Further Mechanics Flashcards
Newton’s 1st Law
An object remains at rest or in uniform motion unless acted on by a resultant force
Newton’s second law
the rate of change of momentum of an object is proportional to the resultant force on it in the direction of the force
Newton’s 3rd law
If object A exerts a force on a second object B, then object B will exert an equal and opposite force on object A.
Force
Force = rate of change of momentum (vector)
units of momentum
kg ms-1
units of rate of change of momentum
kg ms-2
Impulse
Force x time for which the force acts so impulse = change of momentum (vector)
units of Impulse
Ns or kg ms-1
area under a graph of force against time
change in momentum or impulse
principle of conservation of linear momentum definition
in a collision or explosion, the total momentum before equals the total momentum after, providing no external forces are acting
elastic collision defintion
a collision where kinetic energy is conserved
inelastic collision definition
a collision where kinetic energy is not conserved but total energy is conserved
displacement equation for an object undergoing SHM
x = Acosωt
velocity equation for an object undergoing SHM
v=±ω√A²-x²
angular speed
angle turned through per second (scalar)
maximum speed
ωA
maximum acceleration
ω²A
units of angular speed
rad s-1
angular speed of earth
ω = 2π/T = 2π/ 24x60x60 = 7.27x10-5 rad s-1
centripetal force
resultant force acting towards the centre of the circular path. F = mv²/r = mω²r
centripetal acceleration
the acceleration produced by a centripetal force due to the object’s constantly changing direction a=v²/r = ω²r
conditions for shm
- acceleration is proportional to displacement
- acceleration is in opposite direction to displacement OR acceleration always acts towards the equilibrium position
relating a = -(2πf)² x to definition of shm
- acceleration is proportional to displacement and hence a = kx, where k is a constant(2πf)².
- acceleration is in the opposite direction to displacement as indicated by the minus sign
gradient of displacement against time
velocity
graphical representations linking x, v, a and t from SHM
velocity –> acceleration = gradient
acceleration –> displacement = flip
just differentiate sinx or cosx
conditions for the time period equation of a pendulum
time period equation for a pendulum is only true for oscillations with a small amplitude, that is, angular displacements less than 10 degrees
dependence of time period on amplitude of an oscillation
time period of oscillation in SHM is independent of amplitude
variation of Ep and Ek with displacement
as Ek increases, Ep decreases so the total energy is constant
resonance definition
when driving frequency = natural frequency of an oscillating system, vibrations with very large amplitude are produced
free oscillation definition
oscillations with a constant amplitude because there are no frictional forces and hence no energy loss so the oscillations continue indefinitely. No change in total energy
forced oscillation definition
oscillation due to external periodic driving force
time period
time taken for one complete oscillation
frequency
number of oscillations per second
amplitude
maximum displacement of a particle from its rest position
damping definition
damping is when frictional forces oppose motion, dissipating energy so the energy of the oscillating system decreases
damping descriptions
light damping: takes a long time for the amplitude to decrease to zero. system oscillates at a natural frequency
critical damping: shortest time for amplitude to decrease to zero. No oscillating motion occurs
Heavy (over)damping: takes a long time for amplitude to decrease to zero. no oscillating motion occurs
phase difference between driver and driven oscillations
f₀ - Natural frequency of driven oscillator
f applied - frequency of driver
fapplied «< fo
- amplitude of oscillation ≈ A applied
- phase difference = 0 rad
fapplied = fo
- amplitude is very large ie»_space;> A applied
- phase difference = π/2 rad or 90°
fapplied»> fo
- amplitude is very small «< A applied
- phase difference = π rad or 180°
what would cause lower peak amplitude on resonance curve
energy losses from system
resonance curves and damping
Light damping = very sharp resonance peak
Heavy damping = much flatter resonance peak
damping in mechanical systems
structures are damped to avoid being damaged by resonance, in particular skyscrapers such as Taipei 101 (giant pendulum)
damping and stationary waves
recording studios use soundproofing on their walls which absorb sound energy converting it to heat. This prevents stationary waves being created between the walls of the room at certain frequencies which would cause resonance reducing sound quality with some frequencies louder than they should be
