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

In summary, the stretch of a spring connecting two masses can be calculated using Hooke's Law, which states that the force exerted by a spring is proportional to its displacement from the equilibrium position. When one mass is pulled, it creates tension in the spring, leading to a stretch that depends on the spring constant and the force applied. The resulting stretch can be determined by the formula \( F = k \cdot x \), where \( F \) is the applied force, \( k \) is the spring constant, and \( x \) is the stretch of the spring. The system's dynamics, including the masses and any friction, also influence the final displacement.
  • #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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FAQ: 2 masses connected by spring, one is pulled, how much does the spring stretch?

What is Hooke's Law and how does it apply to this problem?

Hooke's Law states that the force exerted by a spring is directly proportional to its extension or compression from its natural length, given by F = -kx, where k is the spring constant and x is the displacement. In this problem, when one mass is pulled, the spring stretches, creating a restoring force that follows Hooke's Law.

How do you determine the effective force acting on the spring?

The effective force acting on the spring is determined by the external force applied to the mass that is being pulled. If a force F is applied to one of the masses, this force will be transmitted through the spring, causing it to stretch. The spring's extension can then be calculated using Hooke's Law.

What are the equations of motion for the masses connected by the spring?

For two masses m1 and m2 connected by a spring with spring constant k, the equations of motion can be written as:\[ m1 * a1 = -k * (x1 - x2) \]\[ m2 * a2 = k * (x1 - x2) \]where x1 and x2 are the displacements of masses m1 and m2 from their equilibrium positions, and a1 and a2 are their accelerations.

How do you calculate the spring stretch when one mass is pulled?

To calculate the spring stretch, you need to know the force applied and the spring constant. Using Hooke's Law, the stretch Δx of the spring can be found by rearranging the formula to Δx = F / k, where F is the force applied to the mass and k is the spring constant.

What factors influence the amount of stretch in the spring?

The amount of stretch in the spring is influenced by the spring constant (k), the magnitude of the applied force (F), and the initial conditions of the system such as the masses of the connected objects and their initial displacements. A stiffer spring (higher k) will stretch less for a given force, while a larger applied force will result in a greater stretch.

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