mechanics one revision notes

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Mechanics 1 ­ Revision notes
1. Kinematics in one and two dimensions
1 2 1 2
v = u + at s = ut + at s = vt ­ at
2 2
1 2 2 s : displacement (m)
s = (u + v)t v = u + 2as u : initial velocity (ms-1)
v : final velocity (ms-1)
a : acceleration (ms2)
t : time (s)
· Always list the variables you have - write down the equation you intend to use.
· Sketch graphs ­ essential for multi-stage journeys
· Retardation / deceleration ­ don't forget the negative sign
Distance/ Displacement ­ time graph
Straight line ­ constant velocity ­ zero acceleration
Travels 12m from a point X, turns round
and travels 15 m in the opposite direction
finishing 3m behind X.
Velocity ­ Time graph
Straight line ­ constant acceleration Displacement
moving forwards
Displacement moving
DISPLACEMENT is represented backwards
by the area under the graph
Changed direction
after 18 seconds

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Acceleration due
to gravity
- the body is a point mass
- air resistance can be ignored
- the motion of a body is in a vertical line
9.8 ms-2
- the acceleration due to gravity is constant Unless given in the
EXAMPLE : A ball is thrown vertically upwards from ground level with a velocity of 28 ms-1
a) What was its maximum height above the ground ?
u = 28 ms-1
a = -9.…read more

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Vector equations ­ for constant acceleration the 5 equations involving, displacement,
velocity etc can be used
· If asked to write an equation in terms of t for displacement/ velocity etc ­ simplify
your equation as far as possible by collecting the i terms and j terms
e.…read more

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For questions involving river
Method 2 ­ Lami's theorem
crossings and current you may
need to use the cosine rule as
T1 T2 12g well as the sine rule to calculate
= =
sin 128 sin 117 sin 115 missing lengths and angles
T1 = 102 N Cosine Rule
T2 = 116 N
2 2 2
a = b + c ­ 2bc Cos A
For any set of three forces P,Q and R in equilibrium
= =
sin a…read more

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Tension / Thrust ­ pulling or pushing force on the body
· Always ­ acts in a direction opposite to that in which the object is moving or
tending to move
· Smooth contact ­ friction is small enough to be ignored
· Maximum Friction (limiting friction) - object is moving or just on the point
of moving :
F = mR where m is the coefficient of friction
· F < m R body not moving
IN EQUILIBRIUM ­ resolving horizontally or in…read more

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Law F = ma Net Force = mass x acceleration
· Always work out and state Net force clearly before equating to ma
· Check - if acceleration is positive ­ net force should also be positive
Example : A taut cable 25m long is fixed at 35º to the horizontal. A light rope ring is placed
around the cable at the upper end. A soldier of mass 8 kg grabs the rope ring and slides
down the cable.…read more

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Finding the acceleration
Coefficient of friction = 0.2 2g ­ T = 2a Friction = 0.2R
T ­ F = 6a R = 6g so F = 11.76 N
2kg 2g ­ T = 2a
T ­ 11.76 = 6a a = 0.98 ms-2
Force on the pulley
Resultant force
Finding the Tension
T = 11.76 + 6a
17.64 = 17.…read more

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Displacement (r) : r = ut+ ½at2
r = Ut cosqi + (Ut sinq ­½9·8t )j
Horizontal dispalcement Height ( vertical dispalcement)
after t seconds after t seconds
To find the range
Height component = 0
Solve 2
Ut sinq ­½9·8t = 0
To find t
Substitute into
Range = Ut cosq
A shot putter releases a shot at a height of 2.5 m and with a velocity of 10ms-1 at 50º to
the horizontal. Find the distance travelled by the shot.…read more

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Modelling Assumptions
Common Terms and Meanings
Term Applies to What is disregarded
Inextensible Strings, rods Stretching
Thin Strings, rods Diameter, thickness
Light Strings, springs, rods Mass
Particle Object of negligible size Rotational motion, size
Rigid Rods Bending
Small Object of negligible size Rotational motion
Smooth Surfaces, pulleys Friction
Assumptions made
· motion takes place in a straight line -
· acceleration is constant
· air resistance can be ignored
· objects are modelled as masses concentrated at a single point (no rotation)
· g is…read more


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