Spring Forces?

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Best answers: Determining a Spring force?
A massless spring is between a 1-kg mass and a 3-kg ,mass, but is not attached to either mass. Both masses are on a horizontal frictionless table. In an experiment, the 1kg mass is held in place and the spring is compressed by pushing on the 3-kg mass. The 3kg mass is released and moves off with a speeed of 10 meters per second.

How do I determine teh final velocity of each mass relative to the table after the masses are released?

isnt the original momentum just mv of the 3 kg mass so 30 and final hast to be 30?? velocities dont change ,no friction?

Answer 1

This problem deals with momentum.

(m1+m2)Vo=m1V1+m2v2
the original speed is zero.
0=m1v1+m2v2

The other relation we know is that energy is conserved.
Work=energy. The only energy put into the system is the energy that is in the first problem. This energy is then converted into kinetic but it's the kinetic energy of the two seperate masses...so..

W=1/2m1v^2+1/2m2v^2

you then do a system of equations to solve for v1 and v2.

0=m1v1+m2v2
W=1/2m1v1^2+1/2m2v2^2

m1=1
m2=3
m1v1+m2v2=0
(1)v1+(3)v2=0
v1=-3v2

W=150J

150J=1/2m1v1^2+1/2m2v2^2
150J=1/2m1(3v2)^2+1/2m2v2^2
150J=1/2(1)(3v2)^2+1/2(3)v2^2
150J=6v2^2
v2=5m/s

v1=-3v2
v1=-3(5)

v1=-15m/s

(..now.. can I have my points please?)

EDIT: the orginal momentum is zero since you start at rest. The energy put in is how ever the energy that is require to make the 3kg block reach a velocity of 10m/s. Once you relase the blocks simultaneously the force that is stored inside the spring is partitioned into the two block. In the first part, only the 3kg block is acted by the force. All the acceleration went in only to that block. When both of them are let go at the same time, each recieve only a portion of the acceleration since the force is spread into two different directions.

Answer 2

Both the 1 and the 3 kg. masses will have the same force applied by the spring. When you let go of them both the 1 kg. will accelerate 3 X's as fast as the 3 kg. When all the springs energy went into pushing the 3 kg. mass it went at 10m/s. M X V = 30. I think the 3 kg. mass will have a speed 5 m/s and the 1 kg. mass a speed of 15 m/s. What happened to acceleration in this problem?