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Chapter 6 Forces in equilibrium (6.3 (Turning effects (Moment= force x the…
Chapter 6
Forces in equilibrium
6.1
Representing a vector
Vector- magnitude and direction e.g
displacement, velocity, force and acceleration
Scalar- magnitude only
Addition of vectors
Scale diagram
Join the vectors tail to head at the correct angle
e.g
O to A=OA and O to B=OB
The distance between the tail of the 1st and the head of the last is the
resultant
Perpendicular vectors
Join two perpendicular vectors tail to head and calculate hypotenuse, using
pythagoras
-This is the resultant
Use trig to calculate angle between resultant and one side
Resolving vectors
Working out the horizontal and vertical components when given magnitude and direction of a vector
Fx= Fcosθ
Fy= Fsinθ
6.3
Turning effects
Moment= force x the perpendicular distance from the line of action of the force to the point
Unit of moments = Nm
Principle of moments
Sum of clockwise moments= sum of anticlockwise moments for an object in equilibrium
Centre of mass
Point through with a single force on the body has no turning effect
Calculating weight of a ruler
Locate CofM
Balance ruler off centre using a known weight
Weight creates anticlockwise moment (W1d1)
Weight of ruler creates a clockwise moment (W2d2)
Calculate weight= (W1d1)/d2
6.4
Support forces
Single
Object in equilibrium- support force is equal and opposite to sum of downwards forces
S=W1+W2+W0
Two
Place pivot at one support (Sy) force and calculate other support force by using W0dy (Weight) = Sxd
Place pivot at other support (Sx) force and calculate Sy by W0dx (weight)= Syd
Always draw a diagram with each distance on it
Couples
Pair of equal and opposite forces acting on a body but not along the same line
Proof
Moment due to F=Fx clockwise
Moment due to F= F(d-x)= Fd-Fx
Total momentum= Fx+Fd-Fx= Fd
6.6
Free body force diagrams
- show forces acting on an object
Triangle of forces
If in equilibrium three forces=closed triangle (F1+F2+F3=0)
Equilibrium conditions
At rest or moving with constant velocity
Forces= zero resultant
Anti-clockwise moments= Clockwise moments
6.2
Equilibrium of a point object
Equilibrium- when an object is at rest or moving at a constant speed- all forces balanced
If three forces act on an object the resultant is zero if the resultant of two of the forces is equal and opposite to the third
To calculate combined effect, resolve each force along the same parallel and perpendicular lines and balance the components along each line
Testing 3 forces in equilibrium
Three forces F1, F2 and F3 acting on P are in equilibrium, test to check that two forces add to the third by measuring the angle between each upper string and the lower string.
Construct a scale diagram using the parallelogram rule
6.5
Equilibrium
Stable
If a body is in stable equilibrium, if it's displaced, it will return to its equilibrium position
Centre of mass is directly below the point of support
Centre of mass raises as it is tilted
Unstable
If displaced from equilibrium and then released it won't return to equilibrium
Centre of mass above point of support
Centre of mass lowers as it's tilted
Tilting and toppling
Tilting
When an object at rest is acted on by a force that raises it up on one side
e.g. Bookcase
Clockwise moment= Fd
Anticlockwise moment= Weightx 1/2 Base
For tilting to occur Fd> Wb/2
Toppling
Tilted object will topple if Centre of mass is beyond the pivot
Slopes
Topple when centre of mass over pivot
Have to resolve forces parallel and perpendicular to the slope
