chapter 4 Flashcards
1
Q
define
centripetal force
A
it is the force towards the centre of revolving which is perpendicular to the direction of velocity
2
Q
what if the centripetal force is removed ?
A
there will be no friction / tension, so the object that was revolving in a circle will move in the direction of the velocity (tangent to the circle) and escape
3
Q
why does an object revolving in a circle have a steady speed but a changing velocity ?
A
because it changes direction, so veloctiy changes with constant value (speed)
4
Q
describe circular motion qualitatively
A
to keep an object moving in circular motion, the velocity changes, so aceleration towards the centre is also needed
5
Q
define
angular velocity
A
it is the change in angle per unit time
6
Q
state the rule
θ = ?
A
S / r
and if θ = 2π
then S = 2πr
7
Q
state the rules
ω = ?
A
= 2π/T
= 2πf
= v/r
8
Q
state the rules
a = ? (centripetal)
a = ? (SHM)
A
- centripetal –> =vω
= (v)^2 / r
= (ω)^2 x r - SHM –> = -(ω)^2 x X
9
Q
state the rules
F = ?
A
= mvω
= (m x (v)^2) / r
= m(ω)^2xr
10
Q
state the rules
KE = ?
A
= 1/2 x m x (v)^2
= 1/2 x m x (ω)^2 x (r)^2
= 1/2 x m x (A)^2 x (ω)^2
11
Q
state the rules
T = ? (mass on a spring)
T= ? (simple pendulum)
A
- mass on a spring –> = 2π√(m/k)
- simple pendulum –> = 2π√(L/g)
12
Q
define
periodic motion
A
it is the motion repeated in equal intervals of time
13
Q
define
simple harmonic motion
A
an oscillation where the acceleration/force is proportional to displacement from the mean position and directed towards the mean position
14
Q
explain the process
ruler and SHM
A
- plastic ruler is released and the restoring force returns it to its equilibrium position
- net force is zero at equilibrium, but the ruler has momentum to the right
- restoring force is in the opposite direction, so it stops the ruler and moves towards equilibrium
- the ruler now has momentum to the left
- in the absence of frictional forces, the ruler reaches its original position and repeats its motion
15
Q
what provides the restoring force ?
A
the forces between the atoms
16
Q
define
displacement
A
the distance from the equilibrium position
17
Q
define
amplitude
A
the maximum displacement of the particle on either side of the equilibrium position
18
Q
define
time period
A
the time required for one oscillation
19
Q
define
frequency
A
the number of oscillations in one second
20
Q
define
phase
A
the state of motion of the particle
21
Q
what will happen when
syncing circular and simple harmonic motions
A
- frequency –> constant and the same for both
- period –> constant and the same for both
- angular velocity –> constant and the same for both
- acceleration –> circular : its value is constant and it is
directed towards the center
–> SHM : its value changes and it is directed
towards the mean position - velocity –> circular : its value is constant and it is tangent
to the direction of motion
–> SHM : its value changes and it is directed
towards the mean position - displacement –> circular : constant
–> SHM : its values change and it is directed
away from the mean position
22
Q
beginning of the displacement-time graph in SHM when :
1. it is oscillating from the equilibrium position
2. it is oscillating from its amplitude position
A
- X = A sin(ωt) = A sin (2πft)
- X = A cos(ωt) = A cos(2πft)
23
Q
SHM ( mass on a spring )
- what are the possible factors affecting periodic time?
- mention possible factors that will not affect the periodic time
- how to calculate the natural frequency of an oscillating mass on a spring?
- explain why the natural frequency of a space car with the same mass and spring constant never change by changing the amplitude or even changing the planet
A
- mass and stiffness
- maximum displacement (amplitude), free fall acceleration, length, shape and volume
- the reciprocal of the equation for periodic time
- these factors do not affect the frequency or the periodic time, and the facotrs that do affect it didn’t change so they both remain unchanged
24
Q
SHM ( simple pendulum )
- what are the possible factors affecting periodic time?
- mention possible factors that will not affect the periodic time
- how to calculate the natural frequency of an oscillating pendulum?
4.explain why the natural frequency of a pendulum with the same length never changes by changing the amplitude or the mass of the bob
A
- length and free fall acceleration
- mass, spring constant, angle and amplitude
- reciprocal of the equation for periodic time
- the amplitude does not affect the frequency or the periodic time, so they do not change due the free fall acceleration and length of the pendulum being constant
25
# at the ends
pendulum system
1. the velocity is zero
2. the displacement and acceleration are at their peak, but when one is positive the other is negative
3. maximum potential energy
26
# at the centre
pendulum system
1. the velocity is at its peak negative or positive value
2. the displacement and acceleration are both zero
3. maximum kinetic energy
27
# state a fact and explain
energy
1. energy is always positive
--> it is never a negative value or zero
28
# describe
the interchange between KE and PE during SHM
- the enegy of the oscillator chnages from potential to kinetic and back to potential in every half cycle interval
- at the equilibrium position, the mass has a maximum KE because its speed is greatest & has zero PE as the spring is neirther compressed nor stretched
- at the ends where the mass stops, KE is zero while its PE is at its maximum value
29
# define
damping
it is the reduction in energy and amplitude of oscillations due to resistive forces on the oscillating system
30
# explain
why are completely undamped harmonic oscillators so rare?
friction of some sort usually acts to dampen the motion so :
--> the motion dies
or
--> it needs more force to continue
31
# explain
the reason for damping
damping exists due to air resistance or some other resistive force causing the oscillations to die away
| the damping force is always less than the restoring force
32
# compare
resistive force and restoring force
1. the resistive force is what opposes the motion of the oscillator and causes damping
2. the restoring force is what brings the oscillator back to the equilibrium position
33
# state
- what remains constant in a damped oscillation ?
- what decreases in a damped oscillation ?
1. the periodic time, frequency and angular frequency
2. total energy of the oscillation and the amplitudes of the oscillations
34
# state and describe three
types of damping
1. light damping (underdamped) --> only a small fraction is lost, so the amplitude decays exponentially with time
2. critical damping -->makes the oscillating object return to its equilibrium position in the shortest time possible without oscillating
3. heavy damping (overdamped) --> it takes a long time for it to return to its equilibrium position without oscillation, and it returns more slowly than the critical damping case
| 2 & 3 have no angular frequency
35
# describe the purpose of
viscous dampers
they are hydraulic devices that, when stroked, dissipate the energy as heat energy into the environment
| the same solution is used for a bridge design
36
# define
resonance
the forced motion of an oscillator characterised by maximum amplitudes when the forcing frequency matches the oscillator's natural frequency
37
# define
forced oscillations
periodic forces which are applied in order to sustain oscillations
38
# define
driving frequency
it is the frequency of forced oscillations (applied frequency)
39
# define
natural frequency
the frequency of an oscillation when the oscillating system is allowed to oscillate freely (resonant frequency)
40
# explain
why is the frequency of free oscillation called natural frequency ?
because the frequency of free oscillation depends on the nature and the structure of the oscillating body
41
# compare between
free oscillations and forced oscillations
1. free oscillations occur when an object is set into motion without any external forces, and the motion continues without any external input
2. forced oscillations occur when an external force is continuously applied to an object causing it to vibrate at a specific frequency
42
# explain
why is it that when the driving frequency applied to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillations increases significantly ?
- this is because at resonance, energy is transferred from the driver to the oscillating system most efficiently
- therefore, at resonance, the system with transferring the maximum KE possible
43
describe graphically how the amplitude of a forced ossicalltion changes with frequency near to the natural frequency of the system
| resonance curve (amplitude frequency graph)
- when the driving frequency is smaller than the natural frequency, the amplitude of the oscillations increases
- at the peak where the drivng frequency is equal to the natural frequency, the amplitude is at its maximum (this is resonance)
- when the driving frequency is greater than the natural frequency, the amplitude of the oscillations starts to increase
| at lower amplitudes, more frequencies btastageeb
44
effect of damping on resonance
- damping reduces the amplitude of resonance vibrations
- the height and shape of the resonance curve will change slightly depending on the degree of damping
45
effect of increasing degree of damping
as the degree of damping is increased, the resonance graph is altered in the following ways :
1. resonant frequency decreases
2. the resonance peak moves slightly to the left of the
natural frequency when heavily damped
3. the sharpness of the resonance peak decreases
4. the amplitude of the forced oscillation decreases at all
driving frequencies
46
# explain
dissipated forces are useful
- building cantilevers are subject to periodic forces such as wind and earthquakes
- the dampers used in them dampen the oscillations of the building by dissipating KE through friction, so the amplitude of the oscillations is reduced and then they stop
47
SHM examples
1. a mass on a spring
2. a horizontal mass-spring system
3. a rotating disk
4. the vibrating strings of a musical instrument
5. an alternating current connected to an oscilloscope
6. a torsion pendulum
7. a ball rolling a curved track
8. a U tube containing liquid
9. a trolley moving between two fixed rubber bands
10. a bar magnet suspended over a fixed magnet
48
circular motion examples
1. vehicle driving around a curve
2. going through a loop on a roller coaster
3. the gravitational pull of the sun on earth
4. electrons circling a nucleus due to the electrostatic attraction force between
5. swinging an object in a circle using a rope
