Moments Flashcards
What is the equation for moment?
A moment is the product of the force and the perpendicular distance from the pivot.
Mathematically,
Moment (M) = Force (F) × Distance (d)
What are moments?
Turning effects produced by forces around a pivot.
What is a pivot?
The point around which an object can rotate or turn, it is also known as the fulcrum.
What are the two types of moments?
Clockwise and anti-clockwise
What does the direction of a moment depend on?
It depends on the direction of the force relative to the pivot.
How do anti-clockwise and clockwise moments act on an object?
The anticlockwise moment acts downward on the left, and the clockwise moment acts downwards on the right
What is a lever arm?
The lever arm is the perpendicular distance between the line of action of the force and the pivot. It directly affects magnitude.
How does the lever arm affect magnitude?
The longer the lever arm the higher the magnitude and the larger the moment
What is the unit of moment?
Nm
A force of 15 N is applied to a door handle, 12 cm from the pivot. Calculate the moment of the force.
Convert centimetres into metres then calculate 15 x 0.12 = 1.8
Question1:
A force of 40 N is applied to a spanner to turn a nut. The perpendicular distance is 30 cm. Calculate the moment of the force.
Question 2:
To open a door, a person pushes on the edge of a door with a force of 20 N. The distance between their hand and the hinges is 0.7 metres. What is the moment used to open the door?
1 = 12nm and 2 = 14nm
What is the principle of moments?
The principle of moments states that for an object to be balanced the total clockwise moment must be equal to the total anti-clockwise moment.
Total anti-clockwise moment = total clockwise moment
What is the difference when using short vs long spanners?
use a short spanner and apply a large force
or
use a long spanner and apply a small force
Using the longer spanner increases the distance from the pivot. This reduces the amount of force needed to undo the nut from the bolt.
Why is a longer lever more efficient?
The longer the lever, and the further the effort acts from the pivot, the greater the force on the load will be. It is easier to use a longer spanner when trying to turn a nut, and easiest to push furthest from the hinge when opening a door.
What does a lever consist of?
A lever consists of:
a pivot
an effort
a load
Why are moments important?
Engineers use moments extensively in designing structures, bridges, and machines. The calculation and consideration of moments ensure the safety and stability of these constructions.#
Moments have practical applications in everyday life, from door hinges to see-saws. Understanding moments helps engineers design stable structures.
How do moments relate to equilibrium?
Equilibrium is achieved when an object is balanced and does not rotate. Moments are central to understanding the equilibrium of objects under various forces. For an object in equilibrium, the sum of all moments should be zero
Why are moments important in rotational dynamics?
Moments are pivotal in rotational dynamics, helping explain how objects rotate and how energy is transferred in systems involving rotation.
Why are moments important in simple machines?
Simple machines like levers, pulleys, and gears operate based on the principles of moments. Understanding moments is fundamental in comprehending the mechanics of these machines.
What is the centre of mass?
The centre of mass of a body is the point through which a single force on the body has no turning effect.
What happens in single support equilibrium?
When an object in equilibrium is supported at one point only, the support force on the object is equal and opposite to the total downward force acting on the object.
S = W1 + W2 + W0, where w0 is weight of rule
If a beam is supported on two pillars, how is the weight of the beam distributed?
If the centre of mass is midway between the pillars, the weight is shared equally between the two pillars.
If the centre of mass is split unequally then moments should be takes where x is in contact with the beam x=wdx/D
where y is in contact with the beam y = wdy/D where D is total distance and Dx Dy is respective distance from the weight
What is a couple?
A pair of equal and opposite forces acting on a body but not along the same line. parallel to eachother
How is the moment of a couple calculated?
Moment of a couple= force x perpendicular distance between the line of action of the forces.
The total moment is the same regardless of which point it is taken from.
What happens when a body in stable equilibrium, is displaced then released? Why?
It returns to its initial position. This is because the support and weight of the object acts as its centre of mass. thus, the support and weight are equal and opposing. When the object is released, the line of action of the wight no longer passes through the point of support which returns the object to equilibrium
Why is it difficult to open a door when you push it near the hinges?
When you push a door near the hinges, the moment arm (distance from the pivot point to the point where the force is applied) is small. According to the moment formula (moment = force × distance), a smaller moment arm requires a larger force to create the same moment. Hence, it’s difficult to open the door because you need to apply more force to overcome the small moment arm.
Why do see-saws balance when children of different weights sit on opposite ends?
A see-saw balances because of moments. When a heavier child sits closer to the pivot and a lighter child sits farther away, the product of their weight and distance from the pivot (moment) on both sides remains equal. This balanced moment keeps the see-saw stable, demonstrating the principle of rotational equilibrium.
Why do engineers consider moments when designing structures like bridges?
Engineers consider moments in bridge design to ensure stability and safety. Bridges experience various forces, including the weight of the bridge itself and the loads from vehicles and pedestrians. By calculating and distributing these loads to create balanced moments, engineers ensure that the bridge structure remains stable and can withstand different forces without collapsing. Understanding moments is essential for designing structurally sound and secure bridges
