Chapter 10- Pressure, Gravity and Moments

Chapter 10-Pressure,Gravity and Moments

Chapter 10- Pressure, Gravity and Moments.

Density = mass/volume unit = kgm-3

Pressure = force/area unit = Nm-2

or the Pascal(Pa)

Liquid at depth ‘h’ and density ‘p’ where acceleration due to gravity is ‘g’, the pressure ‘P’ due to the liquid is : P = pgh.

Pressure in a liquid :

Increases with depth
Acts perpendicular to any surface put in the liquid
Is the same in all directions at a given depth.

Archimedes’ Principle :states that when an object is partially or completely immersed in a fluid it experiences an upthrust equal in magnitude to the weight of the fluid displaced.

The Law of Flotation: states that the weight of a floating body is equal to the weight of the fluid it displaces.

There fore, upthrust = weight of displaced fluid =weight of object

When an object is placed in a liquid, as well as the force of upthrust (buoyancy) acting on it, viscosity opposes its downward motion as well. This means the tendency of the water particles to cling together, instead of separating.

Hydrometers : an instrument used for measuring the density of liquids; it sinks less in denser liquids. Used to measure:

% of alcohol in wines, spirits and beers.
Density of sulphuric acid in car batteries.
% of fat in milk.

Average value of atmospheric pressure is 1×105 Pa. To demonstrate atmosphericpressure, use the collapsing can.

In this experiment, the can is filled with water, and the water is then boiled, escaping as steam. The can is sealed, and cooled, resulting in the remaining steam particles condensing, and leaving a partial vacuum in the can. The atmospheric pressure outside the can is then greater than that inside the can, and the can collapses.

Aim : To verify Boyle’s Boyle’s Law : states that at constant temperature the volume of a fixed mass of gas is inversely proportional to its pressure.

Mathematically, p α 1/V, therefore p = k(1/V).

For a fixed mass of gas at constant temperature,

pV = k, where k is a constant.

Law

Method :

Set up the apparatus as shown in the diagram.
Pump air in until the gauge reads its max value.
Wait a minute, then measure the pressure of the gas, using the gauge, and record the volume of the gas, from the vertical scale.
Open the tap and release some air. Close the tap, and take the two readings again, after waiting a few minutes. This is important, as the temperature of the gas may change, as the pressure changes, and Boyle’s Law is dependant on constant temperature.
Repeat step four, until the pressure has returned to standard atmospheric pressure.
Graph p against 1/V.

Result:

The graph is a straight line through the origin.

Conclusion:

1. P is inversely proportional to V, hence verifying Boyle’s Law.

Newton’s Law of Universal Gravitation states that any two point forces in the universe attract each other with a force that is directly proportional the products of their masses and inversely proportional to the square of the distance between them.

F = Gm1m2/d2

Where F is the force, G is the Universal Gravitational Constant, m1 and m2 are the masses of the point forces, and d is the distance between them.

The force between two objects always acts as if all the mass of the objects were at their centre, and the distance was the distance between their centres.
The gravitational force between two objects is negligible, unless at least one of them has a very large mass. This is because the value of G is 6.7×10-11m2kg-2
As F α 1/d2, this is an example of an inverse square law. This means that as d is doubled, F is halved, etc.

Relationship between g and Mass of a body.