connected particles Flashcards
what are the 3 assumptions when working with connected particles?
string is light - tension is the same
string is inextensible - acceleration is the same at both ends
pulley is smooth - tension is equal on both sides of the plane
what is newtons third law?
for every action, there is an equal and opposite reaction
what kind of connectors are used in connected particles?
either use a light inextensible string (which will always be taut or a solid rod, which is also light
if the string is taut, tension works in both directions equally
how do you find the acceleration of connected particles?
take the total resultant force and the total mass of the whole system and divide force by mass
how do you find tension in the connector between 2 bodies?
use the mass of ONE BODY with the overall acceleration to find the tension since tension =+ opposite to force exerted by one body to the other
trust me it works
ALWAYS ESTABLISH A POSITIVE DIRECTION
how do you find acceleration of masses connected by pulley?
work with each mass separately, defining positive direction as down.
establish which mass is heavier; this will be the mass moving down, hence acc will be down. for the other mass, acc. will be equal but up so if mass B is heavier than A then express T:
T - Ag = Aa where g = 9.8 and
-T + Bg = Ba a = acc.
solve these simultaneously.
this will give acc and tension
how do you deal with connected bodies when movement of one stops but the other continues?
separate the motion into halves.
first half: how whole system behaves, suvats until collision.
second half: using final v from first half, use suvats and RF manipulation
how do you deal with connected particles on a slope?
resolve wight components first, (using trig ratios) then find resultant forces and follow procedure for norman pulley system (RF = ma for each plane, solve simultaneously)
how do you find overall tension on a pulley?
reorganise into a force triangle and solve trigonometrically, alternatively use equation
2T Cos θ = total force
