Y2, C4 - Moments Flashcards
Formula for the moment of force
Moment of force = force x perpendicular distance
What is the unit for a moment
Newton Metre
Nm
What is a lamina
A 2d object whose thickness can be ignored
What is the resultant moment if a beam has a moment of 4 Nm clockwise and 8 Nm anticlockwise
8 - 4 = 4
4 Nm anticlockwise
What does it mean if the clockwise moments = anticlockwise moments
The rigid body is in equilibrium
Resultant moment about ANY point is 0
What does it mean if the resultant force in any direction is 0
The rigid body is in equilibrium
Forces up = forces down
What point of an equilibrium rigid body can you take moments about
ANY point
Where does the weight act on a uniform body
The centre
What forces do supports create on rigid bodies
Reactant forces (normal contact)
What cancels out if you take moments about a support
The reaction force of the support
How can you find 2 unknown reactant forces if you cannot cancel either one out
Take moments about two different points
Solve simultaneous equations to find the two reactant forces
Can you do up = down without worrying about distances when a rigid body is in equilibrium
YES
A uniform beam AB of mass 40kg and length 5m rests horizontally on supports C and D where AC=DB=1m. When a man of 80kg stands on the beam at E, the magnitude of the reaction at D is twice the magnitude of the reaction at C. How would you find the distance AE
1) Up = down to find the resultant force R (Rc = R, Rd = 2R)
R + 2R = 40g + 80g, R = 40g
2) Take moments about A to find the distance AE
R + 8R = 100g + 80g * d
d = 3.25m
OR
Find moments about C and D and solve simultaneously
If a hanging beam has more weight on the left of it’s centre, will the tension on the left string or right string be more
The left string as it is ‘carrying’ more weight
What does m(A) mean
Moments taken about the point A
What does it mean if a rod is non-uniform
It’s weight does not act at the centre
If you know the magnitude of the forces acting downwards and all the forces acting upwards are in terms of R, how do you find R
Upwards forces = downwards forces
Rearrange to solve for R
What does it mean if rigid body is on the point of tilting about a pivot
The reaction at any other support (or tension in any other wire / string) is zero
A rod has pivots A and B and is at the point of tilting about B, what is the reactant force at A
0 Nm
CHAPTER 7 (PART 2)
What is the alternative way of saying moment = force x perpendicular distance
moment = perpendicular force x distance
What does the sum of the moments mean
The resultant moment
At a hinge / pivot point (P), what moment do all forces acting directly from it create (clockwise / anticlockwise)
NOTHING (perpendicular distance of zero)
If you pull on a point, there is NO moment as it is not spinning
If you pull up, left, right, down on a point, what is the moment of each force
ZERO for all (perpendicular distance of zero)
If a force is pointing directly at or away from the pivot (P), what is the magnitude of the moment
ZERO
(perpendicular distance of 0)
What should you do if you cannot see a perpendicular distance of the lines for moments drawn
Extend the lines forwards or backwards until they create a perpendicular
What is special about the distance between a pivot and a perpendicular moment force
It is the shortest distance
At an angled rod / beam, what forces act at the hinge
Normal reaction
Friction
What steps should you always take with moments questions (4)
1) Resolve vertically
2) Resolve horizontally
3) Take moments about A (usually the floor)
4) Remember to take perpendicular distances
What direction does the normal reaction from a peg act when a rod lies on top of it
Perpendicular to the rod
You know that tan(α) = 3/4. How would you find the value of β if tan(β - α) = 1/4
Double angle formula:
(tanβ-tanα) / (1 + tanβtanα) = 1/4
4tanβ - 4tanα = 1 + tanβtanα
tanβ = 16/3
β = 50.9
What does it mean if you need to find the least value of μ
The system is in limiting equilibrium
Where do you usually take moments with a ladder question
From the bottom
What are the 4 steps for a ladder problems
1) Resolve vertically
2) Resolve horizontally
3) Take moments about A (usually the floor)
4) Remember to take perpendicular distances
What direction does the resultant force from the wall act with ladder
Perpendicular to the wall where the ladder touches
How would you find the range of possible values for an additional frictional force (P) at the base for which a ladder remains in equilibrium
Set P(min) for when the ladder slips down the wall
–> P acts towards the wall and so does μR
–> P + μR = N
Set P(max) for when the ladder slips up the wall
–> P acts towards the wall but μR acts away from the wall
–> P = N + μR
Where N is the normal reaction of the ladder from the wall
When finding the range of possible values for an additional frictional force (P) at the base to keep the ladder in equilibrium, do we include P(min) and P(max)
Yes
ans = P(min) <= P <= P(max)
How does a builder standing at the bottom of a ladder stop the ladder from slipping (3 marks)
Reaction force from the floor (R) would increase, therefore so would friction (μR) which stops it slipping.
If m(A), the extra force from the builder won’t affect the value of the reaction force against the wall (N)
What do R and μR become if a static body is hinged to the floor rather than stuck there
R becomes Y (vertical component)
μR becomes X (horizontal component)
Knowing X and Y at a hinge, how do you find the reaction force R
Trigonometry of the triangle (R is the hypotenuse)
When finding the magnitude and direction of the vertical component of the force acting on the road at a hinge, what could the direction be
Up or down
Do ropes attaching beams to walls have a reaction force from the wall
NO
If a rope was not modelled as being light, how would this affect the tension (2 marks)
The tension would not be equal throughout
It would increase towards the top of the rope because it has to support it’s own weight too
What should you do if a question doesn’t say a rod is touching the floor
Don’t add a normal reaction or frictional force at the base
What does it mean if a rod is about to slip
The friction has reached it’s maximum value
