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AS Mathematics- Mechanics 1
Chapter 1: Mathematical Models in Mechanics
Common models and modeling assumptions needed to know:
Particle: The mass of it can be concentrated at a single point
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Rod: The mass of it is distributed along a straight line and it is rigid (so does not bend
or buckle)
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Uniform body: The mass of an object is evenly distributed over its entire volume
(not a sharpened pencil)
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Strings and pulleys are often said to be light
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Smooth surface: There is no friction between the surface and the object that is
moving along it
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Wire: A rigid thin length of metal, which is one-dimensional
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Bead: A particle which can be threaded into and freely move along a wire or string
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Wind: Unless otherwise told, you can ignore any effects due to wind in your models
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Gravity acts
downwards with constant acceleration 9
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If you use this approximation to two
significant figures in your explanation, you will need to use the same degree of
accuracy in you’re answer
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Friction: the force that opposes the motion between two rough surfaces
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Compression/thrust: the force acting on the object, when it is pushed along using a
light rod
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Coefficient of friction: roughness of a surface
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For smooth surface there is no friction so coefficient of
friction=0
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This is called deceleration or
retardation
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8m/s2
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-Finding acceleration:

change of velocity a= v - u

t
time
-Finding distance travelled:
Area under the graph  Areas of trapezium=average of paraellel sides x height 
Gradient of line 

1
(a + b) ´ h
2

Chapter 3: Dynamics of a Particle Moving in a Straight Line
Newton’s Law:
Resultant force = mass × acceleration
F=ma
Formula for weight of a particle:
Weight = mass × gravity
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 First resolve the perpendicular force, R() and then the direction of the
acceleration, F()
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Formula for maximum of limiting value of friction:
Maximum limiting value of the friction: coefficient of friction × normal reaction
between two surfaces
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A particle placed on a rough inclined plane will remain at rest if tanθ≤μ, where θ is
the angle the plane makes with the horizontal and μ is the coefficient of friction
between the particle and the plane
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However if not, you have to treat the system as different particles
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Momentum is measured in Ns
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The units for impulse are Ns
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 This is a vector equation, so a positive direction must be chosen and each
value given the correct sign
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-Technique in exam:
 Draw a diagram showing he velocities before at top and after at the bottom
after the collision with arrows
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 Chose a positive direction and apply the Impulse-Momentum Princple and/or
the principle of Conservation of Momentum
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This means the resultant force is equal to 0, and the particle will
remain at rest, or stationary, as it is not subject to acceleration
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 Resolve the forces into horizontal and vertical components, or if the particle is
on an inclined plane, into components parallel and perpendicular to the plane
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 Solve the resulting equations to find the unknown force(s)
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Solving statics problems using friction:
-When a body is in equilibrium you need to consider whether the body is on the point
of moving or not
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The body is the said to be in limiting
equilibrium
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In these situations the
equilibrium is not limiting
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Chapter 5: Moments
Moment:
-A force applied to a rigid body can cause the body to rotate
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The moment of a force depends on the magnitude of the force and its distance from
the axis of rotation
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-Units:
Magnitude of force= Newtons (N)
Distance= metres (m)
Moment= Newton-metres (Nm)
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-You can solve problems about bodies resting in equilibrium by equation the
clockwise and anticlockwise moments
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Solving problems about non-uniform bodies:
The mass of a non-uniform rigid body can be modelled as acting at its centre of
mass
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Adding and representing vectors:
A vector can be represented as a directed line segment
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-The length of the line is the magnitude of the vector
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But it can also be written as a ora
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Two vectors are parallel when they have the same direction
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Describing vectors using i, j notation:
A unit vector is a vector of length 1
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You can write any two-dimensional vector in the form ai + bj
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You subtract vectors in a
similar way
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The magnitude of a vector a is written a
Expressing the velocity of a particle as a vector:

-The velocity of a particle is a vector in the direction of motion
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The velocity is usually denoted by v
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-The acceleration of a particle tells you how the velocity changes with time
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If a particle with initial velocity u
moves with constant acceleration a then its velocity, v, at time t is given by:
 v = u + at
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The force causes the particle to accelerate:
 F = ma, where m is the mass of the particle
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This means the sum of the vectors of the force is the zero vector

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