Mechanics-1
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CONTENTS:
• Length and time
• Motion
• Mass and weight
• Density
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Length :Measurement
• Rulers can be used to measure small distances of a few cm.
They are able to measure to the nearest mm.
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Length : Measurement
• When measuring larger distances (of
a few metres) a tape measure is more
appropriate or, when measuring even
larger distances, a trundle wheel.
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Length : Measurement
• When measuring very
small distances (less than
a centimetre) a micro
meter is the most
appropriate instrument.
• Micrometers can measure
distances to the nearest
1/100th of a mm
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Length : Measurement
Vernier Calipers:
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Time : Measurement
• Stop-clocks and stopwatches can be used to measure time
intervals
• An important factor when measuring time intervals is human
reaction time.
• This can have a significant impact upon measurements when
the measurements involved are very short (less than a second).
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Accurate Method of Measurement
Multiple Readings:
• Suppose you have to measure the thickness of a sheet of paper.
• The thing that you are trying to measure is so small that it would be very
difficult to get an accurate answer
• If, however, you measure the thickness of 100 sheets of paper you can do
so much more accurately.
• Dividing your answer by 100 will then give an accurate figure for the
thickness of one sheet
• This process of taking a reading of a large number of values and then
dividing by the number, is a good way of getting accurate values for small
figures, including (for example) the time period of a pendulum – measure
the time taken for 10 swings and then divide that time by 10
• TEST YOURS
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Mass & Weight-Measurement
Mass & Weight: Basics
• Mass (measured in kilograms, kg) is related to the amount of matter
in an object
• Weight (measured in newtons, N) is the force of gravity on a mass
• The size of this force depends on the gravitational field
strength (often called gravity, g, for short)
weight = mass x gravitational field strength W = m x g
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Mass & Weight-Measurement
• The value of g (the gravitational field strength) varies from
planet to planet.
Diagram showing the gravitational field strengths of
the planets in our solar system
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Mass & Weight-Measurement
The weight (and hence mass) of two objects can be compared
using a balance
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Mass & Weight-Measurement
The Significance of Mass
• Mass has two significant effects in Physics:
• The mass of an object’s opposed any attempt to change
that object’s motion
The greater the mass of an object, the more difficult it is to
speed it up, slow it down or change its direction
This property of mass is sometimes referred to as inertia
• Mass is also the source of an object’s weight – the force of
gravity on a mass
The greater the mass, the greater the weight.
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Measurement-Volume:
• Measuring cylinders can be used to
measure the volume of liquids or, by
measuring the change in volume, the
volume of an irregular shape
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Density-Measurement
• Density is the mass per unit volume of a material:
• Objects made from low-density materials typically have a low mass,
whilst similar-sized objects made from high-density materials have a
high mass
(Think of how heavy a bag full of feathers is compared to a similar bag
full of metal)
• Density is related to mass and volume by the following
equation:
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Density-Measurement
• The units of density depend on what units are used for mass
and volume:
• If the mass is measured in g and volume in cm3, then the
density will be in g/cm3
• If the mass is measured in kg and volume in m3, then the
density will be in kg/m3
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Density-Measurement
Floating
• In general, an object will float in a
liquid if the average density of that
object is less than the density of
the liquid it is placed in
• Water, for example, has a density
of about 1 g/cm3
• If an object has a density of less than
1 g/cm3 then it will float in water
• If an object has a density that is
greater than 1 g/cm3 then it will sink
in water
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Density-Measurement
• To measure the density of an object, we must measure its mass
and volume and then use the following equation:
• The mass of an object can be measured quite simply by placing
it on a top pan balance.
• Always zero a top pan balance before taking any
measurements
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Density-Measurement
• In the case of a liquid, the liquid must be placed in a container,
the mass of which should be measured both when it is empty
and when it contains the liquid.
• The mass of the liquid will be the difference between the two
values
The volume can be determined in a couple of ways:
Regular shapes (e.g. cubes, spheres, cylinders):
• The width (and length) can be measured using a ruler or a pair
of digital calipers
• To make the measurements accurate, several measurements
should be taken between different faces or points on the
circumference, and an average taken
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Density-Measurement
When measuring the width (or diameter) take several readings
between different points and take an average
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Density-Measurement
Irregular shapes:
• The volume can be found using a Eureka can:
• Placing an object in a full Eureka can will displace water equal
to its volume
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Density-Measurement
• Fill the Eureka can with water
• Place an empty measuring cylinder below its spout
• Now carefully lower the object into the Eureka can (use a piece
of string, perhaps)
• Measure the volume of displaced water in the measuring
cylinder
• Alternatively, the object can be placed in a measuring cylinder
containing a known volume of liquid, and the change in volume
then measured
• Once the mass and volume of the shape is known, its
density can be calculated
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Motion-Speed & Acceleration
Vectors:
The physical quantities which have both direction and magnitude are
called vector quantities.
Example: Velocity, acceleration, force , displacement
Scalars:
The physical quantities which have only magnitude and no direction
are called scalar quantities.
Example: Speed, work, distance
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Motion-Speed & Acceleration
Distance
• Distance is a measure of how far an object moves. It is a scalar
quantity and only requires the magnitude (size) along with an
appropriate unit to describe it.
• If someone was asked how far their house was from school and
they answered, “2” it would not be a complete answer. The
follow up question would be, “2 what?” If they then answer,
“2km” only then is a full description of the magnitude of the
distance from their house to school is given. Thus, distance is a
scalar quantity meaning it can be fully described by the
magnitude and appropriate
unit.
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Motion-Speed & Acceleration
Displacement
• Displacement is the distance travelled in a particular direction
from a specified point.
• It includes both the distance an object moves, measured in a
straight line from the start point to the finish point and the
direction of that straight line.
• It is a vector quantity as it has both magnitude (size) and
direction.
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Motion Speed & Acceleration
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Speed:
• Speed (measured in metres per second) is the distance moved
by an object each second
• The average speed of an object is given by the equation:
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Motion-Speed & Acceleration
Velocity
• Velocity is a similar quantity to speed, but includes a direction
(the direction of travel) as well as its value (its magnitude)
• Two objects can have equal speeds but might have opposite
velocities (if they are travelling in opposite directions)
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Motion-Speed & Acceleration
Acceleration
• Acceleration is the rate of change of velocity: In other
words, how much the velocity of an object changes by every
second
• Acceleration is given by the equation:
The units of acceleration are m/s2, which mean the same thing
as m/s/s – the change in velocity (in m/s) every second
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Motion-Speed & Acceleration
Deceleration
• In the case where an object is slowing down (decreasing
velocity) the acceleration is in the opposite direction to the
moving object.
• This is referred to as negative acceleration or retardation or
deceleration.
Steady or Constant Acceleration:
• A uniform acceleration is known as steady or constant acceleration
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Motion-Distance-Time Graphs
• Constructing graphs of an objects motion gives a better idea of
the behaviour of the moving object.
• A distance-time graph is constructed by having the distance as
the vertical axis and the time as the horizontal axis.
• By recording the distance travelled over different intervals of
time and plotting these values a distance-time graph can be
plotted.
• From this plot information about the moving object can easily
be extracted.
• Distance-time graphs are also known as position-time graphs or
displacement-time graphs. Don’t be fooled by these different
names: they describe LMOIS-CIS
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Motion-Distance-Time Graphs
In a distance-time graph:
• A horizontal line means stationary
• A straight line means constant speed
• If the gradient increases the object is speeding up (accelerating)
• If the gradient decreases the object is slowing down (decelerating)
• If the line is going down, the object is moving backwards.
• On the distance-time graph, the gradient of the line is numerically
equal to the speed.
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Motion-Distance-Time Graphs
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Motion-Distance-Time Graphs
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Motion-Distance-Time Graphs
Calculating Speed
The speed of an object is given by the gradient of the line
Distance-time graphs are also known as position-time graphs or
displacement-time graphs. Don’t be fooled by these different
names: they describe the same kind of thinDistance-time graphs
are also known as position-time graphs or displacement-time
graphs. Don’t be fooled by these different names: they describe
the same kind of things.gs.
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Motion-Distance-Time Graphs
Velocity-Time Graphs
• A velocity-time graph is constructed by having the velocity as
the vertical axis and the time as the horizontal axis.
• By recording the velocity over different intervals of time and
plotting these values a velocity-time graph can be plotted.
• From this plot information about the moving object can easily be
extracted.
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Motion-Velocity-Time Graphs
Velocity-Time Graphs
Graph showing how the velocity (speed) of an object
changes over time
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Motion-Velocity-Time Graphs
• If the line is horizontal, the velocity is constant (no
acceleration)
• If the line slopes upwards then the object
is accelerating (speeding up)
• If the line goes down then the object is decelerating (slowing
down)
• The area under the graph gives the total distance travelled.
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Motion-Velocity-Time Graphs
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Motion-Velocity-Time Graphs
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Motion-Velocity-Time Graphs
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Motion-Velocity-Time Graphs
• Calculating Distance
The distance travelled can be found from the area
beneath the graph
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Motion-Velocity-Time Graphs
• If the area beneath the graph forms a triangle (the object is
accelerating or decelerating) then the area can be determined
using the formula:
area = ½ x base x height
• If the area beneath the graph is a rectangle (constant velocity)
then the area can be determined using the formula:
area = base x height
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Motion-Velocity-Time Graphs
• Calculating Acceleration
• The acceleration of an object is given by the gradient of the
graph:
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Motion-Velocity-Time Graphs
• Lines that slope downwards have negative gradients and so
can be said to have negative accelerations: This is the same
thing as a deceleration
• If the gradient of the line changes then the acceleration of the
body must be changing:
• A line with constant gradient represents constant
acceleration (linear motion)
• A curved line represents changing acceleration – either
decreasing (if the gradient gets smaller) or increasing (if the
gradient gets large)
•
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Motion-FREE FALL
• In the absence of air resistance, all objects fall with the same
acceleration, regardless of their mass.
• The force that resists the motion of an object through a gas and
liquid is called drag or air resistance
• This acceleration is equal to the gravitational field strength and is
approximately 10 m/s2 near the Earth’s surface.
• So long as air resistance remains insignificant, the speed of a falling
object will increase at a steady rate, getting larger the longer it falls
for.
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Motion-FREE FALL
In the absence of air resistance objects fall with
constant acceleration
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Motion-FREE FALL
Terminal Velocity
When a parachutist
jumps out of an
aeroplane, two main
forces act:
• Weight (the force of
gravity)
• Air resistance
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Motion-FREE FALL
• Initially the air resistance is very small. There is a downwards
unbalanced force and the skydiver accelerates
• As the skydiver speeds up, the air resistance increases
• Eventually the air resistance balances the weight and so the
skydiver travels at a constant speed – terminal velocity
• When the parachute is opened the increase air resistance on
the parachute creates an upwards unbalanced force, making
the parachuting the slow down
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Motion-FREE FALL
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