Momentum of spring between two objects

In summary, two carts with masses 5 kg and 2.5 kg are connected by a massless spring with a spring constant of 20 N/m on a frictionless surface. When the spring is compressed 1.2 m, it has a potential energy of 14.4 J. After the carts are released, their final speeds can be calculated using the conservation of energy and momentum equations, resulting in v1=2.94 m/s and v2=5.88 m/s. However, this calculation is incorrect as the kinetic energy should be calculated separately for each cart. After correcting this error, the final speeds are v1=3.67 m/s and v2=2.94 m/s.
  • #1
moonbase
21
0

Homework Statement


A massless spring of spring constant 20 N/m is placed between two carts on a frictionless surface. Cart 1 has a mass M1 = 5 kg and Cart 2 has a mass M2 = 2.5 kg. The carts are pushed toward one another until the spring is compressed a distance 1.2 m. The carts are then released and the spring pushes them apart. After the carts are free of the spring, what are their speeds?

Homework Equations


PEspring=0.5kx2
KE=0.5mv2=p2/2m
p=mv

The Attempt at a Solution


I plugged in the given values to find that the potential energy of the spring is 14.4 J. Since there is no friction, the energy is conserved and the resulting kinetic energy should be the same value, and plugging it into the equation in terms of momentum results in p=14.69 since momentum is also conserved. So when I plug that into p=mv, I get v1=2.94 and v2=5.88 but apparently these are incorrect. Am I skipping a step?
 
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  • #2
Your calculations are not correct. check it
 
  • #3
Well I'm trying to figure out where exactly I went wrong. What I did so far:

0.5*20*1.22=14.4 J

p2/2(7.5)=14.4 -> p2=216 -> p=14.69

v=p/m -> 14.69/5=2.94 m/s and 14.69/2.5=5.88 m/s

Any ideas?
 
  • #4
moon,

[tex]K=\frac{p^2}{2m_1}+\frac{p^2}{2m_2}[/tex]
 
  • #5
Oh okay, I was combining them but I see now. Thank you!
 

Related to Momentum of spring between two objects

What is momentum of spring between two objects?

Momentum of spring between two objects refers to the amount of force and motion that is transferred between the two objects as a result of the compression or expansion of a spring.

How is momentum of spring between two objects calculated?

The momentum of a spring between two objects can be calculated by multiplying the force applied to the spring by the distance it is compressed or expanded. This can be represented by the equation P = F*d, where P is momentum, F is force, and d is distance.

What factors affect the momentum of spring between two objects?

The momentum of a spring between two objects can be affected by various factors such as the mass of the objects, the stiffness of the spring, and the initial velocity of the objects.

How does the momentum of spring between two objects change over time?

The momentum of spring between two objects can change over time as the spring continues to compress or expand. Initially, the momentum increases as the spring is compressed or expanded, but it decreases as the objects move away from each other and the spring returns to its original state.

What are the real-life applications of momentum of spring between two objects?

The concept of momentum of spring between two objects is commonly applied in various fields such as physics, engineering, and mechanics. It can be used to analyze and design systems that involve springs, such as shock absorbers, car suspension systems, and even trampolines.

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