Moments

Have you ever wondered why door handles are always on the opposite side of the door hinges? It's because when you push a door near its hinge, it's harder to close it. But when you push it at the opposite end where the door handle is, it's much easier to close. This is because the further away you are from the hinge, the more leverage you have to turn the door. These small moments can make a big difference in everyday life.

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:

Two forces acting on an object at different points

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In the first example, we saw that when two forces of equal magnitude act on a bar in opposite directions at the same point, the bar remains stationary. The moment of a force is measured in Newton-metres (Nm) and is calculated by multiplying the force in Newtons by the distance in metres from the pivot.

We can apply this concept to explain why door handles are placed on the opposite side of the door hinges, which act as the pivot. By increasing the distance between the force at the door handle and the pivot, we can increase the moment and make it easier to open or close the door. This is why wrenches have long handles, to increase the moment and make it easier to tighten bolts.

Now, let's apply this concept to a problem. If a 100kg weight is suspended 30m away from a pivot on which rests a steel bar (assuming the weight of the bar is negligible), what is the turning moment about the pivot? We can use the formula: moment = force x distance. In this case, the force is the weight of the suspended weight, which is 1000N (100kg x 9.81m/s^2). The distance is 30m. So, the moment is:

moment = 1000N x 30m = 30,000 Nm

Therefore, the turning moment about the pivot is 30,000 Nm.

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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:

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:

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.

Turning a steering wheel is an example of a couple

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The moment of a couple is calculated using this equation:

Let’s calculate the couple produced by the forces acting on this 1m long steel bar.

*Two forces acting on a steel bar and producing a couple*

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All we need to do is to apply the equation, using the values provided above:

Principles of moments

Moments can be either clockwise or anti-clockwise depending on the direction they turn. To illustrate this concept, let's consider two children playing on a seesaw. The boy sitting on the left produces an anti-clockwise moment, while the girl on the right produces a clockwise moment. If the seesaw is balanced, it means that the two moments cancel each other out, resulting in no overall turning effect. This is known as the principle of moments.

Now, let's apply this principle to a problem. In the following diagram, we have a balanced seesaw with a block on the left of the pivot. We want to calculate the weight (W) of the block using the principle of moments. We know that the total anti-clockwise moment produced by the block and the weight on the right side of the pivot is equal to the total clockwise moment produced by the weight on the left side of the pivot. Mathematically, we can express this as:

W x 1m = 2kg x 0.5m

where 1m and 0.5m are the distances from the pivot to the block and weight respectively, and 2kg is the weight on the right side of the pivot. Solving for W, we get:

W = (2kg x 0.5m) / 1m = 1kg

Therefore, the weight of the block on the left of the pivot is 1kg.

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I apologize for the mistake in my previous response. The correct calculation to find the weight (W) of the block on the left of the pivot is:

W x 1m = 2kg x 0.5m + 3kg x 0.75m

where 1m and 0.5m are the distances from the pivot to the block and weight on the right side of the pivot respectively, while 0.75m is the distance from the pivot to the weight on the left side of the pivot. Solving for W, we get:

W = (2kg x 0.5m + 3kg x 0.75m) / 1m = 3.25kg

Therefore, the weight of the block on the left of the pivot is 3.25kg.

In summary, moments are the turning effect produced by a force, and we can calculate them by multiplying 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, and 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.