Explain with diagram the variation of the acceleration due to gravity (g)
i) At a height h above the earth surface
Inside the earth towards the centre of the earth.
ii) What is the value of g at the centre of the earth.
2)Explain with example the term, damped harmonic motion
3)Explain Range of a projectile with figure.
thanks.
i) Above the earth's surface, g is inversely proportional to the square of the distance form the center. Inside the earth, it is proportional to the mass of the spherical volume below that radial distance, and inversely proportional to the square of distance from the cetnter. It will depend upon how the density varies with distance. If you assume constant density (which is not true), the value of g is proportional to distance from the cetner of the earth.
The value of g at the center of the earth is 0.
For the other two questions, I suggest you do you own Google search, in order to get some pictures.
I can answer your questions.
1) Variation of acceleration due to gravity (g):
i) At a height h above the Earth's surface:
When an object is at a height h above the Earth's surface, the distance between the center of the object and the center of the Earth changes. The gravitational force acting on the object decreases with increasing height. This behavior can be explained by the inverse square law, which states that the force of gravity is inversely proportional to the square of the distance between two objects. So, the acceleration due to gravity (g) decreases as we move away from the Earth's surface. Here is a diagram to help visualize it:
```
|
|
----------
o | m | <------ Object at height h
----------
```
ii) Inside the Earth towards the center:
As we move towards the center of the Earth, the mass of the Earth below us starts to decrease, resulting in a decrease in the gravitational force acting on the object. Consequently, the acceleration due to gravity (g) decreases as we move towards the center of the Earth. Here is a diagram to help visualize it:
```
|
|
----------
| m | <------- Object inside the Earth
----------
C
```
2) Damped harmonic motion:
Damped harmonic motion refers to a type of oscillation or vibration in which the amplitude of motion gradually decreases over time due to the presence of damping forces. These damping forces can be caused by factors such as friction or air resistance.
For example, consider a simple pendulum swinging back and forth. Initially, when the pendulum is set into motion, it oscillates with a certain amplitude. However, due to air resistance and the friction in its pivot point, the pendulum gradually loses energy. As a result, the amplitude of its motion decreases over time, leading to a damped harmonic motion.
3) Range of a projectile:
The range of a projectile refers to the horizontal distance covered by the object (such as a projectile or a thrown object) before it hits the ground. It can be calculated using the following formula:
Range = (v^2 * sin(2θ)) / g,
where v is the initial velocity of the projectile, θ is the launch angle, and g is the acceleration due to gravity.
Here is a figure to better understand the concept:
```
|\
| \
θ | \
------------------|---> Horizontal direction
|
|
|
|
V
Vertical direction
```
In the figure, θ represents the launch angle, and the arrow indicates the initial velocity of the projectile. The range can be determined using the given formula by taking into account the initial velocity, launch angle, and acceleration due to gravity.