7. Further Mechanics Flashcards
What is linear speed?
the distance travelled per second
What is the equation for linear speed?
v = d/t
What is angular speed?
the angle turned through per second
What is the equation for angular speed?
ω = θ/t
Where is centripetal acceleration directed?
towards the centre of the circle and perpendicular to the velocity
What are the two equations used to calculate centripetal acceleration?
a = ω²r
a = v²/r
What is the centripetal force?
the resultant force acting on a object in circular motion
Where is centripetal force directed?
towards the centre of the circle and perpendicular to the velocity
What are three examples of centripetal force?
- gravity
- friction
- tension
What will happen if an object is moving in a circular path and the centripetal force is removed?
the object will fly off at a tangent
What are the two equations used to calculate centripetal force?
F = mω²r
F = mv ²/r
For motion in a vertical circle, what is centripetal force at the top of the circle?
CF = T + W
For motion in a vertical circle, what is the centripetal force at the bottom of the circle?
CF = T - W
When a car is going over a small hill, what is the centripetal force at the top of the hill?
CF = W - R
When a car is going over a hill, at what point will the car lose contact with the road?
when reaction force = 0N
At the moment of loosing contact, what is the centripetal force?
CF = W
What will an aircraft use when it needs to change direction?
banking
What is banking?
when the lift force, which normally acts upwards, provides a horizontal component
Give two examples of simple harmonic oscillators (SHO)
- a simple pendulum
- a mass on a spring
What is the full definition describing an object on simple harmonic motion?
an oscillation in which the acceleration of an object is directly proportional to its displacement from its equilibrium position in the opposite direction, and is directed towards the equilibrium
Why is acceleration proportional to negative displacement?
because acceleration is always directed towards the equilibrium
What is a restoring force?
a force that tries to return the oscillator to the equilibrium
Give two examples of restoring forces
- gravity
- tension
What is the relationship between the size of the restoring force and the size of the displacement from equilibrium?
directly proportional
When is the total energy equal to max kinetic energy in SHM?
at the equilibrium position
When is the total energy equal to max potential energy?
at the amplitude/points of maximum displacement
How do you calculate the displacement from equilibrium of an object moving with SHM?
x = Acos(ωt)
How do you calculate the velocity of an object moving with SHM?
v = +/- ω√(A² - x²)
When is the velocity of an oscillator greatest?
at the equilibrium when x = 0
How do you calculate the maximum velocity of an object moving with SHM?
v max = +/- ωA
How do you calculate the acceleration of an object moving with SHM?
a = - ω²x
When is the acceleration of an oscillator greatest?
at the amplitude when x = A
How do you calculate the maximum acceleration of an object moving with SHM?
a max = ω²A
How do you calculate the maximum kinetic energy of an object in SHM?
Ek max = 2mπ²f²A²
How do you calculate the maximum elastic potential energy for an object in SHM?
Ep max = 1/2 kA²
How do you calculate the time period of a simple pendulum?
T = 2π √(l/g)
What is the criteria for the equation used to calculate the time period of a simple pendulum?
the equation only works for small oscillations (angles no greater than 10˚)
How do you calculate the time period of a mass spring system?
T = 2π √(m/k)
What is a free vibration?
- involves no transfer of energy to or from the surroundings
- objects oscillate at their natural (resonant) frequency
What is a forced vibration?
- when there is a periodic, external driving force applied at a the driving frequency
What is resonance?
- when the driving frequency is equal to the natural frequency
- maximum energy transfer
- rapid/dangerous increase in amplitude
What is the amplitude of oscillation and phase difference between the driver and the oscillator when the driving frequency is less than the natural frequency?
- small
- 0 (in phase)
What is the amplitude of oscillation and phase difference between the driver and the oscillator when the driving frequency is equal to the natural frequency?
- very large
- π/2
What is the amplitude of oscillation and phase difference between the driver and the oscillator when the driving frequency is greater than the natural frequency?
- small
- π (anti-phase)
How does a guitar use resonance and stationary waves in combination?
- stationary waves are forced on the guitar strings
- this vibrations move little air so produce very quiet sounds
- the body of the guitar is designed to have a natural frequency similar to the stationary waves
- this causes the large body of the guitar to resonate
- moving much more air
What is damping?
any frictional force that acts in the opposite direction to the oscillator’s motion, causing it to lose energy
In what direction does the damping force always act?
in the opposite direction to motion
What are the four different types of damping?
- light damping
- heavy damping
- critical damping
- over damping
Can damping stop resonance completely?
no - damping can only reduce the size of the amplitude
What two main variables do not affect the time period of a mass spring system?
- initial displacement/amplitude
- gravity
What two main variables do not affect the time period of a simple pendulum?
- initial displacement/amplitude
- mass of bob
The value of L in the equation for the time period of a simple pendulum is measured from where to where?
from the pivot point to the centre of mass of the bob
