Combining conservation laws (momentum and energy)

In summary, the conversation discusses the application of conservation of momentum and energy to solve for the maximum distance that a 15kg block will compress a spring after being struck by a 3kg stone traveling at 8m/s. The solution involves finding the final velocity of the block (2 m/s) and using it to solve for the maximum compression distance of the spring (0.346m). The solution is correct and it is suggested to show more detailed work for better understanding.
  • #1
malignant
42
1

Homework Statement


A 15kg block is attached to a very light horizontal spring of force constant 500 N/m and is resting on a frictionless horizontal table. It is struck by a 3kg stone traveling horizontally at 8m/s to the right, whereupon the stone rebounds at 2 m/s horizontally to the left.

Find the maximum distance that the block will compress the spring after the collision.

Homework Equations


m1v1i + m2v2i = m1v1f + m2v2f
ΔKE + ΔEE = 0

The Attempt at a Solution


Using conservation of momentum I ended up with v2 final (the 15kg block) being 2 m/s.
Then I plugged that into 1/2mv^2 - 1/2kx^2 = 0 and solved for x.

I got 0.346m, is this correct?
 
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  • #2


I would like to point out that your solution is correct. You have correctly applied the principles of conservation of momentum and conservation of energy to solve for the maximum distance that the block will compress the spring after the collision. Good job! However, I would also like to suggest that you show your work and calculations in more detail to provide a better understanding of your solution. This will also help others who are trying to learn from your answer. Keep up the good work!
 

1. What are conservation laws?

Conservation laws are fundamental principles in physics that state that certain properties of a system remain constant over time. These properties can include momentum, energy, and mass.

2. Why are momentum and energy conservation laws important?

Momentum and energy conservation laws are important because they help us understand and predict the behavior of physical systems. They also provide a framework for understanding the underlying principles of the universe.

3. How are momentum and energy related?

Momentum and energy are related through the principle of conservation of energy. This states that the total energy of a closed system remains constant over time, and can be transferred between different forms (such as kinetic and potential energy) but cannot be created or destroyed.

4. How are conservation laws applied in real-world scenarios?

Conservation laws are applied in real-world scenarios in a variety of ways. For example, in engineering, they are used to design efficient machines and structures, while in astrophysics, they help us understand the behavior of celestial bodies. In everyday life, they can be seen in action in phenomena such as the conservation of momentum in billiard balls or the conservation of energy in a rollercoaster.

5. Can conservation laws be violated?

No, conservation laws cannot be violated. They are fundamental principles that have been observed and tested in countless experiments and have been found to hold true in all cases. If a system appears to violate a conservation law, it simply means that there is a missing piece of the puzzle that we have not yet discovered.

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