Further Mechanics Flashcards

1
Q

Newton’s 1st Law

A

An object remains at rest or in uniform motion unless acted on by a resultant force

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2
Q

Newton’s second law

A

the rate of change of momentum of an object is proportional to the resultant force on it in the direction of the force

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3
Q

Newton’s 3rd law

A

If object A exerts a force on a second object B, then object B will exert an equal and opposite force on object A.

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4
Q

Force

A

Force = rate of change of momentum (vector)

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5
Q

units of momentum

A

kg ms-1

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6
Q

units of rate of change of momentum

A

kg ms-2

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7
Q

Impulse

A

Force x time for which the force acts so impulse = change of momentum (vector)

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8
Q

units of Impulse

A

Ns or kg ms-1

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9
Q

area under a graph of force against time

A

change in momentum or impulse

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10
Q

principle of conservation of linear momentum definition

A

in a collision or explosion, the total momentum before equals the total momentum after, providing no external forces are acting

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11
Q

elastic collision defintion

A

a collision where kinetic energy is conserved

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12
Q

inelastic collision definition

A

a collision where kinetic energy is not conserved but total energy is conserved

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13
Q

displacement equation for an object undergoing SHM

A

x = Acosωt

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14
Q

velocity equation for an object undergoing SHM

A

v=±ω√A²-x²

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15
Q

angular speed

A

angle turned through per second (scalar)

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16
Q

maximum speed

A

ωA

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17
Q

maximum acceleration

18
Q

units of angular speed

19
Q

angular speed of earth

A

ω = 2π/T = 2π/ 24x60x60 = 7.27x10-5 rad s-1

20
Q

centripetal force

A

resultant force acting towards the centre of the circular path. F = mv²/r = mω²r

21
Q

centripetal acceleration

A

the acceleration produced by a centripetal force due to the object’s constantly changing direction a=v²/r = ω²r

22
Q

conditions for shm

A
  1. acceleration is proportional to displacement
  2. acceleration is in opposite direction to displacement OR acceleration always acts towards the equilibrium position
23
Q

relating a = -(2πf)² x to definition of shm

A
  1. acceleration is proportional to displacement and hence a = kx, where k is a constant(2πf)².
  2. acceleration is in the opposite direction to displacement as indicated by the minus sign
24
Q

gradient of displacement against time

25
graphical representations linking x, v, a and t from SHM
velocity --> acceleration = gradient acceleration --> displacement = flip just differentiate sinx or cosx
26
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
27
dependence of time period on amplitude of an oscillation
time period of oscillation in SHM is independent of amplitude
28
variation of Ep and Ek with displacement
as Ek increases, Ep decreases so the total energy is constant
29
resonance definition
when driving frequency = natural frequency of an oscillating system, vibrations with very large amplitude are produced
30
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
31
forced oscillation definition
oscillation due to external periodic driving force
32
time period
time taken for one complete oscillation
33
frequency
number of oscillations per second
34
amplitude
maximum displacement of a particle from its rest position
35
damping definition
damping is when frictional forces oppose motion, dissipating energy so the energy of the oscillating system decreases
36
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
37
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 >>> A applied - phase difference = π/2 rad or 90° fapplied>>> fo - amplitude is very small <<< A applied - phase difference = π rad or 180°
38
what would cause lower peak amplitude on resonance curve
energy losses from system
39
resonance curves and damping
Light damping = very sharp resonance peak Heavy damping = much flatter resonance peak
40
damping in mechanical systems
structures are damped to avoid being damaged by resonance, in particular skyscrapers such as Taipei 101 (giant pendulum)
41
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