6. Further Mechanics Flashcards
What’s an impulse, △p?
Impulse is the change in momentum, △p, of an object when a force acts on it for a short period of time.
F=△p/△t
△p=F x t
△p=impulse (Ns)
F=Force(N)
t=time (s)
This formula comes from re-arranging F=ma
F=m△v/t
F=△p/t
Only used when force, F is a constant
What’s the principle of conservation of linear momentum?
The total momentum before a collision = the total momentum after a collision provided no external force acts
Momentum, like energy, is always conserved
What’s an elastic collision?
When kinetic energy is conserved
So no energy is lost
After the collision, the objects may bounce off each other
Common in idealized systems (e.g., gas particles, perfectly elastic objects)
What’s an inelastic collision?
When kinetic energy isn’t conserved
So energy is lost
Objects may stick together after collision
Perfect inelastic collision is when the maximum possible kinetic energy is lost
What’s the equation for kinetic energy, E(k)?
E(k) = 1/2 mv^2
E(k) = kinetic energy (J)
What happens when balls hit each other at an angle in an elastic collision?
The balls will move apart at 90°
What’s the derived equation of E(k) in terms of momentum, p
E(k)=p/2m
What’s a radian?
A radius length around the circumference
Just a proportion of the arc length to the radius
Measurement of an angle
θ=S/r
S=rθ
where θ is in radians
Where S = arc length (m)
What’s angular velocity, ω?
The rate of change of angular displacement
So it’s the change in angle per second
ω=△θ/△t
where △θ is in radians
ω=rad s^-1
A there’s 2π radians in a full circle, it takes 2π/T where T is the time period in seconds, s
ω=2π/T
ω=2πf
The angular velocity is also how fast the linear velocity to move around the whole radius
ω=v/r
What’s the linear velocity in circular motion?
Linear velocity (v) in circular motion refers to the speed of an object moving along the circular path
v=rω
velocity changes round the circle due to different directions
but the speed and will be constant
What is centripetal acceleration?
As the linear velocity is always changing as it moves around the circle, there must be an acceleration in the direction of the centre of the circle
This is called centripetal acceleration
The acceleration always directed to the centre of the circle
‘centripetal’ as its directed to centre of orbit
a=v^2/r
For instantaneous acceleration, so centripetal acceleration
as v=ωr
a=rω^2
a=vω
What’s centripetal force, F?
As there’s a centripetal acceleration, there must be a directly proportional centripetal force, as F=ma
The centripetal force keeps the body in circular motion
It’s the resultant force of the object
As a=v^2/r
F=mv^2/r
What’s vertical circular motion?
The movement of an object in a circular path within a vertical plane, where gravity affects its speed and forces vary at different points
As the centripetal force is always the resultant force:
Top of circle
- T(1) + mg = mv^2/r
Bottom of circle
- T(2) - mg = mv^2/r
Where T=tension
What’s horizontal circular motion?
Where there is tension, T from above the centre of a flat, horizontal circular motion
like a ball attached to string being whirled in a circle
The resultant force (centripetal force) is perpendicular to gravity, mg
So the 2 vertical forces must cancel:
Tcosθ=mg
Hence, the resultant force must be the only horizontal force:
Tsinθ=mv^2/r
Using the opposite and adjacent from θ:
tanθ=(mv^2/r)/(mg)
tanθ=v^2/gr
