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[Noam M]

went through all the similar questions in the forum and failed to find a similar one to mine.

Question: On a frictionless table there are two masses , one of size m with velocity V0 (I'll call it the small mass) and one with mass M that is currently resting (the "big" mass). We connect a spring (with spring constant k,and l0 is its resting length) to the big mass so that the small one hits it and sticks to it, while not losing any energy.
What is the velocity of the big Mass as a function of its location regarding the center of mass? (After the collision)

My attempt: First of all, I know that the velocity of the CM is constant. I tried writing the energy equation and start from it:

E=0.5mV1^2+0.5MV2^2+0.5k(X2-X1-l0)^2 = 0.5mV0^2

V1-Speed of mass m, V2-Speed of mass M, X1,X2 - locations as above.

After rearranging the equation I only needed to find V1 but I failed to do so. I tried from the momentum equation but it didn't help.

Note: I am not suppose to solve any ODE or use the fact that we have harmonic movement.

*Also, Is there a guide on how to write math equations here?

 

[haruspex]

As a first step, I would introduce a variable for the position of the large mass relative to the common mass centre. You need this in the answer. You should be able to express the extension in terms of that.
The momentum conservation should give you a relationship between the two velocities, allowing you to eliminate the small mass velocity. What remains should be the equation you need.

 

[gneill]

Hi Noam M, Welcome to Physics Forums.

Please keep and use the formatting template that is provided in the edit window when a new thread is started here in the homework area.

went through all the similar questions in the forum and failed to find a similar one to mine.

Question: On a frictionless table there are two masses , one of size m with velocity V0 (I'll call it the small mass) and one with mass M that is currently resting (the "big" mass). We connect a spring (with spring constant k,and l0 is its resting length) to the big mass so that the small one hits it and sticks to it, while not losing any energy.
What is the velocity of the big Mass as a function of its location regarding the center of mass? (After the collision)

Okay, the wording of the question is a bit puzzling. How are we to interpret "its location regarding the center of mass"? Should we transform the problem to the center of mass frame first and then describe the motion? And by "after collision" do they mean the instant after the small block contact the spring, or after maximal compression of the spring, or perhaps when the spring first returns to its relaxed length? Something else?

My attempt: First of all, I know that the velocity of the CM is constant. I tried writing the energy equation and start from it:

E=0.5mV1^2+0.5MV2^2+0.5k(X2-X1-l0)^2 = 0.5mV0^2

V1-Speed of mass m, V2-Speed of mass M, X1,X2 - locations as above.

After rearranging the equation I only needed to find V1 but I failed to do so. I tried from the momentum equation but it didn't help.

Note: I am not suppose to solve any ODE or use the fact that we have harmonic movement.

So they want just an instantaneous velocity with respect to the center of mass at some instant?

*Also, Is there a guide on how to write math equations here?

Sure. Check the help section: LaTeX Primer