Scalars & Vectors
Scalar A scalar quantity is a physical quantity which is completely defined by its
.
Vector A vector quantity is a physical quantity which is completely defined by its
.
: A distance is simply the length of a journey.
: displacement is the distance moved in a given direction.
: The speed of an object is the rate at which distance is increasing.
: velocity is the rate at which displacement is changing.
Velocity should always be quoted with a direction.
The combined effect of a number of vectors can be found by adding the vectors together.
The result of the addition is the
.
The process of replacing a vector by its rectangular components is known as
.
Acceleration (a) : Acceleration is
Acceleration is a
second (
.
quantity measured in metres per second per
).
Measurement of acceleration : To measure the acceleration of an object we require to
measure the
of the object at two points in its journey and the
taken to travel between the two chosen points.
Equations of motion
The equations of motion are used to describe motion in a straight line involving uniform
. There are three equations.
Projectile motion is motion in two dimensions. This problem is dealt with by converting
to two separate motions in one dimension : resolving into horizontal and vertical
and dealing with each component independently.
Newtons Second Law.
Newtons’ Second Law deals with the effect of forces on moving objects, and provides
a means to define the unit of
.
If the mass is measured in kg, and the acceleration is measured in
, then force is
measured in
1
is the resultant force which will accelerate an object with mass
at a rate of
.
Work Done.
Work is done on an object when a force is used to move the object. The Work
Done is given by: work done = force applied x distance moved.
If the force is in a different direction from the movement, then the work done is given by:
work done =
Momentum
x distance moved.
The momentum of a moving object is the product of its
and
Momentum is a
.
quantity measured in
.
Any process which changes the speed of an object, will change its momentum.
A resultant force will cause a change in velocity (F = ma). The change in momentum
caused by a resultant force is called an
.
Conservation of Momentum .
When two objects collide, the vector sum of the momentums before the collision is equal
to the vector sum of the momentums after the collision provided there are no external
forces involved.
Explosions.
When an object explodes into different fragments, the only forces involved are inside the
object. With no external forces, the
applies.
The sum of the momentums of the fragments is equal to the original momentum of the
object.
Elastic and inelastic collisions
An elastic collision is one where there is no loss of
during the
collision. Elastic collisions take place between the particles in a gas and their container,
and between charged or magnetised objects where no contact occurs.
Kinetic energy is
during an inelastic collision. Some kinetic energy is
usually converted to
or work done bending the colliding objects.
Total Energy is always
during collisions.
Newtons’ Third Law
During a collision between two objects A and B, the force on A due to B is
and in the
direction to the force on B due to A.
This is a direct result of the conservation of momentum. The change in
experienced by A is equal and in the opposite direction to the change in
experienced by B.
Density
The density of a substance is the mass per unit volume of that substance. Density is
measured in kilograms per cubic metre (
).
Solid, Liquid and Gas
When comparing the densities of the different phases of a substance, we find that the
densities of the solid and liquid phases are roughly
gas is
, but the density of the
than the liquid or gas.
The size of the particles in a substance are unaffected by the changes between solid,
liquid and gas. The difference in density is due to the difference in the spacing between
the particles. The particles in a gas are
times further apart than the particles
in the liquid or solid.
Pressure
Pressure is a measure of the effect of forces on surfaces. Pressure is the
, when the force acts normal to the surface.
If the force is not normal to the surface then the component of the force, normal to the
surface is used.
Pressure is measured in
, where 1
= 1 newton per square metre.
Pressure in Liquids
The pressure in a liquid or gas increases with
.
The pressure at a point in a liquid at rest is given by the relationship;
pressure =
Upthrust.
An object, immersed in a liquid or a gas experiences a force which acts vertically
upwards. This force, termed the upthrust on the object, is caused by the pressure on the
deeper bottom of the object being
top. Pressure
than the pressure on the shallower
with depth.
Boyles’ Law
The pressure in a fixed mass of gas at constant temperature varies
as the
volume of the gas.
Charles’ Law
The volume of a fixed mass of gas at constant pressure varies
temperature measured on the
as its
scale
T ( K ) = T ( OC ) +
Pressure Law
The pressure of a fixed mass of gas at constant volume varies
temperature of the gas measured on the
as the
scale of temperature.
Gas laws and Kinetic Theory
Boyles’ Law Increasing the volume available to a gas increases the
between collisions with the walls of its container. This decreases the number of collisions
and with it, the
on the walls. The average
per collision depends on the average speed of the particles which
remains the same at constant
.
Charles’ Law Increasing the temperature causes the particles to speed up. This increases
both the average
per collision and the number of collisions
.
To maintain a constant pressure, the volume increases to reduce the number of collisions
. Volume varies directly as temperature for constant pressure.
Pressure Law Increasing the temperature causes the particles to speed up. This increases
both the average
If the volume remains
per collision and the number of collisions
.
, the pressure will increase. The pressure of
a gas varies directly as the temperature for constant volume.