A2 - Further Mechanics Flashcards
What type of quantity is momentum?
Vector.
What are the units for momentum?
kgms-1 =Ns
Define impulse
Change in momentum - F(8)t =m(8)v
f=m(v-u)/t
What is the force-time graph for a rocket? What does the area under a F-T graph represent?
Triangular shape.
Area represents impulse - change in momentum.
State N3L and explain how this affects a gas molecule on impact with a gas cylinder
When two objects interact, they exert equal and opposite forces on each other.
Gas molecule exerts the same force on cylinder on impact as cylinder exerts on it, there is just more of a visible effect because the gas molecule is accelerated more due to its lower mass.
Define an inelastic collision.
Momentum is conserved, kinetic energy is not
Define an elastic collision
Momentum and kinetic energy is conserved
Give 2 examples of inelastic collisions
Explosion, coalescence
Give an example of an elastic collision
Hard material rebounding
What is the rule for conservation of momentum?
It is always conserved unless external forces act on the object.
Is an explosion elastic or inelastic?
Inelastic.
What is the kinetic energy just after an explosion of two trolleys
It is equal to the kinetic energy stored in the springs = 0.5kl^2
What are the units for angular displacement?
radians
What are the units for angular velocity? Which greek letter is used to represent it?
rads-1
omega
In which direction does the force need to act for an object in circular motion?
Towards the centre
When an object is in vertical circular motion, when is the force towards the centre maximum?
When the object is at the bottom of the circle, as it does not have mg working in the same direction and has to overcome this to give a constant centripetal acceleration.
How do you find angular velocity?
angular displacement/time (rads^-1)
What is frequency?
Number of oscillations/revolutions per second
What is period?
The time taken for one oscillation/revolution
At which point is the string of a vertically rotating object most likely to break and why?
The bottom, as the tension causing the centripetal acceleration must counter the weight of the object, so this is where the maximum force is.
What is damping?
Application of friction to an oscillating system that causes the amplitude to decrease over multiple periods.
What is heavy damping?
A large frictional force is applied that causes the amplitude to decrease quickly
What is light damping?
A small frictional force is applied such that the amplitude decreases slowly.
What is critical damping?
Where the frictional force is such that the oscillation is reduced to zero as quickly as possible.
What is free oscillation?
Where the oscillator is released and allowed to oscillate at its natural frequency.
In a physical system, why does the amplitude not constantly increase?
Damping limits the effects of the increasing amplitude.
What happens when an oscillator is damped?
The period is not affected, the amplitude decreases. It is an exponential decay, so the follows a constant ratio.
For a simple pendulum system, where does the resultant force act?
Towards the equilibrium position.
Which two things change the frequency of a mass-spring system?
extra mass
Weaker springs
What are forced oscillations?
An oscillating system will respond to forced oscillations depending on the frequency of the driving oscillation.
What is resonance?
when the driving (applied) frequency equals the natural frequency, the oscillator is (pi)/2 radians out of phase with the driver
What is the phase difference between the driver and oscillator under resonant frequency?
pi/2
What is the phase difference between driver and oscillator when not under natural frequency?
increases from pi/2 to pi as driving frequency increases.
In barton’s pendulums, what does the amplitude of each pendulum depend on, including the one of the same length as the driver?
Driver responds in resonance because the natural frequency of both match, the others oscillate depending on proximity to the driver
What is the shape of kinetic energy vs displacement for a pendulum?>
Inverted parabola
If two spheres both have their radii doubled, what happens to the force?
Each mass increases by 8x, so the force increase due to the mass is 64x
This is divided by an increase in radius of 2x, so r^2=0.25, hence 64/0.25= 16x increase
When an object is in SHM on a spring, what is the overall direction of the force at the top and bottom of the stroke?
top - downwards due to gravity
Bottom - upwards due to force in spring (proportional to extension)
What are the principles of conservation of energy and momentum and how do they apply to a probe exhausting a capsule to increase velocity?
Energy is always conserved, but in an explosion, is converted into other forms, such as heat. Momentum is always conserved unless an external force acts.
In an explosion of this kind, since momentum is a vector, and there is no vertical momentum, the capsule is exhausted directly backwards.
What happens when the driving frequency increases above resonant frequency?
Phase difference increases from pi/2 to pi rad out of phase
