Unit 4- Turning Effects Of Forces Flashcards
(26 cards)
The turning effect of a force is called its _____________.
Moment
What is the definition of the moment of a force?
The moment of a force about a pivot is the product of the force and the perpendicular distance from teh pivot to the line of action of the force.
What is the formula of moment?
Moment = F x d
The line of action is drawn using a __________ and can be ___________. The dotted line is the ______________________.
The line of action is drawn using a dashed line and can be extended to any length. The dotted line is the perpendicular distance (which is also the shortest distance) between the line of action and the point O about which the moment is calculated.
What is the SI unit of moment?
Nm
Even though Nm is the same as ___________, _________ is a ______________________.
Even though Nm is the same as the joule when expressed into S.I. Base units, moment is a different physical quantity from work or energy. Furthermore, moment is a vector quantity while work and energy are scalars.
What should you take note for your answer when expressing moment?
Make sure to have the magnitude, the units (Nm) and the direction (clockwise moment/direction or anti clockwise moment/ direction)
What is the principle of moment?
The principle of moment states that for a body in equilibrium, the algebraic sum of the moments of all the external forces acting on the body about any axis is equal to zero.
The principle of moments states that for a body in equilibrium, the algebraic sum of the moments of all the external forces acting on the body about any axis is equal to zero.
What does algebraic sum mean?
Algebraic sum refers to summing with the signs of the quantities taken into account. We usually divide moments into those that cause the object to turn clockwise and those that cause the object to turn anti clockwise. If we assign a positive sign to the former, than the latter will automatically be negative.
For an object in equilibrium, about any axis (or pivot),
Sum of clockwise moments = sum of anti-clockwise moments
What does it imply for an object in equilibrium, about any axis (or pivot)?
Sum of clockwise moments = sum of anti-clockwise moments
What is the definition of centre of gravity?
The centre of gravity of an object is the point at which the whole weight of the object appears to act.
Can the centre of gravity be at the same position as the centre of mass?
Yes. In a uniform gravitational field (which is the case in our daily lives), the centre of gravity is at the same position as the centre of mass.
Is the centre of gravity at the midpoint or the centre of the objects?
Yes, for regular objects, the centre of gravity is at the midpoint or the centre of the objects.
The centre of gravity does not need to be located on the object. True or false and why?
Note that the centre of gravity of an object need not be located on the object. For example, the centre gravity of an L-shaped structure is located outside it.
Imagine this:
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|__ __ __
The centre of gravity for the horizontal block is at the centre the middle (second block) and the centre of gravity for the vertical block is at the centre (the second block) so if you draw a dotted line to connect the both points, you will know that the CG will be somewhere lying on the dotted line.
Another example is a doughnut. The CG can be in the hole (which is located outside of the object)
What are the steps to determining CG of an irregularly shaped lamina?
For an irregularly shaped object like a lamina (a thin sheet), we can determine its CG using the plum line (pendulum) method.
Step 1: Suspend the lamina at one end using a pin on a retort stand and hang a plum line from the pin. Use a ruler and draw a vertical line as shown by the plum line.
Step 2: hang the lamina from another end and place the plum line in front of the lamina. Use a ruler and draw a new vertical line as shown by the plum line.
Step 3: The intersection of the two lines will be the CG of the object. We can check by repeating step 2 using a third point of suspension.
Precautions:
- The holes must be small so that not too much of the lamina is removed
- the lamina should be free to swing about its point of suspension.
What should you always have in your working when trying to equate sum of clockwise moments = sum of anti-clockwise moments?
Taking moments about pivot O (for e.g.)
Sum of clockwise moments = sum of anti-clockwise moments
What is the definition of stability?
The stability of an object is a measure of its ability to return to its original position after it is slightly displaced.
How do you increase the stability of an object?
To increase the stability of an object,
- its centre of gravity should be kept as low as possible (i.e. more mass packed at its bottom)
- its base area should be kept as wide as possible
Describe the scenario when the object will not topple with reference to the diagram below
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- - \
- - \
\. \
\. \
\. \
\. C /
\ /
\ /
\A
/
When the line of action through the centre of gravity of the object lies within its base, there is a clockwise moment about point A due to the weight. The object will not topple.
Describe the scenario when the object will topple with reference to the diagram below
- - \
- - \
. \
. \
. C \
. /
\ /
\ /
\A
/
However, when the line of action through the centre of gravity of the object lies outside its base, there is an anti clockwise moment about point A due to the weight (line of action). The object will topple.
As the angle increases (the angle on the right that is between the horizontal and the hypotenuse), the anti clockwise moment about point A increases.
What are the keywords that you should have in your question when evaluating on whether an object will topple over.
- considering _____ as the pivot
- the object have their lines of cation of their weights passing to the left/right of the pivot
- hence, this results in clockwise/anti-clockwise moments about the pivots
- topple or do not topple the object
What are the two conditions needed for an object to be in equilibrium?
An object is in equilibrium if it is in
(A)
Translational equilibrium i.e. the resultant force acting on it is zero.
(B)
Rotational equilibrium i.e. the resultant moment acting on it is zero.
The equilibrium of an object can be described as….
Stable, unstable or neutral
Explain stable equilibrium.
Let’s say the object is a cone.
if the cone is slightly tilted,
- its centre of gravity rises before returning to its original height;
- the line of action through its weight W still lies within its base;
- the moment of its weight about the contact point C causes the cone to return to its original position
