Further Mechanics

Question 1

Newton’s 1st Law

Answer 1

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

Question 2

Newton’s second law

Answer 2

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

Question 3

Newton’s 3rd law

Answer 3

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

Question 4

Force

Answer 4

Force = rate of change of momentum (vector)

Question 5

units of momentum

Answer 5

kg ms-1

Question 6

units of rate of change of momentum

Answer 6

kg ms-2

Question 7

Impulse

Answer 7

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

Question 8

units of Impulse

Answer 8

Ns or kg ms-1

Question 9

area under a graph of force against time

Answer 9

change in momentum or impulse

Question 10

principle of conservation of linear momentum definition

Answer 10

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

Question 11

elastic collision defintion

Answer 11

a collision where kinetic energy is conserved

Question 12

inelastic collision definition

Answer 12

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

Question 13

displacement equation for an object undergoing SHM

Answer 13

x = Acosωt

Question 14

velocity equation for an object undergoing SHM

Answer 14

v=±ω√A²-x²

Question 15

angular speed

Answer 15

angle turned through per second (scalar)

Question 16

maximum speed

Answer 16

ωA

Question 17

maximum acceleration

Answer 17

ω²A

Question 18

units of angular speed

Answer 18

rad s-1

Question 19

angular speed of earth

Answer 19

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

Question 20

centripetal force

Answer 20

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

Question 21

centripetal acceleration

Answer 21

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

Question 22

conditions for shm

Answer 22

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

Question 23

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

Answer 23

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

Question 24

gradient of displacement against time

Answer 24

velocity

Question 25

graphical representations linking x, v, a and t from SHM

Answer 25

velocity –> acceleration = gradient
acceleration –> displacement = flip

just differentiate sinx or cosx

Question 26

conditions for the time period equation of a pendulum

Answer 26

time period equation for a pendulum is only true for oscillations with a small amplitude, that is, angular displacements less than 10 degrees

Question 27

dependence of time period on amplitude of an oscillation

Answer 27

time period of oscillation in SHM is independent of amplitude

Question 28

variation of Ep and Ek with displacement

Answer 28

as Ek increases, Ep decreases so the total energy is constant

Question 29

resonance definition

Answer 29

when driving frequency = natural frequency of an oscillating system, vibrations with very large amplitude are produced

Question 30

free oscillation definition

Answer 30

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

Question 31

forced oscillation definition

Answer 31

oscillation due to external periodic driving force

Question 32

time period

Answer 32

time taken for one complete oscillation

Question 33

frequency

Answer 33

number of oscillations per second

Question 34

amplitude

Answer 34

maximum displacement of a particle from its rest position

Question 35

damping definition

Answer 35

damping is when frictional forces oppose motion, dissipating energy so the energy of the oscillating system decreases

Question 36

damping descriptions

Answer 36

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

Question 37

phase difference between driver and driven oscillations

Answer 37

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&raquo_space;> A applied
- phase difference = π/2 rad or 90°
fapplied»> fo
- amplitude is very small «< A applied
- phase difference = π rad or 180°

Question 38

what would cause lower peak amplitude on resonance curve

Answer 38

energy losses from system

Question 39

resonance curves and damping

Answer 39

Light damping = very sharp resonance peak
Heavy damping = much flatter resonance peak

Question 40

damping in mechanical systems

Answer 40

structures are damped to avoid being damaged by resonance, in particular skyscrapers such as Taipei 101 (giant pendulum)

Question 41

damping and stationary waves

Answer 41

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