6.5 - stability

if a body in stable equilibrium is displaced then released, what does it do?

return to its equilibrium position

here

what is stable equilibrium?

when an object returns to its equilibrium position after being displaced then released

why does an object in stable equilibrium return to its equilibrium position after being displaced?

cuz the object’s centre of mass is directly below the point of support when the object is at rest

where is the point of support when an object at stable equilibrium is at rest?

what acts as the centre of mass for an object at stable equilibrium?

the object’s weight

for an object at stable equilibrium, what does the object’s weight act as?

the object’s centre of mass

which objects are usually in stable equilibrium in problems?

hanging / suspended objects

what does equilibrium position mean for an object in stable equilibrium?

when the object is at rest, i.e., not actively displaced

here

what is the support force of an object in stable equilibrium equal to when the object is in equilibrium?

support force and weight are directly equal and opposite (balanced) when the object is in equilibrium / rest

here

for an object in stable equilibrium, when are the support force and weight balanced?

when the object is at equilibrium / rest (i.e., not actively displaced)

here

for an object in stable equilibrium, why are the support force and weight balanced when the object is in equilibrium?

because the centre of mass of the object is directly below the point of support when the object is at rest

here

why does an object in stable equilibrium return to equilibrium position after being displaced?

the line of action of the weight no longer passes through the point of support, so the weight returns to equilibrium

what happens when an object in stable equilibrium is displaced?

it returns to equilibrium position

what is unstable equilibrium?

• when an object will not return to its equilibrium position after being displaced

• when a system is balanced, but any small displacement will cause it to be unbalanced

what is the difference between stable and unstable equilibrium?

an object in stable equilibrium will return to equilibrium position after being displaced, then released. an object in unstable equilibrium will not

what is an example of an object in unstable equilbrium?

here

a plank on a ball, because if the system is displaced slightly from equilibrium then the plank will roll off the ball

why doesn’t a plank on a ball, in unstable equilibrium, return to equilibrium position after being displaced?

• when displaced, the plank’s centre of mass is no longer directly above the ball

• therefore the forces in the system are not balanced as the plank’s weight is no longer equal and opposite to the support force from the ball

• as a turning effect occurs when a force acts through any point but the centre of mass, the weight therefore acts to rotate the plank further from the equilibrium position

how can an object in unstable equilibrium be returned to equilibrium after displacement?

it must be done manually, as the system will not return to equilibrium by itself

for a plank on a ball at unstable equilibrium, which forces are balanced when the system is in equilibrium?

the weight of the plank and the support force from the ball

for a plank on a ball in unstable equilibrium, when is the system in equilibrium?

when the plank’s centre of mass is directly above the ball

for a plank on a ball in unstable equilibrium, why is the system in equilibrium when the plank’s centre of mass is directly above the ball?

because at this point, the weight of the plank acts downwards on the ball. the plank’s weight is equal and opposite to the support force from the ball, therefore the forces in the system are balanced and the system is at equilibrium

where is the centre of mass on a plank on a ball, in unstable equilibrium, when the system is in equilibrium?

here

centre of mass of the plank is directly above the point of support from the ball

where is the support force on a plank on a ball, in unstable equilibrium, when the system is in equilibrium?

directly below the centre of the mass of the plank, where the plank’s weight acts

forces for stable equilibrium at equilibrium here

forces for stable equilibrium after displacement here

forces for unstable equilibrium at equilibrium here

forces for unstable equilibrium after displacement here

are short or tall objects easier to knock over?

tall

why are tall objects easier to knock over? HERE

their centre of mass is high, and the lower a centre of mass is of an object the more stable the object is STILL ASK WHY

what is tilting?

when an object at rest on a surface is acted on by a force that raises it up on one side

here

for which kind of objects can undergo tilting

objects at rest on a surface

what does an object tilt about?

a pivot

for an object being pushed to the right, what is the clockwise moment?

here

the force acting on the object

here

for an object being pushed to the right, what is the anticlockwise moment?

here

the object’s weight

for an object being pushed to the left, what is the clockwise moment?

here

the object’s weight

for an object being pushed to the left, what is the anticlockwise moment?

here

the force applied to the object

label this force diagram for a tilting object

here

here

what is the entire support force from acting on a tilting object?

from the floor

what is the line of action?

a horizontal line from where a force acting on a tilting object

here

for a tilting object, what is the moment from the tilting force?

here

moment from tilting force = tilting force x vertical distance from pivot to line of action

for a tilting object, where is the moment from the weight?

here

moment from weight = object weight x base / 2

for the moment of the weight of a tilting object, why is the distance base / 2?

here

because the centre of mass is in the centre of a uniform object, the distance from the centre (where the weight acts) to the pivot is half the length of the base

what is required for an object to tilt?

• moment from the tilting force > moment from the object’s weight

• i.e. Fd > WB / 2

when doesn’t an object tilt?

• when the moment from the object’s weight > moment of the tilting force

• WB / 2 > Fd

Fd > WB / 2 - does the object tilt at this point?

yes

why does an object tilt when Fd > WB / 2 ?

because the moment from the tilting force is larger than the counteracting moment from the weight

WB / 2 > Fd- does the object tilt at this point?

no

why doesn’t an object tilt when WB / 2 > Fd ?

because the moment from the weight is larger than the counteracting moment from the tilting force, therefore the tilting force is of insufficient magnitude to tilt the object

what is the line of action of the weight?

a vertical line through an object’s centre of mass

when does an object topple?

when its tilted far enough for the line of action of the object’s weight passes the pivot

here

when won’t an object topple?

• if its tilted, but not enough for the weight’s line of action to passes the pivot

• when the weight’s line of action passes through the pivot

• when the weight’s line of action passes the pivot, but a secondary object prevents our tilting object from toppling

what happens when the weight’s line of action of a tilting object passes the pivot?

here

the object will topple

what happens when the weight’s line of action of a tilting object passes through the pivot?

that is the maximum point an object can be tilted without toppling

what is the maximum point an object can be tilted without toppling?

when the weight’s line of action passes through the pivot

here

why is the maximum point an object can be tilted before toppling the point at which the weight’s line of action passes through the pivot?

• the object’s weight is balanced with the support force from the surface ASK !!!

• the weight’s line of action has not passed the pivot yet, therefore is still in stable equilibrium

what is the difference between the weight’s line of action passing the pivot, and passing through the pivot?

here

which object is in stable equilibrium - a tilting or toppling object?

tilting object

why is a tilting object in stable equilibrium?

because it will return to equilibrium position if the tilting force stops being applied

which object is in unstable equilibrium - a tilting or toppling object?

toppling object

why is a toppling object in unstable equilibrium?

because it will not return to equilibrium position if the tilting force stops being applied

what two things can cause an object to topple?

• when a tilting force applied to an object on a flat surface causes the object’s weight’s line of action to pass the pivot

• when a tall object (usually a vehicle) is on a sloped surface and object’s weight’s line of action

when will a tall object on a sloped surface topple?

when the weight’s line of action lies outside the perimeters of the object

here

when won’t a tall object on a sloped surface topple?

when the weight’s line of action lies inside the perimeters of the object

here

what does it mean for the weight’s line of action to be within the perimeters (or wheelbase) of a tall object on a sloped surface?

here

what does it mean for the weight’s line of action to be outside the perimeters (or wheelbase) of a tall object on a sloped surface?

here

what are the forces at play for a tall object on a sloped surface?

here

• weight

• a support force on each wheel base

• friction

in which direction does the weight of an object act?

straight down, despite the object’s tilt

how do you find the equilibrium of a tall object on a sloped surface?

resolve the forces parallel and perpendicular to the slope

here

for a tall object on a slope, how do you resolve the forces parallel and perpendicular to the slope?

• find the horizontal and vertical components of the weight by IDK

HERE maybe ask zanas?

for a tall vehicle on a sloped surface, which wheel base has the greater support force?

here

for a tall vehicle on a sloped surface, why does this wheel base have the greater support force?

here

because it is higher up the slope than the other WHICH MEANS ITS ACCOUNT FOR MORE FORCE?

why does toppling in regards to an object on a slope only really apply to tall objects?

because tall objects have a higher centre of mass, and the lower the centre of mass the more stable an object is. tall objects are less stable for this reason, therefore more likely to topple on a sloped surface

tilting diagram here flat surface

toppling diagram here flat surface

toppling diagram here sloped surface

what does the object’s weight’s line of action pass through?

the object’s centre of mass