Section 6- Further Mechanics And Thermal Physics Flashcards
What is uniform motion in a circle?
An object rotating at a steady rate.
Describe what you need to measure to find the speed of an object moving in uniform circular motion.
Circumference of the wheel: 2(pi)r
The frequency of rotation: f=1/T
v=2(pi)r= 2(pi)rf
T
Define angular displacement and angular speed.
Angular displacement: the angle in radians of the object in time t.
2(pi)t= 2(pi)ft
T
Angular speed (w): angular displacement per second
Why is velocity not constant when an object is travelling uniformly in a circle?
The object is accelerating.
What is the directions of the acceleration?
The direction changes continually as the object moves and the acceleration is always towards the centre of the circle. It is called centripetal acceleration.
What is the equation for centripetal force?
F=(mv)^2= mw^2r
r
Explain why a passenger is thrown outwards if the car rounds a bend too quickly.
The centripetal force is provided by the sideways force of friction between the vehicle and the road.
For no skidding the force of friction between the tired and road must be less than that the limiting value F which is proportional to the vehicles weight.
Describe what happens between an passenger and the seat when travelling over a curved bridge.
At the top of the hill the support force from the road is directly up and mg is directly down. The resultant force acts towards the centre of the hill.
What forces provide the centripetal force on a banked track?
There is no sideways friction if the speed v is such that:
v^2=grtan0
Most tight bends on race tracks are banked to enable the car to drive at higher speeds.
When is the contact force on a passenger on a Big Dipper ride is the greatest?
At the bottom because
S-mg=mv^2
r
What is the condition that applies when a passenger fails to keep in contact with their seat?
v^2=gr so R=0 so there would be no force on the person
What is meant by one complete oscillation?
T=1/f
Define amplitude, frequency, period and free vibrations.
Amplitude: maximum displacement of object from equilibrium
Frequency: number of cycles per second
Period: time for one cycle of oscillation
Free vibration: constant amplitude with no frictional forces
Describe the phase difference between two oscillators that are out of step.
Their phase difference (rad) stays the same=
2(pi)🔺t
T
State two fundamental conditions about acceleration that apply to simple harmonic motion.
Acceleration is proportional to the displacement.
The acceleration is in the opposite direction to the displacement.
Describe how displacement, velocity and acceleration vary with time.
The displacement starts at maximum displacement and one oscillation will be at T.
The velocity is 1/4 cycle out with displacement.
The acceleration is 1/2 cycle out with displacement (the opposite direction).
What equation relates displacement to time for a body moving with simple harmonic motion?
2(pi)t=wt
T
Applies from equilibrium.
What conditions music be satisfied for a mass-spring system or simple pendulum to oscillate with simple harmonic motion?
The acceleration must be proportional to displacement and always acts toward the equilibrium.
How does the period of a mass-spring system depend on mass?
The extra mass increases the interia. The trolley would be slower so each oscillation would take longer.
Describe how the period of a simple pendulum depends on its length.
The longer the spring the longer it will take to complete an oscillation.
How does, in simple harmonic motion, kinetic energy vary with displacement?
At maximum displacement the energy is all potential energy.
At 0 displacement the energy is all kinetic energy.
Describe the effects of damping on the characteristics of oscillations.
Light damping: each cycle takes the same length but the amplitude slowly decreases.
Critical damping: stops the object oscillating and return the object to equilibrium in the shortest time possible.
Heavy damping: object returns to equilibrium slowly without oscillations.
What circumstances do resonance occur in?
The periodic force is exactly in phase with the velocity of the oscillating system.
What is the difference between free vibrations and forced vibrations?
Forced vibrations have a periodic driving force applied to the oscillating system. The free vibrations do not.
