Title: InkMaths / Further Mechanics 1: impulse, energy and collisions
On every note of this deck, unless a note says otherwise:
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Front: STANDARD RESULT — LEARN IT
Bouncing ball:
dropped from h: next height? total distance?
Back: e^2h, h(1 + e^2)1 - e^2

Front: STANDARD RESULT — LEARN IT
Work and power:
work = ?, P = ?
Back: Fd cos θ, Fv

Front: DEFINE
Define: conservation of momentum.
Back: In a collision the internal forces are equal and opposite for the same time, so the impulses cancel and the total momentum before equals the total after. It holds whatever happens to the energy.

Front: STANDARD RESULT — LEARN IT
Impulse:
I = ?
Back: Ft = mv - mu: a vector, in N s

Front: SPOT THE ERROR
Say what is wrong with this claim:
A ball that bounces back off a wall at the speed it arrived has received no impulse.
Back: Momentum is a vector. Reversing it removes the original momentum and supplies the same again the other way, so the impulse is the mass times the sum of the two speeds, not their difference.

Front: CHECK YOURSELF
Why is momentum not conserved when a ball bounces off the floor?
Back: The floor is attached to the Earth, so the ball alone is not an isolated system and receives an external impulse. Only the law of restitution applies.

Front: STANDARD RESULT — LEARN IT
Hooke's law:
T = ?
Back: λ xl: x is the extension, l the natural length

Front: DEFINE
Define: impulse in two dimensions.
Back: The i components and the j components each obey I = mv − mu on their own. Take magnitudes only at the end: a change of direction at constant speed still needs an impulse.

Front: DEFINE
Define: kinetic energy in an impact.
Back: Momentum is always conserved; kinetic energy is lost unless e = 1. Find the loss by adding ½mv² for both spheres before and after and subtracting.

Front: DEFINE
Define: oblique impact.
Back: A smooth surface leaves the parallel component untouched and multiplies the perpendicular one by −e. The outgoing path therefore always hugs the surface more closely than the incoming one.

Front: DEFINE
Define: work-energy principle.
Back: The total work done by all the forces equals the change in kinetic energy. The normal reaction never contributes, since it acts at right angles to the motion.

Front: STANDARD RESULT — LEARN IT
Elastic energy:
EPE = ?
Back: λ x^22l: the triangle under the Hooke line

Front: STANDARD RESULT — LEARN IT
Newton's law of restitution:
e = ?, range?
Back: separation speedapproach speed, 0 ≤ e ≤ 1