Modelling Assumptions Flashcards
Light string
The mass is negligible
Particle
Dimensions of the object are negligible
Particle Assumption
- Mass of the object is concentrated at a single point
- Rotational forces and air resistance can be ignored
Rod
All dimensions but one are negligible, like a pole or a beam
Rod assumptions
- Mass is concentrated along a line
- No thickness
- Rigid (does not bend or buckle)
Lamina
Object with area but negligible thickness,like a sheet of paper
Lamina assumption
Mass is distributed across a flat surface
Uniform Body
Mass is distributed evenly
Uniform Body assumption
Mass of the object is concentrated at a single point at the geometrical centre of the body - centre of mass
Light Object
Mass of the object is small compared to other masses, like a string or a pulley
Light Object Assumptions
- Treat as having zero mass
- Tension the same at both ends of a light string
Inextensible string
A string that does not stretch under load
Inextensible string assumption
acceleration is the same in objects connected by a taut inextensible string
Smooth surface assumption
Assume that there is no friction between the surface and any object on it
Rough Surface Assumption
Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
Wire
Rigid thin length of metal
Wire Assumption
Treated as one dimensional
Smooth and Light pulley
All pulleys you consider will be smooth and light
Smooth and Light pulley Assumptions
- Pulley has no mass
- Tension is the same on either side of the pulley
Peg
A support from which a body can be suspended or rested
Peg Assumptions
- Dimensionless and fixed
- Can be rough or smooth as specified in the question
Air resistance
resistance force experienced as an object moves through the air
Air Resistance Assumption
usually modelled as being negligible
Gravity
Force of attraction between all objects. Acceleration due to gravity is denoted by g
Gravity assumptions
- Assume that all objects with mas are attracted towards the Earth
- Earth’s gravity is uniform and acts vertically downwards
- g is constant and is taken as 9.8m/s-2 unless otherwise stated in the question
What does particle moving at a constant velocity mean?
forces parallel to the slope are balanced.
Thrust
Opposite to tension (happens when car brakes)
Limitations of Q (car)
- The force due to air resistance will reduce as the car slows.
- If the skid causes the tyres to heat, the value of μ is also likely to vary.
Particle hanging (lightbulb)
Only has one tension (going up)
Velocity
Magnitude and direction
Displacement from starting point ÷ time
Uniform rod
Mass is in centre
Newton’s first law
every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force.
Newton’s second law
The acceleration of an object depends on the mass of the object and the amount of force applied
Newton’s third law
for every action (force) in nature there is an equal and opposite reaction.
Suggest one improvement that could be made in the model (pulleys)
Do not model ball B as a particle but give its dimensions so distance it falls changes
What makes acceleration in a pulley the same?
If the string is modelled as a light inextensible string
Identify one limitation of the model that will affect the accuracy of your answer (pulley)
Weight of string
Find the force on the pulley
Tension x2
The string is not light. How would this impact the equation?
The tensions would be different
A heavier block is placed on the slope with the same friction. Why does it remain at rest?
The friction will increase in the same proportion as the weight
Instantaneous rest
Differentiate to find subject
(Sub into equation and add for distance)
Acceleration of velocity and time equation
Differentiate
Finding position vector
Integrate and sub in point and 0
Fulcrum
A pivot
When loads are suspended on a rod/bar
The loads have no reaction force (normal reaction)
Smooth support
No normal reaction
Train moving on tracks (SUVAT). State an improvement to the model
- A smooth change from acceleration to constant velocity
- have the train accelerating at a variable rate
Limiting equilibrium
Forces = 0
Maximum value of mass on pulley
Moving in that direction
Modelled as a particle
we can ignore the effects of air resistance, the weight of the ball and any energy or path changes caused by the spin of the ball.
Hinge reaction
Up and friction reaction
Moments units
Distance must be in m
Position vector
Integrate velocity
Find displacement, velocity and acceleration
S-v-a
Differentiate
(Kinematics)
Find the distance of P from O at the instant when P changes its direction of motion
When v=0 to find time
Substitute into s equation
Find the value of t at the instant when P is moving in a direction perpendicular to i
i of v =0
r relation to s
r = s
Take up as positive (are acceleration and displacement pos or neg)?
If moving like a quadratic = s+ and a-
If moving down from a raised point = s- and a-
Finding speed from acceleration and time
a = Δv/Δt
is moving due north with speed 0.6 m s–1.
V only has j vector
Find the value of t when the boat is north-east of O.
V —> i = j
Parallel vectors
Have same length (magnitude) and same direction. Parallel vectors are multiples of each other e.g. i+2j-3k and 2i+4j-6k
Position vectors: AB=
OB-OA
RUVAT
r= ut + 0.5at^2
At constant velocity: s=
vt
Highest point on projectile
v =0
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find equation for time of flight?
(2Usinx)/g
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find the time to reach the greatest heigh?
(Usinx) / g
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find an equation for the range on horizontal plane?
(U^2sin2x)/g
A particle is projected from a point on a horizontal plane with an initial velocity U at an angle x above horizontal moves freely under gravity until it hits the plane at point B
Find an equation for the equation of trajectory?
Acceleration in velocity time graph
y=mx
v=mt
v=at
Speed regarding velocity
Magnitude of velocity
) the speed of the stone when it is 10.8 m above sea level, giving your answer to 2 significant figures.
Vertical: v^2=u^2+2as
Horizontal: u
Speed = magnitude of velocity = square root of v^2+u^2
Find the velocity of P at the instant before it collides with Q.
Find velocity of vertical and horizontal
- find magnitude to find speed
- use tan and velocities to find angle
- speed^-1 downwards at angle to the horizontal
Colliding particles in kinematics
Equate displacement from both equations
Suggest two refinements to the model that would make it more realistic. (Pulley)
- have the model consider air resistance
- have the model use an extensible string
Why will pushing the object make the acceleration less than pulling?
Pushing the object will increase friction since normal reaction is greater
Velocity time graph for pulley
Constant velocity
Why will someone standing the the ladder help it from slipping?
Pushing the object will increase friction since normal reaction is greater
If a particle comes to rest, then what is acceleration?
a= -9.8
Instantaneous rest
V=0
Finding maximum/minimum velocity
Differentiate v equation and set =0 to find t
Sub into original equation
If acceleration is 0
U and V is the same
Position vector
Displaced,ent + initial position vector
Constant acceleration
Use suvat
Why is the reaction perpendicular to the object/drum?
There is no friction so the reaction is perpendicular
When to use μR or F?
For limiting friction, use μR otherwise use F
What is the horizontal velocity when the ball is moving up?
The horizontal velocity stays constant
Weight
Don’t use g
Find the position vector of Q when Q is due West of P
equate the j vectors of Q and P
Show that at t=3,5m both particles are moving in the same direction
If both particles are moving in the same direction then velocity should be ratios of each other.
- Velocity if one particle = lambda velocity of other particle
Assumptions of uniform rod
uniform – mass is or acts at midpoint of plank; centre of mass is at middle of plank; weight acts at the middle of the plank, centre of gravity is at midpoint
rod - plank does not bend, remains straight, is inflexible, is rigid
How have you used the fact that the block is modelled as a particle
Masses concentrated at a point or weights act at a point
How have you used that fact that the block is modelled as a particle?
Masses concentrated at a point or weights act at a point
Brick Q is now projected with speed 0.5 down a line of greatest slope of the plane. Describe the motion.
Brick Q slides down at a a constant speed (there’s not resultant force down the plane so no acceleration)
P moves along the a Xia with displacement x=0.5t^2(t^2-2t+1).
Show that P will never move along the negative along the x axis
Complete the square to show x with never be negative
Speed from acceleration and time
V=at
The direction of motion/moving is north east
Find velocity and equate i and j vectors
Find the value of t when the object is north east of O
Find s or r and equate i and j vectors
parallel to vector I
J=0
Explain why the frictional force acting on the rod at A acts horizontally to the right
The horizontal component of T acts to the left and since the only other horizontal force is friction, it must act to the right oe
