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Force &
Momentum - Coggle Diagram
Force &
Momentum
Momentum
& Impulse
Momentum
When 2 bodies collide, effect depends on mass and velocity
Sir Isaac Newton - realises force needed to change obj.
velocity; force effect must also depend on mass, force magnitude; defined momentum = mass * velocity
His laws provide math rules for all motion accept in the atom
(quantum physics), hi-speed/gravity fields (theories of relativity); Einstein showed his theories of relativity simplify into Newton's laws w/ weak gravity, lower
Momentum v Newton's Laws of Motion
1st Law - Object remains at rest/uniform motion unless
acted on by a force, force needed to change momentum = resultant force, mass change results in gain/loss of velocity
2nd Law - Resultant force proportional to momentum change per second, F = ma >>> final p (mv) - initial p (mu)
over time (t) = change in p >>> F ∝ (mv-mu)/t = m(v-u)/t = ma
F = kma (k = 1 as F meas. in N - 1N = 1kg accel. 1ms-2)
Momentum in General
F = Δ(mv)/Δt
m changes at constant rate - Δ(mv) = vΔm
>>> F = vΔm/Δt, change of mass per second
m is constant - Δ(mv) = mΔv >>> F = mΔv/Δt
Δv/Δt = a
Impulse
defined as force * time (for which force acts)
Impulse equals change in momentum, FΔt = Δ(mv)
Force-Time Graph
F = (mv-mu)/t >>> Ft = mv-mu
Area under line of a force-time graph
represents change of momentum/force impulse
(momentum meas. in "kgms-1" or "Ns")
Impact
Force
Ball Impact
If ball is initially stationary, impact causes it to accelerate to speed v in time t, gain of momentum = mv (m constant)
If ball is moving w/ initial velocity, impact changes velocity v
in time t, change of momentum = mv-mu
Force-Time Graph for Impact
Force sensor connected w/ long wires/radio link to comp.
Sensor on bat, force changes eq/opp to ball, force variation
w/ time displayed on screen >>> area under graph = change of momentum/impulse
Rebound Impacts
Along the normal - momentum is reversed
initial velocity is (+)u, final velocity is -v; mu >>> -mv
F = (-mv) - (mu) / t
No Loss of speed means u = v >>> F = -2mu/t
Oblique impact - rebounds at an angle, normal components reversed (+u cosθ >>> -v cosθ)
No Loss of speed means u = v >>> F = -2mu cosθ/t
Conservation
of Momentum
Third Law of Motion
Every action has an equal and opposite reaction
Forces must be same type acting on different objects
(Weight - Normal reaction don't count)
e.g. Plant on table, table on plant
Principle of Conservation of Momentum
For a system of interacting objects, total momentum remains constant, if no external resultant force acts on the system Two objects collide - change of momentum of one eq/opp to the other; F1 = (m1v1 - m1u1) / t; F2 = (m2v2 - m2u2) / t
F1 = -F2 >>> m1v1 + m2v2 = m1u1 + m2u2
Total Final Momentum = Total Initial Momentum
Testing Conservation of momentum
Motion sensor, trolley 1 moves towards trolley 2
Trolleys stick together after collision
(m1 + m2)V = m1u1
Measurements do show total momentum of both
trolleys after collision equals trolley 1 before collision
Head-on Collisions
2 Obj. moving in opposite directions collide
Vector nature of momenta are opposite (-/+)
Both will stop only if momentum is eq/opp
-
Explosions
Recoil
2 objects flying apart from each other, recoil w/
eq/opp momentum; total initial momentum = 0
total final momentum should be 0
m1v1 + m2v2 = 0 >>> m1v1 = -m2v2
(-)sign shows 2 masses moving apart, opp. directions
Testing Model Explosion
Distance ratio equals speed ratio
thus ratio of speed, distance is inverse of mass ratio
Trolley A travels 2x distance of Trolley B
= Trolley B is 2x mass of Trolley A
Energy can still be dissipated in explosions
KE of objects flying apart =/= chem. energy relased
(heat, sound, light)