2 masses connected by spring, one is pulled, how much does the spring stretch?

  • #1
Obliv
52
1
Homework Statement
The masses are connected by a massless spring on a frictionless surface. One of the masses is pulled by a force F, how much does the spring stretch if at all?
Relevant Equations
F = ma, F = -kx
View attachment 332091
Hi, I am having trouble with this problem. I'm thinking the solution is this but I'm not sure. Fnet=m1a+m2aFnet=m1a+m2a , m1a=kxm1a=kx, m2a=F−kxm2a=F−kx so x=m1ak=−(m2a−F)kx=m1ak=−(m2a−F)k
 
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  • #2
nvm
 
  • #3
So what answer did you finally get? Does it reduce to what you would expect in the limiting cases ##m_1<<m_2## and ##m_1>>m_2##?
 
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Likes MatinSAR and PeroK
  • #4
... I suggest first assuming that ##m_1## is so large that it doesn't move. That gives you an easier problem to get you started.
 
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Likes MatinSAR

1. What is the equation for calculating the spring stretch?

The equation for calculating the spring stretch is F = kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

2. How does the mass of the pulled object affect the spring stretch?

The mass of the pulled object does not directly affect the spring stretch. However, it does affect the force applied to the spring, which in turn affects the spring stretch according to the equation F = kx.

3. What is the spring constant and how does it impact the spring stretch?

The spring constant, represented by the symbol k, is a measure of the stiffness of the spring. A higher spring constant means the spring is stiffer and will stretch less for a given force, while a lower spring constant means the spring is more flexible and will stretch more for the same force.

4. Can the spring stretch be negative?

Yes, the spring stretch can be negative. This indicates that the spring has been compressed rather than stretched. The negative value simply means that the displacement of the spring is in the opposite direction of the applied force.

5. Is the spring stretch affected by the distance the spring is pulled?

Yes, the spring stretch is affected by the distance the spring is pulled. According to Hooke's law, the spring stretch is directly proportional to the distance the spring is pulled. This means that the more the spring is pulled, the more it will stretch.

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