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Physics AS
Unit 1 Mechanics
Displacement
Time Graphs
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A: Positive acceleration
B: Constant positive velocity
C: Positive Deceleration
D: Stationary
E: Negative acceleration
F: Constant negative velocity
G: Negative deceleration (with negative displacement)
Velocity
Time Graphs
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A: Increase in rate of positive acceleration
(Starting to speed up)
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B: Constant positive acceleration
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D: Constant positive velocity
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F: Constant negative acceleration
C: Decrease in rate of positive acceleration
(This is not slowing down but the rate of acceleration has slowed)
E: Increase in rate of negative acceleration
(starting to slow down)
G: Stationary
H: Increase in rate of negative acceleration
(starting to speed up in opposite direction)
Equations of Motion
Equation
Excluded element
v = u + at
s
s = ut + ½at²
v
s = vt - ½at²
u
v² = u² + 2as
t
s = ½ut + ½vt
a
Using Vectors
• By resolving vectors into horizontal and
vertical components it allows for a
resultant triangle (ABC) to be calculated.
• A = X + α = Z Cosψ + γ Cosϴ
B = Y + β = Z Sinψ + Z Sinϴ
Using Vectors
and Work
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Two Triangles 3 Methods
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1: Find the component of the force which is
acting in the direction of travel (B) and multiply by
the distance travelled (C)
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2: Find the component of the distance travelled
which is in line with the force (D) and multiply by
the magnitude of the force (A)
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3: Calculate the energy transformed as this is
also equal to the work done
Galileo and Aristotle
• Aristotle:
An object has an inherent tendency to reach as low a
point as possible.
A moving object will continue to move until the force
that started it runs out.
• Galileo:
Carried out experiments on slopes to ‘dilute’ the
effects of gravity.
Showed that a projectile had a constant horizontal
velocity and a changing vertical velocity.
Projectile Movement
• Any thrown object will have a constant
horizontal velocity (if air resistance is
ignored) and a vertical acceleration of
9.81ms-2
• To solves these problems you therefore
have to establish how long the projectile is
in the air for.
Force
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A force is a push or a pull that results in either an acceleration or a
change in shape. This is measured in Newtons (N)
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Force = mass x acceleration = change in momentum/time
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Reactive forces are the equal and opposite forces experienced by two
different objects
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Mass is a scalar quantity which is defined as the property of an object
that resists motion and is measured in kg
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F = ma can be rewritten in the case of weight to read W = mg
g is the gravitational field strength or acceleration of free fall
g therefore has units of N kg-1 or m s-2 as these are the same thing
A resultant force is the sum of two or more forces acting on the
same object
Torque, moments
and turning effect
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moment = magnitude of force x perpendicular distance
(quick version)
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Two triangles same solution:
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2: Multiply (Y) x (B)
(B) = The magnitude of the force applied
(Y) = The perpendicular distance between the line of the force
applied (B) and the pivot point (P)
1: Multiply (A) x (X)
Where (X) is the distance between the pivot point (P)and the
point of action (Q)
(A) is the component of the force which is perpendicular to (X)
All Torque no Action
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Couples
A couple is a pair of forces equal in magnitude, opposite in direction
but not in line which cause a turning effect on an object.
torque of a couple = magnitude of one of the forces x
the perpendicular distance between them
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Equilibrium
An object is in equilibrium when there are resultant forces or
torques acting on it.
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Centre of Gravity
The point on an object where all of the moments of that object are
balanced.
Car Safety
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Stopping distance = thinking distance + braking distance
Thinking distance = thinking time x speed
Braking distance found using v2 = u2 + 2as
(where v2 = 0 and a is a deceleration and therefore -ve)
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Factors affecting thinking distance:
(Speed, age, alcohol or drugs, tiredness)
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Factors affecting braking distance
(If you double the speed you quadruple the braking
distance, as well as the deceleration being affected by
road surface, tyre wear, weather conditions)
Deforming solids
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Two forces that extend an object are called tensile
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A ductile material stretches a lot beyond the elastic limit
Two forces that shorten an object are called compressive
The elastic limit is the force beyond which a material will not
return to its original shape
A brittle material snaps when it reaches the elastic limit
A polymeric material does not show linear material
Symbols
Words
W = Fs
Work done = Force x displacement = Energy Transferred
ρ = m/v
Density = mass/volume
P = W/t
Power = work done/time
η = Pout/Pin
Efficiency = Useful energy out/total energy in
Ek = ½mv²
Kinetic Energy = half mass times velocity squared
Ep = mgh
Gravitational potential energy =
mass x acceleration of free fall x height
F = ma
Force = mass x acceleration
W = mg
Weight = mass x acceleration of free fall
F = kx
Force = extension x force constant
Eep = ½Fx
Elastic potential = half force times extension
ε = ∆l / l
Strain = extension / original length
σ=F/A
Stress = load / area
E=σ/ε
Youngs Modulus = Stress / Strain