# Conservation of Momentum and Mechanical Energy

• TG3
In summary, a 20 g projectile with an initial horizontal velocity of 100 m/s collides with a wood block of mass 0.402 kg attached to a massless spring with a spring constant of 143 N/m. Using the principles of conservation of momentum and energy, the maximum compression of the spring can be determined to be 0.26 meters. However, in the presence of friction, the kinetic energy of the block must also be considered, leading to a more complex calculation.
TG3

## Homework Statement

A projectile with a mass of 20 g has an initial horizontal velocity of 100 m/s when it hits and stops in a wood block of mass 0.402 kg. The block is sitting on a horizontal frictionless surface and is attached to a massless spring, initially relaxed, with spring constant 143 N/m. What is the maximum compression of the spring?

P= MV
K=1/2 MV^2
F=-kx

## The Attempt at a Solution

Initial Momentum of the Bullet = .02 x 100 = 2
Initial momentum of the Bullet/Wood system = 2 due to conservation of momentum.
2= .404 V
V= 4.95 m/s is the velocity of the block/bullet system.
K = 1/2 (.404) 4.95^2
K= 4.95 Due to conservation of Energy, this is also the amount of energy the spring exerts.
4.95 =143X
Wrong. I suspect the error in my calculation is near the end, but I don't know that for certain.

Thanks- once I used energy not force it was easy to find the distance. (.26 meters.)
In the second part though, there is friction (with a coefficient of friction of .25).

How do I deal with that using the energy relationship?

KE of block = PE gained by spring + work done against friction

## 1. What is conservation of momentum and mechanical energy?

Conservation of momentum and mechanical energy is a fundamental principle in physics that states that the total momentum and mechanical energy of a closed system remains constant over time, regardless of any internal changes or external forces acting on the system.

## 2. How does conservation of momentum apply to collisions?

In a collision between two objects, the total momentum of the system before and after the collision remains the same. This means that the momentum lost by one object is gained by the other, resulting in a balanced exchange of momentum.

## 3. What is the role of mechanical energy in conservation of momentum?

Mechanical energy, which is the sum of potential and kinetic energy, is also conserved in a closed system. This means that in a collision, the total mechanical energy before and after the collision remains the same, even if some energy is lost to other forms such as heat or sound.

## 4. How is conservation of momentum and mechanical energy used in real-world applications?

Conservation of momentum and mechanical energy are used in many real-world applications, such as designing car safety features, understanding the behavior of objects in space, and analyzing sports movements and impacts.

## 5. Can conservation of momentum and mechanical energy be violated?

No, conservation of momentum and mechanical energy are fundamental laws of physics and cannot be violated. However, they may appear to be violated in certain situations due to external factors like friction or external forces that are not accounted for in the system.

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