Forces in equilibrium (topic 6) Flashcards
Vector (definition)
Physical quantity that has both direction and magnitude
Scalar (definition)
Physical quantity that has magnitude and is not directional
How is displacement represented on a scale diagram?
An arrow from the first point to the second point; where the length of the arrow is in proportion to the shortest distance between the points
How is velocity represented on a diagram?
Arrow in the direction of motion; where the length is proportional to the speed of the object
How are force and acceleration represented on a diagram?
Arrow in the appropriate direction and in proportion to the magnitude of the object. Acceleration is a double-headed arrow.
Rule for adding two vectors (example)
OB = OA + OB
How to find the result of two perpendicular vectors
The resultant vector forms the hypotenuse of a right-angle triangle, so answer can be found with Pythagoras and tan theta = o/a
How to find the result of two vectors acting along the same line
- The sum if both act in the same direction
- The difference if they act in opposite directions
Equilibrium (definition)
An object is not accelerating in any direction as all forces acting on it are balanced
How to see if an object is in equilibrium if its forces are acting at different angles
Resolve to get all forces on horizontal/vertical planes
Method for testing the how equilibrium occurs with three forces acting on an object
A string is hung between two pulleys on clamp stands, with weightds either side to create tension. A second string with a weight attached is tied in the middle of the hanging string. Where the two strings meet now shows the angles between the three tensions acting at that point.
What is parallelogram rule?
For an object in equilibrium with three forces acting in different directions, the third has magnitude equal to the diagonal length of a parallelogram formed from the other two forces.
Moment equation
moment = Fd
where d is PERPENDICULAR distance from line of action to pivot
Unit of moments
Newtonmetres
Principle of moments
If a body is in equilibrium, then clockwise moments = anticlockwise moments
Body (definition)
Object not modelled as a particle
Centre of mass (definition)
The point in a body through which a single force on the body has no turning effect
Test to find centre of mass (3)
Hang object from different points behind a mass on a plumb line. Draw in pencil along the string. Where lines cross is centre of mass
Calculating weight of a metre rule using balance (3)
With a weight tied to one side balance object on a sharp edge. Measure distance from pivot to centre and distance from pivot to weight on the other side. Use principle of moments with the known moment of the weight to find force of ruler’s weight.
Rule for an object with one support
Total downwards force = support force
Will taking moments from a different point give different answers?
No. Moments can be taken from any point.
Equation for support force in two-support problems
S = Wd / D
Wd= moment of weight on support
D = distance between supports
If the centre of mass of a beam is equal distances from supports at either end, then…
Weight of the beam is shared equally so support force = W/2
How to eliminate an unknown turning effect in a moments question
Take all moments from the point at which the unknown moment acts, so d = 0; Fd = 0.
Couple (definition)
Pair of equal and opposite forces acting on a body, but not along the same line
Stable equilibrium (definition)
A body that will returns to its equilibrium position if displaced (e.g. hanging basket)
When does stable equilibrium occur?
Centre of mass of the object is directly below the point of support when the object is at rest
Why does stable equilibrium occur?
The support force is above the centre of mass When the object is moved so centre of mass is not in line with support, greater vertical component returns object to equilibrium.
Unstable equilibrium ( definition)
A body that will not return to equilibrium if displaced and released.
Why does unstable equilibrium occur?
The centre of mass is above the support force, so if the body is displaced, the vertical component increase will make the body move further away from the equilibrium position.
Tilting (definition)
An object at rest on a surface is acted on by a force that raises it on one side only. (e.g. bookshelf tilting along one edge)
What must be true for tilting to occur?
Fd > Wb/2
The clockwise moment from the force F causing tilting must be greater than the anticlockwise moment of weight W (b/2 is the horizontal distance from W to pivot)
Toppling (definition)
An object is tilted so that its centre of mass is is beyond the pivot, so it falls over.
How to make an object more stable?
- increase width of base
- change distribution of mass so that centre of mass is lower
Why is it easier for an object to topple when on a slope?
The horizontal base of the object has decreased (as it is diagonal). Hence it is easier for the centre of mass to go beyond the pivot.
How to work with forces in different directions with a body on a slope?
Resolve weight and use adjusted vertical and horizontal components
What does a free body diagram show?
Only the forces acting on an object (not the forces it exerts on other objects)
Triangle rule
If three forces are in equilibrium, then vectors of F1, F2 and F3 should have sum of 0, as any two of the forces have a resultant equal and opposite to the third force.
What must be true for three forces to be in equilibrium, and why?
Their lines of action must all intersect at the same point otherwise they will produce a turning force.
Two requirements for a body to be in equilibrium
1) resultant force must be 0
2) moments of forces about the same point must balance (principle of moments)
