Apparent Weight, Weightlessness, and Newton's Law of Gravitation Explained

Apparent Weight

Understanding Apparent Weight

APPARENT WEIGHT

The weight that you feel to possess during up and down motion, is not same as your actual weight. Apparent weight is the weight of the body acquired due to the action of gravity and other external forces acting on the body.

Let us see this from the following illustration:

Let us consider a person of mass m, who is travelling in lift. The actual weight of the person is W = mg, which is acting vertically downwards. The reaction force exerted by the lift’s surface ‘R’, taken as apparent weight is acting vertically upwards.

Let us see different possibilities of the apparent weight 'R' of the person that arise, depending on the motion of the lift; upwards or downwards which are given in Table 1.2

Table 1.2: Apparent weight in different scenarios.

1. Weightlessness

Have you gone to an amusement park and taken a ride in a roller coaster? or in a giant wheel? During the fast downward and upward movement, how did you feel?

Its amazing!!. You actually feel as if you are falling freely without having any weight. This is due to the phenomenon of ‘weightlessness’. You seem to have lost your weight when you move down with a certain acceleration. Sometimes, you experience the same feeling while travelling in a lift.

When the person in a lift moves down with an acceleration (a) equal to the acceleration due to gravity (g), i.e., when a = g, this motion is called as ‘free fall’. Here, the apparent weight (R = m (g – g) = 0) of the person is zero. This condition or state refers to the state of weightlessness. (Refer case 4 from Table 1.2).

The same effect takes place while falling freely in a roller coaster or on a swing or in a vertical giant wheel. You feel an apparent weight loss and weight gain when you are moving up and down in such rides.

2. Weightlessness of the astronauts

Some of us believe that the astronauts in the orbiting spacestation do not experience any gravitational force of the Earth. So they float. But this is absolutely wrong.

Astronauts are not floating but falling freely around the earth due to their huge oribital velocity. Since spacestation and astronauts have equal acceleration, they are under free fall condition. (R = 0 refer case 4 in Table 1.2). Hence, both the astronauts and the spacestation are in the state of weightlessness.

3. Application of Newton’s law of gravitation

• Dimensions of the heavenly bodies can be measured using the gravitation law. Mass of the Earth, radius of the Earth, acceleration due to gravity, etc. can be calculated with a higher accuracy.
• Helps in discovering new stars and planets.
• One of the irregularities in the motion of stars is called ‘Wobble’ lead to the disturbance in the motion of a planet nearby. In this condition the mass of the star can be calculated using the law of gravitation.
• Helps to explain germination of roots is due to the property of geotropism which is the property of a root responding to the gravity.
• Helps to predict the path of the astronomical bodies.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail for 10th Science : Chapter 1 : Laws of Motion : Apparent Weight.

Understanding Gravitation: Newton's Law, Acceleration Due to Gravity (g), and Earth's Mass

Gravitation

Newton's Universal Law of Gravitation

GRAVITATION

This law states that every particle of matter in this universe attracts every other particle with a force. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between the centers of these masses. The direction of the force acts along the line joining the masses.

Force between the masses is always attractive and it does not depend on the medium where they are placed.

Let, m₁ and m₂ be the masses of two bodies A and B placed r metre apart in space

Force F ∝ m₁ × m₂

F ∝ 1/ r²

On combining the above two expressions

Where G is the universal gravitational constant. Its value in SI unit is 6.674 × 10^–11 m²kg^–2.

2. Acceleration due to gravity (g)

When you throw any object upwards, its velocity ceases at a particular height and then it falls down due to the gravitational force of the Earth.

The velocity of the object keeps changing as it falls down. This change in velocity must be due to the force acting on the object. The acceleration of the body is due to the Earth’s gravitational force. So, it is called as ‘acceleration due to the gravitational force of the Earth’ or ‘acceleration due to gravity of the Earth’. It is represented as ‘g’. Its unit is m s^–2

Mean value of the acceleration due to gravity is taken as 9.8 m s^–2 on the surface of the Earth. This means that the velocity of a body during the downward free fall motion varies by 9.8 m s^–1 for every 1 second. However, the value of ‘g’ is not the same at all points on the surface of the earth.

3. Relation between g and G

When a body is at rests on the surface of the Earth, it is acted upon by the gravitational force of the Earth. Let us compute the magnitude of this force in two ways. Let, M be the mass of the Earth and m be the mass of the body. The entire mass of the Earth is assumed to be concentrated at its centre. The radius of the Earth is R = 6378 km (= 6400 km approximately). By Newton’s law of gravitation, the force acting on the body is given by

Here, the radius of the body considered is negligible when compared with the Earth’s radius. Now, the same force can be obtained from Newton’s second law of motion. According to this law, the force acting on the body is given by the product of its mass and acceleration (called as weight). Here, acceleration of the body is under the action of gravity hence a = g

4. Mass of the Earth (M)

Rearranging the equation (1.14), the mass of the Earth is obtained as follows:

Mass of the Earth M = g R²/G

Substituting the known values of g, R and G, you can calculate the mass of the Earth as

M = 5.972 × 10²⁴ kg

5. Variation of acceleration due to gravity (g):

Since, g depends on the geometric radius of the Earth, (g ∝ 1/R²), its value changes from one place to another on the surface of the Earth. Since, the geometric radius of the Earth is maximum in the equatorial region and minimum in the polar region, the value of g is maximum in the polar region and minimum at the equatorial region.

When you move to a higher altitude from the surface of the Earth, the value of g reduces. In the same way, when you move deep below the surface of the Earth, the value of g reduces. (This topic will be discussed in detail in the higher classes). Value of g is zero at the centre of the Earth.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

10th Science : Chapter 1 : Laws of Motion : Gravitation