Spring in between two masses

In summary, when two masses attached by a string and a compressed spring between them are released, their momentums will be equal and their kinetic energies will be equal if the masses are equal. If the masses are not equal, the velocities of the masses will be different.
  • #1
kyrillos
2
0
Let's say there are two masses, attached together by a string, and there's a compressed spring in between them. When the string in between is cut off, the spring unloads, pushing both masses in opposite directions.

My thinking:
1. Their momentums will be equal to each other.
Their momentum before the string is cut is equal to zero (because they were not moving). So the sum of their final momentums should be also zero.
2. Their kinetic energies will be equal to each other.
The spring unloads in both direction at equal rates, so I assume that their kinetic energies must also be equal. (I couldn't find a mathematical evidence in my Giancoli book to see if I am actually right)

Are my conclusions right?
 
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  • #2
kyrillos said:
1. Their momentums will be equal to each other.
Their momentum before the string is cut is equal to zero (because they were not moving). So the sum of their final momentums should be also zero.
Yes, that is correct.

kyrillos said:
2. Their kinetic energies will be equal to each other.
The spring unloads in both direction at equal rates, so I assume that their kinetic energies must also be equal
This is only correct if the masses are equal. Can you think what will happen if the masses are not equal?
 
  • #3
Dale said:
Yes, that is correct.

This is only correct if the masses are equal. Can you think what will happen if the masses are not equal?
Well:
0 = m1v1 + m2v2
v1 = -m2v2/m1

And:
0.5m1v12 + 0.5m2v22 = 0.5kx2

I don't know what to do next, since I also don't know the value of the elastic potential energy. Could you help me?
 
  • #4
kyrillos said:
I don't know what to do next, since I also don't know the value of the elastic potential energy. Could you help me?
You can just leave the elastic potential energy as you have written it. So the next step is just to substitute

kyrillos said:
v1 = -m2v2/m1
into
kyrillos said:
0.5m1v12 + 0.5m2v22 = 0.5kx2
and then solve for the velocity.
 

1. What is "Spring in between two masses"?

"Spring in between two masses" is a concept in physics that refers to a system where two masses are connected by a spring, allowing them to move relative to each other. This system is commonly used to model oscillating systems, such as a mass suspended on a spring or a pendulum.

2. How does the spring behave in this system?

The spring in this system behaves according to Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the masses from their equilibrium position. This means that as the distance between the masses changes, the spring will exert a restoring force in the opposite direction to bring the masses back to their equilibrium position.

3. What factors affect the behavior of the spring in between two masses?

The behavior of the spring in this system is affected by several factors, including the stiffness of the spring (measured by its spring constant), the mass of the two objects, and the initial displacement of the masses from their equilibrium position. These factors can impact the frequency and amplitude of the resulting oscillations.

4. How is energy conserved in this system?

Energy is conserved in this system as the spring and masses oscillate back and forth. The potential energy stored in the spring is converted into kinetic energy as the masses move, and then back to potential energy as the spring pulls them back towards their equilibrium position. This process continues, with the total energy remaining constant throughout.

5. What are some real-life examples of "Spring in between two masses"?

Some real-life examples of "Spring in between two masses" include a swing (where the swing seat and the support ropes act as the two masses connected by a spring-like motion), a car's suspension system (where the car body and the wheels act as the two masses connected by springs), and a diving board (where the diver and the board act as the masses connected by a spring).

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