Why are door handles always on the opposite side of the door hinges? If you try pushing a door near its hinge and then at the opposite end, you’ll notice a big difference. While near the hinge, it’s hard to close the door; at the door handle, it’s rather easy. The reason for this is that further away from the hinge, you get a much larger turning effect.
What causes a turning effect?
If an object is stationary or in static equilibrium, all the forces acting on that object cancel each other out. But if they cancel each other out, and there is no overall force, does that mean the object is in static equilibrium?
Take a look at the following diagram:
Fig. 1 - Two forces acting on an object at different points
In the first example, both forces are of equal magnitude and act at the same point but in the opposite direction, which causes the bar to remain stationary.
In the second example, because the forces do not act at the same point, they create a turning effect known as torque. In this case, the bar will start to rotate anti-clockwise and is, therefore, not in static equilibrium.
Moments
The magnitude of the turning effect produced by a force is called the moment of the force. This occurs when forces cause an object to rotate around some pivot.
The moment of a force is calculated as follows:
Moment = (Force) · (Perpendicular Distance from the Force to Pivot)
Moments are measured in Newton-metres, written Nm. The force is in Newtons and the distance in metres.
What we have explored so far explains why door handles are placed on the other side of the door hinges, which act as the pivot. Maximising the distance between the force we apply at the door handle and the pivot results in a greater moment. This makes it easier to pull a door open or to push it shut. The same principle applies to wrenches that have long handles to increase the moment’s magnitude, thus making it easier to tighten bolts.
A 100kg weight is suspended 30m away from the pivot, on which rests a steel bar. Assuming the weight of the bar is negligible, what is the turning moment about the pivot?
Fig. 2 - A mass of 100kg creating a moment
First, we need to determine the force caused by the mass. This is its weight or its mass multiplied by the constant of gravitational acceleration. This gives us:
\(F = mass \cdot g = 100 \cdot 9.81 = 981 N\)
Now we have the force applied to the bar, while the perpendicular distance from the force to the pivot was specified above. All we then need to do is use the moment of a force equation as follows:
Moment = (Force) · (Perpendicular Distance from the Force to Pivot)
Couples
A unique case of moments is when two parallel forces that are equal in magnitude but opposite in direction and also separated by a distance d cause an object to rotate. This is known as a couple.
A couple does not have a resultant force; it only produces a turning effect.
An example of this is your hands producing a couple on the steering wheel of a car in order to turn the wheel.
Fig. 3 - Turning a steering wheel is an example of a couple
The moment of a couple is calculated using this equation:
Couple = (Magnitude of one Force) · (Perpendicular Distance between the Two Forces)
Let’s calculate the couple produced by the forces acting on this 1m long steel bar.
Fig. 4 - Two forces acting on a steel bar and producing a couple
All we need to do is to apply the equation, using the values provided above:
\(Couple = F \cdot d = 15 \cdot 1 = 15 \space Nm\)
Principles of moments
Moments can be clockwise or anti-clockwise.
Imagine two children playing on a seesaw, with a boy sitting on the left and a girl on the right.
The weight of the boy on the left produces an anti-clockwise moment, while the weight of the girl on the right produces a moment that turns the seesaw clockwise.
What would it mean for the two moments produced by the children if the seesaw was balanced? For an object to be in equilibrium – for the seesaw to be balanced – there must be no overall turning effect at any point. The clockwise and anti-clockwise moments, therefore, must cancel each other out.
This is summed up by the principle of moments. An object is in static equilibrium when:
Sum of the clockwise moments = Sum of the anti-clockwise moments
The seesaw in the following diagram is balanced. Calculate W, the weight of the block on the left of the pivot, using the principle of moments.
Fig. 5 - Different forces acting on a seesaw
To calculate W, we apply the equation, adding the values from the diagram:
Sum of the anti-clockwise moments = Sum of the clockwise moments
\(W \cdot 1.5 = (300 \cdot 1) + (550 \cdot 1.5)\)
\(W \cdot 1.5 = 300 + 825 = 1125 Nm\)
\(W = 750 N\)
Moments - key takeaways
- A moment is the turning effect produced by a force.
- To calculate the moment, we multiply the force and the perpendicular distance between the force and the pivot.
- A couple is a turning effect produced by two equal forces acting in opposite directions.
- According to the principle of moments, for an object in static equilibrium, the sum of the clockwise moments is equal to the sum of the anti-clockwise moments at any given point.
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