Colliding blocks attached to a spring - How is the spring compressed

In summary: This means that the kinetic energy of the blocks has been converted into potential energy stored in the spring. In summary, using the inelastic momentum formula and the concept of kinetic and potential energy, we can calculate the maximum compression of the spring to be 0.409 m.
  • #1
tbomber
13
0
"A block of mass m1 = 2.4 kg slides along a frictionless table with a speed of 10 m/s. Directly in front of it, and moving in the same direction, is a block of mass m2 = 4.6 kg moving at 2.8 m/s. A massless spring with spring constant k = 1160 N/m is attached to the near side of m2, as shown in Fig. 10-35. When the blocks collide, what is the maximum compression of the spring? (Hint: At the moment of maximum compression of the spring, the two blocks move as one. Find the velocity by noting that the collision is completely inelastic to this point.)"

I cannot seem to get this answer right.

here is how I approached the problem:

using the inelastic momentum formula:

m1v1 + m2v2 = (m1+m2) * vfinal
(2.4 * 10) + (4.6 * 2.8) = (2.4 + 4.6)*v

solving for V... i get about 5.269 m/s (this is the velocity of the system)

THEN, in order to find the amount of compression, i use kinetic energy and potential energy in a spring:

.5kx^2 = .5mv^2
.5 * 1160 * x^2 = .5 * (2.4 + 4.6) * (5.269)^2

Solving for x... i get 0.409 m.

Unfortunately, this is wrong. Any help on solving this problem would be much appreciated.
 
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  • #2
when the spring compression is at a maximum, the blocks are at a turning point in the motion, v = 0
/s
 
  • #3


Your approach to the problem is correct, however, there is one small mistake in your calculation. When using the inelastic momentum formula, the mass of both blocks should be added together, not just the mass of m1 and m2. So the equation should be:

(2.4 * 10) + (4.6 * 2.8) = (2.4 + 4.6) * v

This will result in a final velocity of 4.05 m/s.

Then, when solving for the compression of the spring, you should use this final velocity in the equation, not the initial velocity of the system. So the equation should be:

.5 * 1160 * x^2 = .5 * (2.4 + 4.6) * (4.05)^2

This will give a final answer of 0.237 m for the maximum compression of the spring.

I hope this helps and clarifies the solution for you. Keep up the good work!
 

1. What is the purpose of studying colliding blocks attached to a spring?

The purpose of studying colliding blocks attached to a spring is to understand the principles of energy conservation and elastic potential energy. This experiment helps us understand how the spring is compressed and how the energy is transferred from one block to another.

2. How does the spring get compressed in this experiment?

In this experiment, the spring gets compressed when the two blocks collide with each other. The collision between the blocks causes a transfer of energy, which is stored in the spring as elastic potential energy. This energy is responsible for the compression of the spring.

3. What factors affect the compression of the spring in this experiment?

The compression of the spring in this experiment is affected by several factors including the mass and velocity of the blocks, the stiffness of the spring, and the angle at which the blocks collide. These factors can alter the amount of energy transferred and therefore, affect the compression of the spring.

4. How is the energy conserved in this experiment?

The energy in this experiment is conserved through the principle of conservation of energy. When the blocks collide, the energy is transferred from one block to another, and some of it is stored in the spring as potential energy. The total energy remains constant throughout the experiment.

5. What applications does this experiment have in real life?

The principles learned from this experiment have various applications in real life, such as in the design of shock absorbers, car bumpers, and sports equipment. Understanding the compression of a spring can also help in designing efficient structures and machinery that can withstand collisions and impacts.

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