Conservation of Energy Challenge Problem

Keep up the good work!In summary, a 2.0 kg cart with a spring attached to its front rolls at 4.0 m/s towards a stationary 1.0 kg cart. The maximum compression of the spring during the collision is 0.046 m. For the second part, the final relative velocity is equal to the initial relative velocity and using the conservation of momentum, two equations can be formed to solve for the final speed of each cart. Alternatively, conservation of total kinetic energy can also be used.
  • #1
bcjochim07
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Homework Statement


A 2.0 kg cart has a sping with k= 5000 N/m attached to its front, parallel to the ground. This cart rolls at 4.0 m/s toward a stationary 1.0 kg cart.

a) What is the maximum compression of the spring during the collision?

b) What is the speed of each cart after the collision?


Homework Equations



KE=(1/2)mv^2 Us=(1/2)kx^2

The Attempt at a Solution



I got the first part:

Using first conservation of momentum and assuming the cars stick together momentarily
then using conservation of energy

(2kg)(4m/s)=(3kg)v1
v1= 2.67 m/s
(.5)(2kg)(4m/s)^2=(.5)(5000N/m)(x)^2 + (.5)(3kg)(2.67m/s)^2
x= .046 m

But I'm not sure what to do with the second part. Any suggestions?
 
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  • #2
But I'm not sure what to do with the second part. Any suggestions?

That's the easiest part. Since this was a completely elastic collision, the elastic co-eff =1. So, final relative velocity = initial relative velocity. This, combined with the conservation of momentum, gives you two unknowns with two eqns.

Of course, you can also use conservation of total KE, but that's lengthier.

Good job in solving part A.
 
  • #3


Great job on solving the first part of the problem! For the second part, we can use the conservation of momentum again to find the final velocity of the combined carts. Since they stick together, the final mass will be 3 kg. We can set up the equation as follows:

(2kg)(4m/s) + (1kg)(0m/s) = (3kg)(vf)

Solving for vf, we get:

vf = 2.67 m/s

This matches the velocity we found for the first cart in the first part of the problem. Therefore, after the collision, both carts will have the same velocity of 2.67 m/s. This makes sense because the collision is elastic and the carts stick together, so they will have a common velocity after the collision.

Great job on solving the problem! Keep up the good work.
 

What is the Conservation of Energy Challenge Problem?

The Conservation of Energy Challenge Problem is a theoretical physics problem that challenges scientists to find solutions for a system that violates the law of conservation of energy.

Why is the Conservation of Energy Challenge Problem important?

The Conservation of Energy Challenge Problem is important because it tests our understanding of one of the fundamental laws of physics and helps to identify any gaps or limitations in our current knowledge.

What are some common approaches to solving the Conservation of Energy Challenge Problem?

Some common approaches to solving the Conservation of Energy Challenge Problem include using mathematical equations, conducting experiments, and using computer simulations.

What are some real-life applications of the Conservation of Energy Challenge Problem?

The Conservation of Energy Challenge Problem has real-life applications in fields such as renewable energy, quantum mechanics, and astrophysics. By understanding the limitations of the law of conservation of energy, scientists can develop more efficient and innovative solutions for energy production and use.

What are some future implications of solving the Conservation of Energy Challenge Problem?

Solving the Conservation of Energy Challenge Problem could lead to a deeper understanding of the laws of physics and potentially open up new possibilities for energy production and utilization. It may also have implications for our understanding of the universe and fundamental principles of nature.

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