Reduced mass for an infinite mass and a finite mass?

In summary, the problem involves a collision between a finite mass steel ball and an infinite mass steel wall, where the goal is to find the maximum compression. The relevant equation for this problem is Em=((5/4b)uv^2)^5/2, where v is the initial velocity upon collision, u is the reduced mass, and b is a constant. The question of what to use as the reduced mass arises, and while mathematically it is m1, physically the given information suggests using m2.
  • #1
cbjewelz
3
0

Homework Statement


We have a collision between a finite mass steel ball and an infinite mass steel wall and must find the maximum compression if we are given the mass of the ball, the initial speed and the constant b (See eq. below).


Homework Equations


We know that the maximum compression for two spheres colliding is given by
Em=((5/4b)uv^2)^5/2 where v is the initial velocity upon collision and u is the reduced mass u=m1m2/(m1+m2). b is a constant.


The Attempt at a Solution


Now my only question is what to use as the reduced mass. Mathematically by putting in infinity as m2 we get a reduced mass of 1. Is this correct?
 
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  • #2
mathmetically it's: m1.
but physically you are given that m2>>m1.
 
  • #3


Yes, using infinity as the mass for the infinite mass steel wall will result in a reduced mass of 1 for the collision between the ball and the wall. This is because when one of the masses is significantly larger than the other, its contribution to the reduced mass becomes negligible. Therefore, in this scenario, the finite mass of the ball will have a larger impact on the reduced mass calculation. It is important to note that this equation assumes perfectly elastic collisions and may not accurately represent real-world collisions. Other factors such as friction and deformation may also play a role in the maximum compression.
 

1. What is the concept of reduced mass?

The concept of reduced mass is used in physics to simplify the equations of motion when two particles are in orbit around each other. It takes into account the masses of both particles and their distance from each other to calculate the overall inertia of the two-body system.

2. How is reduced mass calculated?

The reduced mass is calculated by taking the product of the two masses and dividing it by their sum. For example, if the two masses are m1 and m2, the reduced mass is given by: μ = (m1 * m2) / (m1 + m2).

3. What is the significance of infinite mass in reduced mass calculations?

Infinite mass is used in reduced mass calculations to represent a situation where one of the particles has a significantly larger mass than the other. This can simplify the equations of motion and make the calculations more manageable.

4. How does the reduced mass change when one of the masses is infinite?

When one of the masses is infinite, the reduced mass becomes equal to the other mass. This is because the infinite mass has a much larger influence on the overall inertia of the system, and the smaller mass can be neglected in the calculations.

5. Can the concept of reduced mass be applied to any two-body system?

Yes, the concept of reduced mass can be applied to any two-body system, as long as the particles are in orbit around each other. This includes celestial bodies, such as planets and stars, as well as subatomic particles, such as electrons and protons.

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