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[PAPER 2 MECHANICS NOTES]







Mechanics
Notes for CCEA Additional Mathematics
Examples and explanations of the Mechanics course for CCEA
Additional Mathematics Paper 2




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[PAPER 2 MECHANICS NOTES]




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Motion with Constant Acceleration
Displacement-Time Graphs

Displacement = speed in a given direction = velocity (m/s)




Average velocity =


Average speed =




Velocity-Time Graphs

Gradient = acceleration

Area under curve = total distance

Continuous line = constant velocity
NOTE: Flat areas are not areas of rest!…

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Vertical Motion under Gravity

NOTE: Gravity is 10m/s2 for CCEA examinations

Example 1: A stone is catapulted vertically upwards at a velocity of 24.5m/s. For how long will it exceed 29.4m?

Remembering that gravity is working DOWN, we use SUVAT to choose a formula.


Therefore, we…

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As acc. Is upwards, 84N is greater than B.




Friction

When an object is `on the point' of tipping, friction is said to be LIMITING.

where R = Normal Reaction
= Coefficient of Friction NOTE:

Example 1: A body of mass 5kg accelerates along a rough…

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The Inclined Plane

Example 1: A body of mass 4kg rests on a rough plane inclined at 40°. When the body is pulled down by a 38N
force, inclined at 21° to the plane, it experiences a constant frictional force of 3N. Find A and the…

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Connected Particles

Example 1: A large train has an engine of 8kg capable of exerting a force of 60N, and 3 carriages of mass 1kg,
3kg, and 4kg. Calculate a, and the tensions T1, T2 and T3 in the couplings.




Using , we get:




T1 =…

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Equating: 20 =6a


Tension: 40 - T= 4(3.33)
T = 26.66 N




Resultant Forces and Components


Gives that




Example 1: A mass of 5kg is supported by two light inextensible strings attached at points P and Q. The mass
rests in equilibrium. Find the tension T…

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NOTE: This can get messy, so check your answer.




Moments

Law 1: To ensure equilibrium, the sum of the components must be zero. Total up = Total down.
Law 2: The sum of moments about a point must equal zero. Total clockwise= Total anticlockwise.

Terminology
Light-…

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