• The density of a substance is defined as its mass per unit volume.
• Density = Mass / Volume = m/v.

• The sl unit for density is kilogram per cubic metre ( kg m-3 ).
• Another commonly used unit for density is gram per cubic centimeter ( g m-3 ).
• Densities of common substances:

• When an object is placed in a liquid of lower density, the object sinks. When it is placed in a liquid if a greater density, it floats.
• For example, a copper sphere of density 8.9 g cm-3 sinks in water of density 1.0 g cm-3 but floats in mercury if density 13.6 g cm-3. The denser the liquid, the higher an object will float in the liquid.
• The hydrometer is used to meausre the density of a liquid.
• The hydrometer is specially designated to float in a liquid and to measure its density.
• If the hydrometer "floats higher", it indicated that the liquid has a higher density.
• Special hydrometers are used to test whether a car battery is fully charged or whether milk has been diluted with water.
• Example of a hydrometer:
  
  
  
  
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Definition of gravitational field and field strength:

• Gravitational field is a region in which the mass of an object experiences a force due to gravitational attraction.


• Gravitational field strength, g, is defined as gravitational force per unit mass.


• Any object placed around the Earth experiences a force pulling it towards the Earth. So, the earth is surrounded by a gravitational field. The force is strongest on the surface of the Earth and gets weaker as we go further away.
  
  

  

• There is gravitational field around the Earth. A gravitational field is the region within which a mass experiences a force of attraction.


• On the earth's surface, the gravitational field strength g is approximately 10N kg-1.


• The gravitational force on:

1) 1kg mass is 10N

2) 2kg mass is 20N.

3) 3kg mass is 30N.

4) m kg mass is mg.

• The gravitational force on a mass is known as its weight. Hence, the weight of a mass m is given by:
  

Weight = mass x gravitational field strength = mg .

• The gravitational field strength of the Earth decreases as the altitude increases.


• On the surface of the Moon, the gravitational field strength is about 1/6 the value of g on the Earth surface.


• Hence, the weight ( w = mg ) of an object is not constant but changes when the value of g changes.


• From the equation, Force = mass x acceleration, an object, of mass m experiences a gravitational force of F, which is equal to mg. Hence, mg = mass x acceleration.


• Acceleration of object on the earth's surface = weight / mass = mg / m = g = 10ms-2.


• The acceleration of an object that falls freelt under the action of gravitational force is known as the acceleration due to gravity.


• On the earth's surface, g = 10ms-2.

G-R-A-V-I-T-Y.

Demonstration of gravity:

Life without gravity ?

• The mass of an object is a measure of the amount of substance in the object.
  Mass is measured in kilograms (kg).
• The weight of an object is the force of gravity acting upon that object.
  Weight, like all forces, is measured in newtons (N).
• As we know from everyday experience, the greater the mass of an object, the greater its weight. The weight can be linked to the mass of Newton's second law. If we let a body of mass, m fall, it moves towards the centre of the earth, with an acceleration of g.
  Using the equation force = mass x acceleration due to gravity.

Weight = Mass x Acceleration due to gravity.
W = Mg

• On earth, g = 9.81 ms-2
  For a 1Kg mass,
  W = mg
  = 1kg x 9.81 ms-2
  = 9.81 N.
• Therefore, every 1Kg of weight = 9.81N.
  ( In calculations, g is usually rounded up to ms-2, so 1kg mass is said to have a weight of
  10N).
• The mass of an object will be the same no matter where the object is located in the universe. This means that the mass of an object will never change. On the other hand, the weight of an object will vary according to where the object is in the universe.
• The acceleration due to the moon's gravity, gm, is about one-sixth of the value on the Earth. The weight of the object measured on the Mooon is therefore also one-sixth of its weight on Earth.
  

Measurement of Mass and weight .

• Mass is measured using a balance such as the beam balance or electronic balance. In the past, the sliding balance, which is basically a beam balance, was used in most laboratories. The unknown mass is placed on the pan of the beams until the beams balance. However, The modern electronic balance, or the "top-pan" balance has become more common now. In this case, the object is placed on a pan and its mass read from a display screen.
• Weight is measured in the laboratory using a Newton-meter (commonly known as spring balance). However, a beam balance can still be used to compare unknown weights against known ones. We do this in exactly the same way as we use the balance to compare masses, since weight is directly proportional to mass.

Sliding balance :

Electronic balance:

Inertia and Mass :

• Definition: The inertia of an object is the reluctance of the object to change either its state of rest or motion.
• The greater the mass of a body, the greater will be its inertia.
• All bodies with mass possess a property known as inertia. The inertia of an object is the reluctance of the object to change either its state of rest, or if it's moving, its motion in a straight line. In fact, this is consistent with Newton's first law of motion, which can also be stated as follows:

A body continues in its state of rest or uniform motion in a straight line unless compelled by a force to do otherwise.

• A force is needed to overcine inertia. This force is the same on the Moon and on the Earth, Inertia depends on mass and not weight.
• We experience inertia when the motor vehicle we are travelling in suddenly stops. We lurch foward because of our tendency to maintain our motion foward.
• The greater the mass of an object, the more difficult it is to start it moving or to stop it.
• This means that the greater the mass of a body the greater will be its inertia.
• Because of its inertia, an object which is at rest will remain at rest unless it is acted upon by an external force. Similarly, a moving object will continue to move in a straight line with uniform speed unless it is acted upon by an external force.
• Below are the situations which can be explained using the main idea of inertia:

1.When a car suddenly speeds off, its passenger is pushed back against the seat. Initially, the passenger is at rest. When the car suddenly speeds off, the passenger tends to remain in a state of rest. He is pushed by the seat.

2. A coin on top of the cup falls into the glass when the card beneath it is quickly pulled away. Initially, the coin is at rest. Because of its inertia, it remains at reast when the card is pulled away quickly beneath it. Hence, the coin falls into the glass.

3. A passenger in a fast moving car is thrown foward when the car suddenly brakes. Initially, rhe passenger is moving. When the car suddenly stops, the passenger tends to continue moving because of his inertia. Hence, he is thrown foward.

An experiment showing Newton's law of inertia.