# Conservation of momentum & energy

• Jngo22
In summary, the problem involves two blocks colliding on a frictionless table, with one block attached to a compressed spring. Using conservation of momentum and energy, the maximum compression of the spring can be calculated to be 0.250 m.
Jngo22

## Homework Statement

A block of mass m1 = 2 kg slides along a frictionless table with speed 10 m/s. Directly in front of it, and moving in the same direction with a speed of 3 m/s is a block of mass m2 = 5kg. A massless spring with spring constant k = 1120 N/m is attached to the second block. The spring is compressed a maximum amount x. What is the value of x?

## Homework Equations

m1v1 + m2v2 = m1vf1 + m2vf2
KEi = KEf + 1/2kx^2

## The Attempt at a Solution

I knew that there would be a maximum compression of the spring when the first block has velocity = 0 m/s. I used cons. of momentum :
(2 kg)(10 m/s) + (5 kg)(3 m/s) = (5 kg)(Vf) to find Vf = 7 m/s
then used cons. of energy:
(0.5)(5 kg)(7 m/s)^2 = 1/2(1120)x^2
and got x = 0.4677 m

but the correct answer is 0.250 m
can anyone help me find the correct answer

After collision both the masses move together until the compression is maximum. At that instant the common velocity is given by
m1v1 + m2v2 = (m1+m2)vf.
Applying the conservation of energy, you can write
m1v1^2 + m2v2^2 = (m1+m2)vf^2 +1/2*k*x^2.
Now proceed to find x.

?

As a scientist, it is important to always double check your equations and calculations to ensure that your answer is accurate. In this case, it seems that there may have been an error in your calculation for the final velocity (Vf). It should be noted that the conservation of momentum equation only applies to systems without any external forces acting on them, and in this scenario, the spring is an external force. Therefore, the equation should be modified to include the force from the spring, which is equal to kx. This would result in the following equation:

m1v1 + m2v2 = m1vf1 + m2vf2 + kx

Using this equation and your values for the masses and initial velocities, we can solve for the final velocity and then plug it into the conservation of energy equation to find the correct value for x. Additionally, be sure to use the correct units throughout your calculations to avoid any errors.

## What is the law of conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. This means that momentum cannot be created or destroyed, it can only be transferred between objects.

## What is the difference between conservation of momentum and conservation of energy?

The conservation of momentum and conservation of energy are both fundamental laws of physics, but they are based on different principles. Conservation of momentum is based on Newton's third law of motion, while conservation of energy is based on the principle of energy conservation. Momentum is a measure of an object's motion, while energy is a measure of an object's ability to do work.

## How is conservation of momentum and energy applied in real-world situations?

Conservation of momentum and energy are applied in various real-world situations, such as collisions between two objects, explosions, and motion of particles in a system. These laws are used in fields such as engineering, physics, and mechanics to understand and predict the behavior of objects and systems.

## What are some examples of conservation of momentum and energy in everyday life?

Some common examples of conservation of momentum and energy in everyday life include a car collision, a game of billiards, a rollercoaster, and a pendulum. In each of these situations, the total momentum and energy before and after the event remains the same, demonstrating the conservation of these quantities.

## What happens when conservation of momentum and energy are not observed?

When conservation of momentum and energy are not observed, it can lead to unexpected or unpredictable outcomes. For example, in a car collision, if the total momentum is not conserved, one car may experience a greater force than the other, leading to more damage and potential injuries. In a system where energy is not conserved, some energy may be lost as heat or sound, which can affect the final outcome of the system.

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