Futher Mecahnics Flashcards
What kind of force is required to keep and object moving in a circle at constant speed
A constant Centripetal force
(a force that is always applied towards the centre of the circle)
Describe the motion of an object traveling at a constant speed within a circle.
1) Accelerating towards a fixed point in the centre,as the direction is always changing, hence the velocity is always changing so the object is accelerating.
2) Angular & linear speed is constant (Radians per second & meters per second )
How do you calculate angular speed (omega)
Omega = Velocity/radius
Omega = 2pifrequency
Omega = (2*pi)/Time period
How do you calculate angular acceleration? (2 ways)
A = Omega^2 * radius
A = Velocity^2 / Radius
What is the formula for centripetal force
F = mA
F = m * velocity^2 / radius
F = m * Omega^2 * radius
What are the conditions for SHM
. Acceleration must be proportional to its displacement from the equilibrium point
. Acceleration is always acting in the opposite direction to displacement
What is displacement as a trig function of time and angular speed
Displacement = Amplitude * cosine( Omega * time)
How do you calculate speed using Angular velocity and Amplitude
Derivative of Amplitude* cosine(omega * time)
Velocity = omega * Amplitude* sine(omega * time)
Note can be cos too depending what you use.
Ho do you calculate maximum speed? (SHM)
Omega*Amplitude
Omega = Angular speed
as cos(wt) = 1
How do you calculate acceleration using angular velocity and amplitude
Derivative of Amplitude* cosine(omega * time) in respect to time
Velocity = (omega)Amplitude sine(omega * time)
Acceleration = Derivative of velocity in respect to time
Acceleration = -1* (omega)^2 * Amplitude * cosine(omega * time)
Note can be cos too depending what you use.
How do you calculate maximum acceleration in shm
Omega^2 * Amplitude
How would you calculate the time period for a mass spring system undertaking in simple harmonic motion
How would you calculate the time period for a simple pendulum undertaking in simple harmonic motion
Draw the graph for the potential energy and kinetic energy against displacement for a SHM system.
Define Free vibrations
oscillations where’re there are no damping frictional forces and the amplitude is constant
Define forced vibrations
When is the amplitude greatest
A periodic driving force causes the system to vibrate at a different frequency then the natural frequency
The amplitude of a forced vibration is greatest when the natural frequency is in phase with the periodic driving force
Define Damping
Draw a graph for a damped system
Damping occurs when an opposing force dissipates energy of the system to the surroundings
Forces such as friction of air resistance
Amplitude decreases as time goes on.
What is critical damping
when the opposing force reduces the amplitude to 0 in the quickest time possible
what is overdamping?
When the opposing force is so strong the the mass returns slowly to the equilibrium without oscillation
What is under damping
When the opposing force causes the mass to oscillate with an exponentially decreasing amplitude.
What happens to a vibrations with greater damping?
Provide a graph
The amplitude is lower at all frequency’s due to the energy losses from the system
The resonant peak is also broader
Resonant peak is at a lower frequency
What happens to a vibration with light damping?
Provide a graph
The resonance peak is sharp
At a slightly lower amplitude to a non-damped system
resonant peak is broader and slightly lower then the natural frequency
What are free oscillations
oscillations where’re there are no frictional forces and the amplitude is constant
Where is displacement measured from in SHM
measured from the equilibrium position
Where is acceleration measured from in SHM
towards the equilibrium position
Draw the graph for displacement over time for SHM where displacement starts from maximum
Draw the graph for accleration over time for SHM where displacement starts from maximum
Draw the graph for velocity over time for SHM where displacement starts from maximum
What is the phase difference between the driving frequency and the natural frequency when
Driving < Natural
Driving = Natural
Driving > Natural
Explain resonance
Violent large vibrations caused when the frequency of the periodic driving force is equal to the natural frequency of the system .They are in phase so waves undergo superposition , Constructive interference then happens repetitively, creating larger and larger vibrations
How do you calculate the reaction force on “the big dipper”?
S = mr Omega^2 + m*g
g = -9.8
Reaction force is equal to the centripetal acceleration with mg taken off it to balance the forces
How do you calculate the reaction force on the very long swing.
S = mr Omega^2 + m*g
then Omega^2 = V^2 / Length of cable
g = -9.8
Reaction force is equal to the centripetal acceleration with mg taken off it to balance the forces
How do you calculate the reaction force on the big wheel
S = mr Omega^2 -m*g
g = -9.8
at maximum height
Reaction force is equal to the centripetal acceleration with the mg as both are acting in the same direction
A ruler is clamped to the edge of a bench. The end of the ruler is displaced downwards by 2.5 cm and released. The ruler oscillates with simple harmonic motion at a frequency of 4.0 Hz. At time t, the end of the ruler is at a distance of 0.20 cm from the midpoint of the oscillation, and the amplitude of the oscillation has been reduced by 80% due to the effects of damping. What is the speed of the end of the ruler at time t?
0.12
Explain the shape of the following Graph
Rotation of the drum forces the whole washing machine to vibrate at the same Frequency as it.
As the Driving frequency approaches the resonant frequency of the washing machine itself (just before 750 rpm), the washing machine begins to resonate, causing the amplitude of the vibrations to increase.
What type of Damping profile should be set for a pair of supermarket scales.
Critical Damping
As this means the scales oscillations stop in the minimum amount of time, so an accurate measurement can be taken in the shortest possible time.
Draw and describe a graph to show the relationship between heavy and light damping, in comparison to the natural frequency of an object
Light damping - Sharp resonance speak, with peak at a lower frequency to the natural frequency , slightly lower peak amplitude.
Heavy Damping - Broader resonance peak, with peak at a lower frequency to the natural frequency
One of the acrobats mass is greater then the other
Explain the consequences for the forces acting on the pole
Increased mass , increases the weight acting on the heavier acrobat. Resulting in a higher tension within the rope for the same angle to vertical
Unbalanced Horizontal forces act on the pole
Causing the pole to sway and wobble the platform towards the more massive acrobat
