# Solving Spring-Carts Exploding: Find Speed of M1 & M2

• huskydc
In summary, a massless spring with a spring constant of 20 N/m is compressed by two carts, one with a mass of 5 kg and the other with a mass of 3.5 kg. After the carts are released, their speeds can be determined using conservation of energy and momentum. The initial and final energy and momentum can be equated to give two equations with two unknowns (v1 and v2), allowing for the calculation of the carts' speeds.
huskydc
A massless spring of spring constant 20 N/m is placed between two carts. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 3.5 kg. The carts are pushed toward one another until the spring is compressed a distance 1.8 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

i know both momentum and energy conservation applies here, but don't know where to start...
both carts are initially at rest,

so I'm guessing : PE(initial) = PE(final) + KE (final)

You are correct: Conservation of energy and momentum is the way to deal with this problem. So your starting point should be obvious: Write down the initial energy and momentum (these are known) and equate them to the final energy and momentum respectively. This will give you 2 equations in 2 unknowns (v1 and v2).

also, wouldn't PE final be zero too? after the carts are released, the spring would be relaxed again, thus no compression, thus zero..

that'll make it: initial PE = final KE

but i don't know where to go from here

Last edited:
That's right, the final potential energy of the spring is zero.
What are the expressions for the initial energy, initial momentum, final momentum and final energy?

now we have initial PE = final KE,

it goes...

.5kx^2 = .5m(1)v(1)^2 + .5m(2)v(2)^2

does it make sense? but the problem now is i have two variables to solve...one equation...

Don't forget conservation of momentum. That will give you the second equation that you need.

## 1. How do you solve for the speed of M1 and M2 in a spring-cart explosion?

The speed of M1 and M2 can be solved using the conservation of momentum and energy principles. The initial momentum and energy of the system can be compared to the final momentum and energy after the explosion to solve for the speeds of M1 and M2.

## 2. What information do you need to solve for the speed of M1 and M2 in a spring-cart explosion?

To solve for the speed of M1 and M2, you will need to know the masses of M1 and M2, as well as the initial velocity of the system before the explosion and any other relevant forces acting on the system.

## 3. Can the speed of M1 and M2 be solved if there are multiple explosions in the spring-cart system?

Yes, the speed of M1 and M2 can still be solved even if there are multiple explosions in the system. Each explosion can be treated as a separate event and the final speeds can be calculated by considering the momentum and energy changes of the system after each explosion.

## 4. Is there a specific formula or equation to solve for the speed of M1 and M2 in a spring-cart explosion?

Yes, there are specific equations that can be used to solve for the speed of M1 and M2 in a spring-cart explosion. These equations involve the conservation of momentum and energy principles and can be derived from Newton's laws of motion.

## 5. Are there any assumptions that need to be made when solving for the speed of M1 and M2 in a spring-cart explosion?

Yes, when solving for the speed of M1 and M2 in a spring-cart explosion, it is often assumed that the system is isolated and there are no external forces acting on the system. Additionally, it is assumed that the spring is an ideal spring with no energy losses due to friction.

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