m a lets say we have a particle of mass (m). we would have to find the force of it. lets say this particle has a distance (a) from the washer.. this washer has a mass (M). this washer has inner radius (Ri) and outer (Ro). FIND: Find the force on the particle of mass
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
![**Calculating Gravitational Force from a Washer**
*Problem Statement:*
Let’s consider a particle of mass \( m \). We need to determine the gravitational force acting on this particle. Let’s assume this particle is located at a distance \( a \) from a washer. The washer has a mass \( M \) and an inner radius \( R_i \), as well as an outer radius \( R_o \).
*Diagram Description:*
The provided diagram depicts:
- A washer (shaded in blue) with mass \( M \) and two concentric circles indicating its inner radius \( R_i \) and outer radius \( R_o \).
- A particle (represented as a small blue circle) with mass \( m \) located at a distance \( a \) from the edge of the washer.
*Objective:*
Determine the gravitational force acting on the particle of mass \( m \) due to the washer.
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*Fundamentals:*
1. *Gravitational Force Formula:*
The gravitational force between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by:
\[
F = \frac{G \cdot m_1 \cdot m_2}{r^2}
\]
where \( G \) is the gravitational constant.
2. *Application to a Disk (Washer):*
To solve for the force due to the washer, you will need to integrate the contributions of differential mass elements of the washer. This involves setting up the integral in cylindrical coordinates and considering the symmetry of the problem.
*Steps to Solve:*
- Set up the coordinate system with the particle at a distance \( a + R_o \) from the center of the washer when considering the farthest element.
- Express the differential mass element, \( dm \), in terms of the surface density (mass per unit area) of the washer.
- Integrate the gravitational contributions of each differential mass element over the entire surface of the washer.
- Simplify to find the net gravitational force.
By following these steps consistent with gravitational field theory, one can derive the exact force acting on the particle due to the washer. This approach incorporates advanced calculus and is typically covered in higher-level physics or engineering coursework.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F737222ef-5c70-4907-93aa-2c2d7afd58f4%2F2d430f26-5dcb-43b2-b5ef-9a92af6d9c5f%2Fa9et23_processed.jpeg&w=3840&q=75)
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