/m2. It is called the pascal (Pa). In atmospheric science, the unit for pressure is called the bar.
1 bar = 105 Pa.
The air pressure at the sea level is called 1 atmosphere.
1 atmosphere = 101 x 103 Pa.
At a depth h below the free surface of a liquid, the pressure exerted by the liquid is hρg. (ρ = density of liquid)
Q. How much pressure do we carry on our heads ? Why don’t we feel it ?
The air pressure at the sea level is about 101x103 Pa. This is the pressure that we carry on our heads. The cavities in our body are filled with air, and arteries and veins are filled with blood. Their pressure balances the pressure due to the atmosphere. Hence, we don’t feel the atmospheric pressure.
Buoyant force : The upward force acting on the object in water or other fluid or gas is called the buoyant force.
It depends on the volume of the object immersed in the fluid (V), the density of the fluid (ρ1) and the acceleration due to gravity (g) at that place. Magnitude of the buoyant force = Vρ1g.
Archimedes‘ principle: When an object is partially or fully immersed in a fluid, a force of buoyancy acts on it in the upward direction. This force is equal to the weight of the fluid displaced by the object.
[Note : The two forces mentioned here are equal in magnitude and opposite in direction]
Q Using Archimedes’ principle, determine the magnitude of the buoyant force.
Let m=mass of the body (Object) immersed in the fluid, V=volume of the body, ρ= density of the body, ρ1= density of the fluid, g =magnitude of the acceleration due to gravity. Suppose that the body is completely immersed in the fluid. Then the volume of the fluid displaced by the body = V. According to Archimedes’ principle, magnitude of the buoyant force= magnitude of the weight of the fluid displaced by the body = mass of the displaced fluid x g = volume of the displaced fluid x density of the fluid x g (as density = mass/volume) = Vρ1g = \(\frac{m}{ρ}ρ_1g = mg\frac{ρ}{ρ_1}\) If the body is partially immersed in the fluid, the volume of the fluid displaced by the immersed part of the body = xV here 0 < x < 1. In this case, the magnitude of the buoyant force = xVρ1g = \(x\frac{m}{ρ}ρ_1g = xmg\frac{ρ}{ρ_1}\)
Applications of Archimedes’ principle. : (1) The working of a lactometer, a device used to determine the purity of a sample of milk, and a hydrometer, a device used to determine the density of a liquid, is based on Archimedes’ principle. The extent to which a lactometer floats (or sinks) depends on the density (and hence purity) ofthe milk. The same thing is true for a hydrometer. The greater the density of a liquid, the less is the extent to which a body (2) Archimedes’ principle is used in design of ships and submarines. A submarine is provided with large tanks at the front and the back. Its weight can be increased by filling the tanks with sea water or air from compressed air reservoirs. The weight can be decreased by pumping out water from the tanks by forcing compressed air in them. By controlling the weight, it can be made to sink or rise to the surface as desired. (3) The density of a body that floats or sinks in water or kerosene can be determined by Archimedes’ principle. (4) The density of kerosene can be determined by Archimedes’ principle, using a body of material that is not affected by water and kerosene.
Q. Why does it happen? A ship dips to a larger depth in fresh water as compared to marine water.
The density of fresh water is less than marine water, due to which the buoyant force on the ship in marine water is more than the fresh water. Hence, the ship dips to a larger depth in fresh water as compared to marine water.
Density = mass/volume. Its SI unit is kg/m3 and CGS unit is g/cm3.
1 g/cm3 = 103 kg/m3.
Relative density = density of a substance/ density of water.
It has no unit. Relative density is also called specific gravity.
Characteristics of the pressure due to a liquid (or a fluid): (1) The pressure at a point in a liquid (or a fluid) is due to the weight of the liquid (fluid) column above that point. (2) It acts on all sides of the container. (3) At a given depth it is the same in all directions. (4) It is independent of the size and shape of the container. (5) It is proportional to the height of the liquid (fluid) column above the given point. (6) It is proportional to the density of the liquid (fluid). (7) It is proportional to the acceleration due to gravity at the given place.