Further Mechanics Flashcards
Describe motion in a circular path at a constant speed
Motion in a circular path at constant speed implies there is an acceleration and requires a centripetal force
Which direction does a Centripetal Force act
A centripetal force always acts towards the centre of the circle
What is Angular Speed
The angle an object moves through per unit time
What are the Equations for Angular Speed
ω = v / r
Angular Speed = Velocity / Distance
ω= 2πf
Angular Speed = 2π x Frequecny
What are the Equations for Centripetal Acceleration
a = v2 / r = ω2r
Acceleration = Velocity2 / Distance = Angular Speed2 X Distance
What are the Equations for Centripetal Force
F = mv2 / r = mω2r
Centripetal Force = Mass x Velocity2 / Distance = Mass x Angular Speed2 x Distance
When is an object experencing simple harmonic motion
When its acceleration is directly proportional to displacement from the equilibrium point and is in the opposite direction
What is the equation for accleration in simple harmonic motion
a = -ω2x
Accleration = - Angular Speed2 x Displacement
What is the equation for displacement in simple harmonic motion
x = A Cos(ωt)
Displacement = Amplitude x Cos(Angular Speed x Time)
What is the equation for velocity in simple harmonic motion
v = ± ± ω √(A2 - x2)
Velocity = ± Angular Speed √(Amplitude2 - Displacement2)
When are velocity and acceleration at their maximum and minimum on a pendulm
- Velocity Max = Centre
- Velcoity Zero = Amplitude
- Acceleration Max = Amplitude
- Accleration Zero = Centre
What are the equations for velocity max and acceleration max
- Vmax = ωA
- amax = ω2A
Describe the displacement-time graph of simple harmonic motion
Describe the Velocity-Time Graph of Simple Harmonic Motion
Describe the Acceleration-Time Graph of Simple Harmonic Motion
Describe the Time Period Equation for a Simple Harmonic Pendulum
T = 2π √(L / g)
Time Period = 2π √ (Length of the String / Acceleration due to Gravity)
Explain why the simple harmonic pendulum only works for small angles
- The angle by which the pendulum is displaced must be less than 10°
- This is because during the derivation of the above formula a small angle approximation is used, and so for larger initial angles this approximation is no longer valid, and would not be a good model
- Therefore the amplitude must be small
What are the Limitations of the Simple Harmonic Motion Equations for a Simple Pendulum
- The amplitude is small
- The string is inextensible
- The bob used is a point mass
How would you measure the time period of the oscillations of a simple pendulum as accurately as possible
- Use a fiducial mark at the centre of oscillations
- Work out 10 oscillations and then divide by 10 to get the mean
Where should you place the fiducial mark
The mark should be at the equilibrium position since this is where the mass moves with greatest speed
Describe the Time Period Equation for a Mass-Spring Simple Harmonic System
T = 2π √ (m / k)
Time Period = 2π √ (Mass / Spring Constant)
Describe the Energy Transfers that occur in a Mass-Spring Simple Harmonic System
- There are two types of mass-spring system, where the spring is vertical or horizontal
- For the vertical system, kinetic energy is converted to both elastic and gravitational potential energy
- In the horizontal system, kinetic energy is converted only to elastic potential energy
Describe the Energy Transfers that occur in any Simple Harmonic System
- Kinetic energy is transferred to potential energy and back as the system oscillates (the type of potential energy depends on the system)
- At the amplitude = maximum amount of potential energy
- As it moves towards the equilibrium position, this potential energy is converted to kinetic energy
- At the centre = maximum kinetic energy
- Then as the system moves away from the equilibrium again, the kinetic energy is transferred to potential energy until it is at a maximum again
- The total energy of the system remains constant (when air resistance is negligible, otherwise energy is lost as heat)
Describe the graph of potential enegery against kinetic energy for a simple harmonic system