3.6.1 Further mechanics Flashcards
Why is an object moving in a circular path at constant speed accelerating?
It has a constantly changing velocity as it is changing direction, so it must be accelerating
What is the force experienced by an object moving in a circle?
The centripetal force
Where does the centripetal force act?
Towards the centre of the circle
What is angular speed?
The angle an object moves through per unit time
What is simple harmonic motion?
When an object’s acceleration is directly proportional to its negative displacement from the equilibrium position, a=-ω²x
Describe the displacement-time graph of an object experiencing simple harmonic motion starting at the maximum positive displacement.
Cosine curve
Describe the displacement-time graph of an object experiencing simple harmonic motion starting at the equilibrium position.
Sine curve
Describe the displacement-time graph of an object experiencing simple harmonic motion starting at the maximum negative displacement.
Negative cosine curve
Describe the velocity-time graph of an object experiencing simple harmonic motion starting at the maximum positive displacement.
Negative sine curve
Describe the velocity-time graph of an object experiencing simple harmonic motion starting at the equilibrium position.
Cosine curve
Describe the velocity-time graph of an object experiencing simple harmonic motion starting at the maximum negative displacement.
Sine curve
Describe the acceleration-time graph of an object experiencing simple harmonic motion starting at the maximum positive displacement.
Negative cosine curve
Describe the acceleration-time graph of an object experiencing simple harmonic motion starting at the equilibrium position.
Negative sine curve
Describe the acceleration-time graph of an object experiencing simple harmonic motion starting at the maximum negative displacement.
Cosine curve
What are simple harmonic systems?
Those which oscillate with simple harmonic motion, such as a simple pendulum or a mass-spring system
Describe a simple pendulum.
- A small, dense bob hangs from a string attached to a fixed point
- When the bob is displaced by a small angle, and let go, it will oscillate with SHM
Why must the angle by which the pendulum is displaced be less than 10°?
The formula is derived using a small angle approximation, so for larger initial angles this approximation is no longer valid, so would not be a good model
How many energy transfer cycles are there in an oscillation of a simple harmonic system?
Two
Describe the energy transfer of a simple harmonic system.
When the displacement is at a maximum, it has maximum potential energy and minimum kinetic energy, when passing equilibrium it has max KE and min PE, and at minimum displacement it has max PE and min KE
What does the total energy of a simple pendulum consist of?
Kinetic and gravitational potential energy
Describe a mass-spring system.
A mass is attached to the end of a spring, and is pulled down/across a small distance and let go, so it undergoes SHM
What is the difference between a vertical and a horizontal mass-spring system?
For a vertical system, kinetic energy is converted to both elastic and gravitational potential energy, whereas for a horizontal system, kinetic energy is converted only to elastic potential energy.
What does the total energy of a vertical mass-spring system consist of?
Kinetic energy, and elastic and gravitational potential energy
What does the total energy of a horizontal mass-spring system consist of?
Kinetic and elastic potential energy
What is damping?
When the energy in an oscillating system is lost to the environment, leading to reduced amplitude of oscillations
What are the 3 main types of damping?
Light damping, critical damping and heavy damping
What is light/under damping?
Where the amplitude gradually decreases by a small amount each oscillation, and the period is not affected
What is critical damping?
Where the amplitude is reduced to zero (returns to equilibrium) in the shortest possible time, without oscillating
What is heavy/over damping?
Where the amplitude reduces slower than with critical damping, but also without any additional oscillations
How do free vibrations occur?
When no external force is continuously acting on the system, and it oscillates at its natural frequency
What is the natural frequency of a system?
The frequency a system oscillates at with free vibrations, where no external force is continuously acting on the system
What are forced vibrations?
Where a system experiences an external driving force, causing it to oscillate
What is the driving frequency of a system?
The frequency of the external driving force causing a system to oscillate with forced vibrations
How does resonance occur?
If the driving frequency is equal to the natural frequency of a system (also known as the resonant frequency)
What is resonance?
Where the amplitude of oscillations of a system drastically increase due to gaining an increased amount of energy from the driving force
What are examples of applications of resonance?
- Instruments: such as a flute, which has a long tube in which air resonates, causing a stationary sound wave to be formed
- Radio: tuned so that their electric circuit resonates at the same frequency as the desired broadcast frequency
- Swing: if someone pushes a swing, they provide a driving frequency, which can cause resonance if it’s equal to the resonant frequency and cause the swing to swing higher
What is the negative consequence of resonance?
It can cause damage to a structure, such as a bridge when the people crossing it are providing a driving frequency close to the natural frequency, it will begin to oscillate violently witch could be very dangerous and damage the bridge
How can the effect of resonance be decreased?
By using damping
What is the effect to the resonant frequency of a system as the degree of damping is increased?
- Resonant frequency decreases (shifts left on a graph)
- Maximum amplitude decreases
- Peak of maximum amplitude becomes wider
How is the velocity-time graph related to the displacement-time graph of an object in SHM?
It is the gradient function of the displacement-time graph, as velocity is the derivative of displacement
How is the acceleration-time graph related to the velocity-time graph of an object in SHM?
It is the gradient function of the velocity-time graph, as acceleration is the derivative of velocity