The usage of the reduced mass calculator is not limited to gravitational problems in mechanics as any relative objects orbiting each other in space (due to any kind of dual force acting upon them) constitute a two-body problem that can be simplified and disintegrated by means of the reduced mass for one whole body. The tool is easy to use all you have to do is provide the respective inputs in the allotted fields and then click on the calculate button to avail the reduced mass in no time.
Reduced Mass Definition
Reduced mass is a physical quantity in any relative system which is used to solve the two-body or multiple-body problem to turn it into an equivalent one-body problem. The complexity of the two-body problem arises from the fact that the movement of one body affects the other which in turn affects the first one. Or even any metaphysical quantity working on one body leads the other bodies present in the system to get affected in an endless loop of additive effects from one body reactions to the other, and hence making the problem difficult to solve.
A typical example of a two-body problem is that of two objects of comparable mass orbiting each other in space with force of gravitation acting on them individually and the attractive forces acting on it relatively.
Reduced Mass Equation or Formula
The formula for the reduced mass of a two-objects system is the inverse of the sum of the inverses of each mass combined, and it is denoted by the Greek letter μ. The reduced mass calculator computes the value of the reduced mass of a two-body system by using the defining reduced mass equation in any given system, under any force that can act upon the bodies.
Reduced mass of the body = m₁ * m₂ / (m₁ + m₂)
How to find the Reduced Mass?
Follow the simple and easy guidelines listed below to determine the reduced mass value easily. They are along the lines
- Step 1: First and foremost step is to find out the masses of two bodies from the given question.
- Step 2: Next step is to obtain the product of their masses as well as sum of their masses.
- Step 3: Then divide the product of masses by the sum of the masses to get the reduced mass of a two body system.
Reduced Mass of a Two Body System Examples
Question 1: In a system of two bodies working together in the same space with same force of gravitation acting on them, calculate the reduced mass of both the bodies present in the system. The mass of body one is 7500 kgs and the mass of the body moving in its own orbital is 6700 kgs?
The Mass of body one is 7500 kgs
The Mass of body two is 6700 kgs
The Reduced mass in the whole relative system is m₁ * m₂ / (m₁ + m₂)
Hence substituting the values in the given formula we have 3538.73 kgs.
So, the reduced mass of the system in the space is 3538.73kgs
Question 2: In the free space of relative bodies where the mass of a satellite orbiting a planet is 9078 kg the force acting on the satellite due to the gravitational pull of other planets is 6.7m/s/s, calculate the reduced mass of the system if an additional frictional force of 789 N acts on the satellite and planet by their own revolutions. Assume the weight of the planet to be 567856 Kg.
The Mass of the satellite is 9078 kg 576934
The mass of the planet is 567856 kg
No gravitational force or frictional force can bring alterations in the reduced mass of the system, hence by neglecting the values of other forces we have:
The reduced mass of the system is m₁ * m₂ / (m₁ + m₂)
Hence substituting the values in the given formula we have
So, the reduced mass of the system in the space is 8935.15 kg
For more concepts check out physicscalculatorpro.com to get quick answers by using the free tools available.
FAQs on Reduced Mass Calculator
1. How do you calculate the reduced mass of a single compound?
The reduced mass of a single compound can not be calculated without the presence of any external body in the same system.
2. Can you calculate the reduced mass of a system in presence of frictional force acting on both bodies?
The reduced mass of any system can be easily calculated with or without the presence of any external force in the system.
3. What is the standard unit of reduced mass of a system?
The standard unit of reduced mass of a system is kg.
4. What is the meaning of the reduced mass of a system?
The reduced mass allows obtaining the reduced mass of a two-body or a multiple-body system in the same space.
5. What is the formula to calculate the reduced mass of the system?
The formula to calculate the reduced mass of the system is m₁ * m₂ / (m₁ + m₂) where m1 and m2 stand for the masses of objects one and two respectively.