How Do Conservation Laws Apply to a Collision and Subsequent Motion?

• merlos
In summary, the conversation discusses a problem involving a 15.0 kg block attached to a spring and being struck by a 3.00 kg stone. The maximum distance that the block will compress the spring after the collision is determined by considering the conservation of kinetic energy and momentum.
merlos
Having a difficult time determining which laws and equations to use?

A 15.0 kg block is attached to a very light horizontal spring of force constant 350 N/m and is resting on a smooth horizontal table. Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left.

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

Think of it as two problems. Take them one at a time:
(1) The collision of stone with block--what's conserved there?
(2) The compression of the spring--what's conserved here?

Combining Conservation Laws; where'd I go wrong?

A 15.0 kg block is attached to a very light horizontal spring of force constant 350 N/m and is resting on a smooth horizontal table. Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left.

Don't know where I went wrong?
Here's my setup:

Collision:

Change in KE(stone) = (1/2)(m)(vfsquared-visquared)
= (1/2)(3.00kg)(-2m/s squared - 8 m/s squared)
= -90

After the collision:

Change in KE(stone) = (1/2)(Force constant)xsquared
-90 = (1/2)(350N/m)xsquared
x = 0.72m

Start by answering the questions I posed in my earlier response.

1.) Kinetic energy
2.) Kinetic energy of block is transferred to the spring, where it's stored as potential energy

merlos said:
1.) Kinetic energy
In general, KE is not conserved in a collision. But what is conserved in every collision?

2.) Kinetic energy of block is transferred to the spring, where it's stored as potential energy
Right!

1.) Momentum

Right. Now use that to find the speed of the block just after the collision.

1. What are conservation laws?

Conservation laws are fundamental principles in science that state that certain physical quantities, such as energy, momentum, and mass, are conserved, meaning they cannot be created or destroyed but can only be transformed or transferred from one form to another.

2. How are conservation laws related to each other?

Conservation laws are closely related to each other and can often be combined or derived from one another. For example, energy conservation can be derived from the conservation of momentum in a closed system.

3. What is the significance of combining conservation laws?

Combining conservation laws allows us to understand and predict complex physical phenomena by considering the relationships and interplay between different conserved quantities. It also helps to simplify and unify our understanding of the laws of nature.

4. Can conservation laws ever be violated?

In general, conservation laws are considered to be fundamental and universal principles that cannot be violated. However, there are some cases, such as in quantum mechanics, where these laws may appear to be violated due to the uncertainty principle or other factors.

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

Conservation laws are applied in a wide range of fields, from physics and engineering to biology and economics. They are used to analyze and understand natural phenomena, design efficient systems, and make predictions about the behavior of complex systems.

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