# Proving Conservation of Energy & Momentum in Free Space Collisions

• supersymm88
This indicates that the original premise, that the electrons simply bounce apart, must be true. In summary, the two problems involve using equations and conditions to find solutions. The first problem involves setting up an inequality to determine when the lower block will leave the floor, while the second problem involves using conservation of energy and momentum to show that a contradiction results, proving that electrons simply bounce apart when they collide in free space.
supersymm88
Please do not answer these, just give hints
A block of mass M is connected to a second block of mass m by a linear spinrg of natural length 8a. When the system is in equilibrium with the first block on the floor, and with the spring and second block vertically above it, the length of the spring is 7a. The upper block is then pressed down until the spring has half its natural length and is then released from rest. Show that the lower block will leave the floor if M<2m.

A simple but violent reaction is H+H->H2+5eV. However when two electrons collide in free space they simply bounce apart. Can you prove this, using conservation of energy and momentum, i.e. show that a contradiction results.

For the first problem, you can use the equations for the potential energy and force of a spring to set up an equation relating the masses and lengths of the spring in the two different states. Then, use the condition that the spring is released from rest to find the velocity of the second block at the moment it leaves the floor. Finally, use the condition that the velocity must be greater than zero for the block to leave the floor to set up an inequality involving the masses.

For the second problem, you can use the conservation of energy and momentum equations to set up a system of equations for the initial and final states of the electrons. Then, use the condition that the final state has a higher total energy to show that a contradiction results.

Hint 1: In order to prove conservation of energy and momentum, you will need to use the equations for kinetic energy and momentum, as well as the concept of elastic collisions.

Hint 2: For the first scenario, consider the initial and final states of the system and apply the equations for conservation of energy and momentum. Use the given information about the natural length of the spring and the position of the blocks to solve for the velocities of the blocks.

Hint 3: For the second scenario, consider the initial and final states of the system and apply the equations for conservation of energy and momentum. Use the given information about the reactants and products to solve for the kinetic energy and momentum of the particles before and after the collision.

## 1. How is conservation of energy and momentum defined in free space collisions?

In free space collisions, conservation of energy and momentum means that the total energy and momentum of the system before and after the collision remains constant. This means that the total kinetic energy and the total momentum of all objects involved in the collision will be the same before and after the collision.

## 2. What is the significance of conservation of energy and momentum in free space collisions?

Conservation of energy and momentum is a fundamental principle in physics that helps us understand how objects interact and behave in collisions. It allows us to make predictions and calculations about the outcome of a collision and is essential in many areas of physics, including mechanics and thermodynamics.

## 3. How is conservation of energy and momentum proven in free space collisions?

In order to prove conservation of energy and momentum in free space collisions, we use equations such as the conservation of energy equation (KEi + PEi = KEf + PEf) and the conservation of momentum equation (Pi = Pf), where KE is kinetic energy, PE is potential energy, and P is momentum. These equations allow us to calculate and compare the total energy and momentum before and after the collision to show that they remain constant.

## 4. Can conservation of energy and momentum be violated in free space collisions?

In theory, conservation of energy and momentum cannot be violated in free space collisions. However, in reality, there may be small losses of energy and momentum due to factors such as friction and air resistance. These losses are typically negligible and do not significantly affect the overall conservation of energy and momentum in the system.

## 5. How does the conservation of energy and momentum apply to real-life collisions?

The conservation of energy and momentum applies to all types of collisions, including real-life collisions. In real-life collisions, there may be external forces and factors that affect the outcome of the collision, but the principles of conservation of energy and momentum still apply. By understanding and applying these principles, we can accurately predict and analyze the behavior of objects in collisions in various real-life scenarios.

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