what is the gravitational force?

The gravitational force is an attractive force that a mass exerts on another mass when the former is placed in the latter’s gravitational field.

 

Fig 1

In fig 1 above we have two masses m₁ and m₂ that are situated at a distance r apart. As you know these two masses will create gravitational fields around themselves such that mass M₁ will exert a gravitational force F₂ on mass M₂ while the mass M₂ will exert a gravitational force F₁ on mass M₁. That is each mass will exert a gravitational force on the other mass. 

And from the third law of motion we know that “For every action there is an equal and opposite reaction.

Hence the gravitational force F₂ will be equal to the gravitational force F₁ .

F₁  = F₂

If the two forces are equal then they have the same magnitude and as a result

|F₁ | = |F₂ | = F

We can thus replace F₁ and  F₂  by F as shown in fig 2 below.

Fig 2

Law of gravitation

In order to calculate the magnitude of the force that each mass will exert on the other the law of gravitation must be used.

It merely states that the gravitational force that the two objects will exert on each other is directly proportional to the product of the two masses and inversely proportional to the square of their distance of separation.

Simply written in an equation it will be as shown below:

Removing the proportionality sign you will obtain the equation below:

Where G is the universal gravitational constant

G = 6.67 x 10^-11N m² kg^-2

Example 1

The moon and the earth are separated by a distance of 3.8x 108 m. The mass of the moon is 6.4 x 1022 kg while that of the earth is 6.0x1024 kg. Calculate the gravitational force between the moon.

Newton’s first law of motion

In order for an object to accelerate it needs to be acted upon by a force. As we have seen in an earlier post on acceleration.

From the post on acceleration we can deduce that there are four changes that can take place if a force acts on an objects:

1. The speed of the object will increase from zero if it was at rest and the object will move in the direction in which the force is acting.
2. The speed of the object will increase if the force is acting in the same direction as the the direction of motion of the object until the force no longer acts on the object.
3. The speed of the object will decrease if the force is acting in a direction opposite to the direction of motion of the object. The speed of the object might decrease to zero if the force acts for long enough.
4. If the object is moving and the force is acting in a direction perpendicular to the direction of motion of the object then the object will move in a circular path. When the application of the force stops the object will leave the circular path and would move in a straight line in a direction tangential to the circular path.

These four changes can be combined together to produce the Newton’s first law of motion as shown below:

Unless a force is applied an object will continue in its state of rest or uniform motion in a straight line.

Another way to write this law:

If a force is applied (i) an objects that was at rest will no longer be at rest or (ii)if moving with a uniform  will no longer have a uniform or constant speed or lastly (iii) if moving in a straight line will no longer move in  the same direction

This law is thus explaining that if a force is acting on an object then the object will experience an acceleration. However we are officially learn this only when we see the Newton’s second law of motion.

What is pressure ?

When you have a force that is applied on a surface over a given surface area then you say that a pressure is being exerted on the surface.

Fig 1

Fig 1 shows a small wooden block placed on a wooden sheet. As you know every object has a weight. This weight as you would remember is a force of attraction that the earth is exerting on the object. Thus it is a downward force.

Hence we can deduce that block of wood due to its weight is applying a force F on the sheet. The force F  would act as shown in fig 2 below.

Fig 2

But we also know that the weight of the object, the force applied on the wooden sheet, is being applied over a surface area A. That surface area is shaded black in fig 3 below.

Fig 3

The pressure exerted on the wooden sheet by the wooden blockis thus the force acting perpendicularly per unit surface area.

Hence to calculate the pressure we have to use the equation below:

Pressure exerted = Force applied / surface area

The unit of pressure is thus the N m^-2

The pressure is a scalar quantity since it is obtained by dividing a vector quantity by a vector quantity.

What is the weight of an object?

Every object has a quantity known as the mass. The mass is simply the quantity of matter that it contains.

When according to the law of gravitation, a mass that is situated inside the gravitational field of the earth would experience an attractive force, a pull, as shown in fig 1 below.

Fig 1

Now this pull on the object is called the weight.

Hence the weight can be defined as the gravitational pull that the earth exerts on an object. 

Since it is gravitational pull it is a  thus a force and its unit is the Newton (N).

The weight is calculated according to the equation below:

weight = mass * acceleration due to gravity

w  = mg 

Example

A stone has a mass of 5.0 kg. Calculate it weight if the acceleration due to gravity is 9.81 m s^-2 .

Weight w = mg

               = 5.0 * 9.81

                = 49.05 N

                = 49 N

Work done

Work done is a very important concept in Physics as it is used in fields, in deriving gravitational potential energy and kinetic energy, etc.

So what is work done?

Let us look at the diagram above. A force F acts on the box at A. During the time the force is acting, the box moves in the direction of the force. When the application of the force stopped the box has moved a distance d.

Using the definition

Work done is the product of the force acting on an object and the distance moved by the object in the direction of the force.

We can deduce that the equation to calculate work done is

Work done = Force * distance moved in the direction of the force

Work done = F *d

Let us have a look at an example.

Example

A man pulls a table by exerting a force of 100 N on it moving it by a distance of 3.9 m.

Calculate the work done by the man?

Work done = Force * distance moved in the direction of the force

Work done = F *d

= 100 * 3.9

= 3900 J

If you have understood the concept do the question below.

Question

A braking force of 2.3*10⁴ N is applied to a car and as a result the car stops in a distance of 23 m. Calculate the work done in stopping the train.

Good luck.