Spring compression with masses in motion

In summary, the conversation discusses a problem involving two blocks of different masses and a spring with a specific spring constant. The question is to determine the maximum compression of the spring when the two blocks collide with specific velocities. The solution involves applying conservation of energy and using center of mass coordinates to simplify the problem.
  • #1
scavok
26
0
https://chip.physics.purdue.edu/protected/Halliday6Mimg/h10p33.jpg
A block of mass m1 = 2.5 kg slides along a frictionless table with a speed of 12 m/s. Directly in front of it, and moving in the same direction, is a block of mass m2 = 6.2 kg moving at 3.7 m/s. A massless spring with spring constant k = 1100 N/m is attached to the near side of m2, as shown in figure above. When the blocks collide, what is the maximum compression of the spring?

There's just too much going on here and I don't know where I'm going on wrong.

m1v1 + m2v2 = (m1+m2)vf
vf=velocity of both masses at the point where maximum compression is reached.

Is this correct?

If so, then the change in kinetic energy of mass m1 equals the work done on mass m1 by the spring:
.5m1vf2-.5m1v12=.5kx2

But this gets me a negative value, which it should since it is losing velocity, but I can't take the square root of a negative value which I need to do when solving for x. This makes me think I'm doing something wrong.
 
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  • #2
Apply conservation of energy: state that the sum of initial kinetic energies of the blocks equals their sums at the point of compression plus the energy stored in the spring.
 
  • #3
scavok said:
https://chip.physics.purdue.edu/protected/Halliday6Mimg/h10p33.jpg
A block of mass m1 = 2.5 kg slides along a frictionless table with a speed of 12 m/s. Directly in front of it, and moving in the same direction, is a block of mass m2 = 6.2 kg moving at 3.7 m/s. A massless spring with spring constant k = 1100 N/m is attached to the near side of m2, as shown in figure above. When the blocks collide, what is the maximum compression of the spring?

There's just too much going on here and I don't know where I'm going on wrong.

m1v1 + m2v2 = (m1+m2)vf
vf=velocity of both masses at the point where maximum compression is reached.

Is this correct?

If so, then the change in kinetic energy of mass m1 equals the work done on mass m1 by the spring:
.5m1vf2-.5m1v12=.5kx2

But this gets me a negative value, which it should since it is losing velocity, but I can't take the square root of a negative value which I need to do when solving for x. This makes me think I'm doing something wrong.

If you are comfortable with it, a way to simplify the problem would be use center of mass coordinates, do the spring problem, then convert back to "lab" coordinates.

-Dan
 

What is spring compression?

Spring compression is the reduction in the length of a spring due to the application of an external force.

How does spring compression occur with masses in motion?

When masses are attached to a spring and set into motion, the spring experiences a force that causes it to compress or extend depending on the direction of motion.

What factors affect the amount of spring compression?

The amount of spring compression is affected by the mass of the objects attached to the spring, the speed and direction of their motion, and the stiffness of the spring.

What happens to the kinetic and potential energy of the masses during spring compression?

As the masses compress the spring, their kinetic energy decreases and their potential energy increases. Once the spring reaches its maximum compression, the potential energy is at its maximum and the kinetic energy is at its minimum. As the spring extends, the potential energy decreases and the kinetic energy increases again.

How is the amount of spring compression calculated?

The amount of spring compression can be calculated using Hooke's law, which states that the force applied to a spring is directly proportional to the amount of compression. The equation is F = -kx, where F is the force applied, k is the spring constant, and x is the amount of compression.

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