Further Mechanics Flashcards
What is a radian?
Uts the ratio of the arc length to the radius
What is 1 radian equal to in degrees?
57.3
What is angular velocity?
The velocity of a particle that travels through an angle
Used in circular motion as particles closer to the centre have different tangential velocity than the outermost particles - But they travel through the same angle so angular velocity used instead
What is tangential velocity?
The velocity of a particle at a tangent to its direction of travel
What is the equation that links tangential and angular velocity?
V=WR
Velocity = angular velocity x radius
Equations for angular velocity?
w=(2 x pi)/time period
w=2 x pi x frequency
Equation for tangential velocity?
v=1/frequency
Examples of angular velocity?
Clock
Engine revolutions
What is centripetal force?
The resultant force that causes an object to move in a circular path
Equation for centripetal acceleration?
a=(v^2)/r
a=(w^2) x r
Equation for centripetal force?
F=(m(v^2))/r
F=m x (w^2) x r
Examples of centripetal force?
Car as it corners - friction
Earth - Gravity
Atoms - Electrostatic
How would you find the centripetal force on an object at an angle? e.g. a car on a banked corner.
- W=mg
- W = Ncos(x) (weight same as vert comp of normal force)
- mg=Ncos(x)
- N =(mg)/Cos(x) (Rearrange for N)
- F=(m(v^2))/r
- Nsin(x) = (m(v^2))/r (Centripetal same as horiz comp of normal)
- mg/cos(x) x sin(x) = (m(v^2))/r (Sub N in)
- tan(x) x g = (v^2)/r
- tan(x) = (v^2)/g x r
How would you find the centripetal force of an object cornering on the flat. (e.g. a car)
Friction would be the resultant force towards the centre
So F=(m(v^2))/r would be the friction and the centripetal force
How would you find the speed limit for and object to successfully corner
Increase the values of V until the friction supplied by the tires can no longer fulfill the centripetal force required for the car to corner
Fr > F
Explain what happens for an object in a vertical loop in terms of the forces at 1 = the bottom of the loop 2 & 4 the sides and 3 the top of the loop
1 = The object will ‘feel’ the most force. As the weight of the object is working downward in the opposite direction to the centripetal force required. So the reactionary force has to overcome the weight and fulfill the centripetal force required. Hence the feeling of ‘being heavier’
2 & 4 = The objects weight is perpendicular to the reaction force and centripetal force so the objects centripetal force can be fulfilled just by the reaction force.
3 = The object has weight and the normal reaction force working in the same direction as the centripetal force required. As weight is constant and contributing towards the centripetal force, the reaction force will lessen hence a feeling of ‘weightlessness’
What 2 requirements are there for an object to be in Simple Harmonic Motion (SHM)
acceleration is directly proportional to displacement from equilibrium
accelerates in the opposite direction to it’s displacement
What effect does increasing the amplitude have on time period and velocity?
Time period remains the same
Velocity must increase as it has to travel further in the same time period
Equation for acceleration in SHM
acceleration = -(angular velocity)^2 x displacement
a= -(w)^2 * x
Equation for displacement in SHM
displacement = Amplitude x cos(angular velocity x time)
x= A x cos(wt)
Equation for velocity in SHM
velocity = + or -(w)sqroot((Amplitude)^2 - (displacement)^2)
Equation for max velocity in SHM
velocity max = angular velocity x amplitude
Vmax = w x A
Equation for max acceleration
acceleration max = (angular velocity)^2 x amplitude
Amax = (W)^2 x A
Time period in SHM for a mass spring system
time period = 2 x Pi x sqroot(mass/spring constant)
T = 2 x Pi x sqroot(m/k)
Time period in SHM for a simple pendulum
time period = 2 x Pi x sqroot(length/gravity)
T = 2 x Pi x sqroot(l/g)
How would you find the value of gravity or the spring constant by using time period of SHM
You would use a graph and plot T squared against either
L (if your trying to find g)
or M (if your trying to find the spring constant).
Then find the gradient of the graph.
As your using T squared, square the whole time period of SHM equation then rearrange and solve for g or k
Describe the correlation between velocity and displacement
90 degrees out of phase
Describe the correlation between velocity and acceleration
90 degrees out of phase
Describe the correlation between acceleration and displacement
180 degrees out of phase
Correlation between potential energy and displacement?
PE directly proportional to Displacement
Corellation between Kinetic energy and velocity?
KE directly proportional to (velocity)^2
When will SHM be damped?
When there are resistive forces present in the system
What does dampening cause in SHM?
It causes the amplitude of the oscillations to decrease with time
