I am having trouble with this problem: A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a horizontal frictionless surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium point. The two objects stick together. (A) By how much does the amplitude of the vibrating system change as a result of the collision. (B) By how much does the period change? (C)By how much does the energy change? (D) Account for the change in energy? This is pretty much a plug-in problem, but my main question is how to solve for the new amplitude and energy after the collision. I am going over the formulas and it seems like the amplitude is in the formula for energy and energy is part of the formula for amplitude, how can I solve for one or the other when they both change after the collision? Can someone give me a clue?
Ignore the spring forces during collision and treat the collision in terms of conservation of momentum. The vertical component will not be a factor; the normal force will stop the vertical motion. Horizontal momentum will be conserved. Calculate the kinetic energy after the collision. Use that to find the maximum displacement of the spring. Use the new mass to find the new period/frequency.
I don't see a "collision". You are not told the height from which the new mass is dropped and it is, anyway, vertical, which will not affect horizontal motion. The only thing that happens is that the mass suddenly changes from 4 to 10 kg.
While the vertical motion doesn't matter, the horizontal motion does. Treat this as an inelastic collision between the moving 4 kg particle and the stationary 6 kg object.
Thanks for all the help. I was able to solve the problem as you all suggested by treating it as an inelastic collision. I solve for the energy of the system before the collision. Using the result of the energy I was able to solve for the initial velocity. Once I had the initial velocity I was able to solve for the final velocity by treating it as an ineslatic collision. Once I had the final velocity, I was able to solve for the new Amplitude and the rest was just plug-in. Thanks again for all the help.