Energy Equation of two masses and spring

In summary, the conversation discusses a problem involving two masses connected by a spring and the need to find the force applied to the second mass to move the first mass. The person seeking help has provided their solution, but has been told that an energy equation needs to be used instead of a force summation solution. Possible difficulties with the solution are also mentioned, such as the need to consider dynamic friction rather than static friction. The person offering help does not see a need for an energy equation and offers to provide an example if needed.
  • #1
pepster
2
0
Hi all,

I'm having a problem with the following question.
I have attached the question and my working for the solution however, I was told that the force summation solution which I have used and which many others have used is incorrect - an energy equation needs to be used.

Basically we are given two masses joint by a spring with coefficients of spring stiffness and coefficient of friction. We need to find the force applied to the second mass to move the first mass.

Any help would be much appreciated.

Thanks,
pepster
 

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  • #2
pepster said:
Hi all,

I'm having a problem with the following question.
I have attached the question and my working for the solution however, I was told that the force summation solution which I have used and which many others have used is incorrect - an energy equation needs to be used.

Basically we are given two masses joint by a spring with coefficients of spring stiffness and coefficient of friction. We need to find the force applied to the second mass to move the first mass.

Any help would be much appreciated.

Thanks,
pepster

I don't see a problem with your work?
The only difficulty I could see with your calculation is that Block B would have to be sliding - or at least have slid a little, before A will begin to move since the spring has to extended beffore it exerts a Force on Block A. As such we may have to use the dynamic friction for Block B rather than the static friction. However, if we were to pause with the spring stretched so that A is on the point of moving, and the net force on the now stationary Block B wa at the points of again moving it, then your answer looks good to me.
I can give you an example of what I was trying to describe there if necessary. Just ask.

ps: I can't see any need for an energy equation to be used.
 

1. What is the energy equation of two masses and a spring?

The energy equation of two masses and a spring is given by:
E = (1/2)kx2 + (1/2)mu12 + (1/2)mu22
where k is the spring constant, x is the displacement of the spring, and mu1 and mu2 are the masses of the two objects attached to the spring.

2. How is the energy equation of two masses and a spring derived?

The energy equation is derived from the principle of conservation of energy. The total energy of a system is the sum of its potential and kinetic energies. In the case of two masses and a spring, the potential energy comes from the spring's deformation and the kinetic energy comes from the motion of the two masses.

3. What is the significance of the energy equation in a two-mass-spring system?

The energy equation helps us understand the relationship between the spring's properties, the masses, and the energy of the system. It also allows us to calculate the potential and kinetic energies at any point during the system's motion.

4. How is the energy equation affected by changes in the spring constant?

The energy equation is directly affected by changes in the spring constant. A higher spring constant means that the spring is stiffer and will require more energy to be deformed. This results in a larger potential energy term in the equation.

5. Can the energy equation be applied to other types of systems?

Yes, the energy equation can be applied to other types of systems as long as they follow the principle of conservation of energy. For example, it can be used to describe the energy of a pendulum or a simple harmonic oscillator.

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