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# Force Energy

In simple terms, a force is nothing but a push or a pull. In scientific terms, a force is a movement produced by an object resulting from its interaction with another object or a field, such as an electric or gravitational field.

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Fig. 1 - A force can be a push or a pull on an object

Of course, a force is not just used to push or pull objects. We can, in fact, perform three types of functions with a force.

• Changing the shape of an object: if, for instance, you bend, stretch, or compress an object, you change its shape.
• Changing the speed of an object: if, while riding a bicycle, you increase the peddling or someone pushes you from behind, the speed of the bicycle increases. Exerting a stronger force thus causes the bicycle to accelerate.
• Changing the direction in which an object is moving: in a cricket match, when a batsman hits the ball, the force exerted by the bat causes the direction of the ball to change. Here, a force is used to change the direction of an already moving object.

## What is energy?

Energy is the ability to do work, while work is equal to the force being applied to move an object a certain distance in the direction determined by that force. So, energy is how much of the work is applied to the object by that force. The unique thing about energy is that it can be transformed.

### Conservation of energy

The conservation of energy states that energy is only transferred from one state to another so that the total energy of a closed system is conserved.

For example, when an object falls, its potential energy is converted to kinetic energy, but the total sum of both energies (the mechanical energy of the system) is the same at every instant during the fall.

Fig. 2 - Conversion from kinetic energy to potential energy in the case of a rollercoaster

## What is a moment?

The turning effect or a force produced around a pivot is called the moment of a force or torque. Examples of pivots are the hinges of an opening door or a nut turned by a spanner. Loosening a tight nut and a door opening around a fixed hinge both involve a moment.

Fig. 3 - Force at a distance from a fixed pivot produces a moment

While this is a rotatory motion around a fixed pivot, there are also other types of turning effects.

## What are the types of moments of a force?

Apart from the rotatory aspect, we also need to note the direction in which the object moves. For instance, in the case of an analogue clock, all its hands rotate in the same direction around a fixed pivot located in its centre. The direction, in this case, is a clockwise one.

### Clockwise moment

When a moment or a turning effect of a force about a point produces a clockwise movement, that moment is clockwise. In calculations, we take a clockwise moment as negative.

### Anticlockwise moment

Similarly, when a moment or a turning effect of a force about a point produces an anticlockwise movement, that moment is anticlockwise. In calculations, we take an anticlockwise moment as positive.

Fig. 4 - Clockwise and counter-clockwise

## How do we calculate a moment of a force?

The turning effect of a force, also known as torque, can be calculated by the formula:

$T = r \cdot F \sin(\theta)$

1. T = torque.
2. r = distance from the applied force.
3. F = applied force.
4. 𝜭 = Angle between F and the lever arm.

Fig. 5 - Moments applied to a perpendicular level (F1) and one that operates at an angle (F2)

In this diagram, two forces are acting: F1 and F2. If we want to find the moment of force F1 around pivot point 2 (where force F2 acts), this can be calculated by multiplying F1 by the distance from point 1 to point 2:

$\text{Moment of force} = F_1 \cdot D$

However, to calculate the moment of force F2 around pivot point 1 (where force F1 acts), we have to improvise a little. Have a look at Figure 6 below.

Fig. 6 - Resolution of the F2 vector to calculate the moment of force F2

F2 is not perpendicular to the rod. We, therefore, need to find the component of the force F2 that is perpendicular to the line of action of this force.

In this case, the formula becomes F2 sin𝜭 (where 𝜭 is the angle between F2 and the horizontal). So, the formula to calculate the torque around the force F2 is:

$\text{Moment of force} = F_2 \cdot \sin(\theta) \cdot D$

### The principle of moment

The principle of moment states that when a body is balanced around a pivotal point, the sum of the clockwise moment equals the sum of the anticlockwise moment. We say that the object is in equilibrium and will not move unless either one of the forces changes or the distance from the pivot of either of the forces changes. See the illustration below:

Fig. 7 - Examples of equilibrium

Calculate the distance from the pivot of the force 250N that must be applied for the seesaw to be balanced if the force on the other end of the seesaw is 750N with a distance of 2.4m from the pivot.

The sum of clockwise moments = the sum of anticlockwise moments.

$F_1 \cdot d_1 = F_2 \cdot d_2$

$750 \cdot d_1 = 250 \cdot 2.4$

$d_1 = 7.2 \space m$

Hence, the distance of the force 250 N has to be 7.2 m from the pivot for the seesaw to be balanced.

## What is a couple?

In physics, a moment of a couple is two equal parallel forces, which are in opposite directions from each other and at the same distance from the pivot point, acting on an object and producing a turning effect. An example would be a driver turning the steering wheel of their car with both hands.

The defining feature of a couple is that, although there is a turning effect, the resultant force adds up to zero. Hence, there is no translational but only rotational movement.

Fig. 8 - A couple is produced if two equal forces are acting in opposite directions at the same distance from the pivot point

To calculate the moment of a couple, we need to multiply either one of the forces by the distance between them. In the case of our example above, the calculation is:

$\text{Moment of a couple} = F \cdot S$

## What is the unit of moment of a force?

As the unit of a force is Newton and the unit of the distance metres, the unit of moment becomes Newton per metre (Nm). A torque, therefore, is a vector quantity as it has a magnitude and a direction.

The moment of a force of 10 N about a point is 3 Nm. Calculate the pivot distance from the line of action of the force.

$\text{Moment of force} = \text{Force} \cdot \text{Distance}$

$$3 \space Nm = 10 \cdot r$$

$$r = 0.3 \space m$$

## Force Energy - Key takeaways

• A force is a push or a pull on an object.
• A force can change the shape of an object along with its speed and the direction in which it is moving.
• Conservation of energy means that energy is only transferred from one state to another so that the total energy of a closed system is conserved.
• The turning effect or a force produced around a pivot is the moment of a force or torque.
• A moment can be in a clockwise or anticlockwise direction.
• The principle of moment states that when a body is balanced around a pivotal point, the sum of clockwise moment equals the sum of anticlockwise moment.
• A moment of a couple is two equal parallel forces, which are in opposite directions from each other and at the same distance from the pivot point, acting on an object and producing a turning effect.

#### Flashcards in Force Energy 193

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How do you calculate the moment of a force?

The moment of a force can be calculated by the formula:

T = rfsin(𝜭)

Are moment and moment of a force the same?

Although moment and moment of a force have the same units, mechanically, they are not the same. A moment is a static force, which causes a non-rotational, bending movement under an applied force. A moment of a force, also called torque, is considered to rotate a body around a fixed pivot.

What is a moment of a force called?

A moment of a force is also called a torque.

What is the law of moment?

The law of moment states that, if a body is in equilibrium, meaning that it is at rest and non-rotational, the sum of clockwise moments equals the sum of anticlockwise moments.

Are moment and energy the same?

Yes. Energy has a unit of Joule, which is equal to the force of 1 Newton acting on a body through a distance of 1 metre (Nm). This unit is the same as the moment.

## Test your knowledge with multiple choice flashcards

In a couple, does the distance of the pivot from both forces have to be the same?

A force acting on a body can:

In a couple, does the resultant force add up to zero?

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