Impulsive Motion: Solving the Riddle

[jimmykb]

Dear all,

I get straight to the problem, that came out of a discussion with friends:

Two bodies are in contact with masses $$m_1$$ and $$m_2$$. Body $$m_2$$ is a pendulum. An impulsive force acts on one end of the body m_1.

(so an $$F\Delta t$$ is applied).

The bodies are elastic, after the impulsive force they both have initial velocities.
As a result the impulse is equal to: $$I=F\Delta t=-m_1v_1+m_2v_2$$.
so the pendulum(body $$m_2$$) will have an initial kinetic energ equal to$$0.5m_2v_2^2$$. What will be the kinetic energy of the pendulum IF I place an absorber between the two bodies?
Is it going to be the same?? this riddle has been keeping me busy for a long time..
If I place a sensor to measure the contact force vs time between the bodies $$m_1$$ and $$m_2$$ what will be the difference if there is an energy absorber in between??Is the sensor going to measure the same impulse??

Thank you all in advance

 

[Andrew Mason]

Two bodies are in contact with masses $$m_1$$ and $$m_2$$. Body $$m_2$$ is a pendulum. An impulsive force acts on one end of the body m_1.

(so an $$F\Delta t$$ is applied).

The bodies are elastic, after the impulsive force they both have initial velocities.

If they are in contact for the time that the force is applied and they are rigid, they will have the same velocity after the force ends.

What will be the kinetic energy of the pendulum IF I place an absorber between the two bodies?

It will be the same if the impulse is the same. The momentum imparted depends only upon the applied Force and its duration. With the absorber in place, the application of that force for that time will require more energy (the force must act over a greater distance due to the compression of the absorber).

AM