Mass-Spring Systems and the Relationship Between Force, Displacement, and Energy

In summary, the conversation discusses a problem involving a mass attached to a spring on a frictionless surface with a constant applied force causing the mass to come to a momentary stop at 10 cm. There is a question about the relationship between the applied force and the distance traveled, and a question about what happens to the kinetic energy gained by the mass. It is determined that the kinetic energy becomes elastic potential energy and allows the mass to pass the point where the two forces are equal, causing oscillation in the system.
  • #1
Raios168
14
0

Homework Statement


A mass is attached to a spring which is mounted onto a wall. This mass is on a frictionless horizontal surface. You apply a CONSTANT force to the mass and it comes to a stop in 10 cm.

My question is, that since the mass comes to a stop in 10 cm then:
Force Applied = kx where x is 10/100 m

Is my reasoning correct? Thanks in advance
 
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  • #2
Hi Raios168. Please use the entire formatting template when you post a problem.

What happens to the kinetic energy that the mass gains while the spring force is less than the applied force?
 
  • #3
Is that the only question in the problem statement given to you; or, are there additional questions to be answered?
 
  • #4
JBA said:
Is that the only question in the problem statement given to you; or, are there additional questions to be answered?

This is not the entire question I just wanted to know if my thinking was correct. The entire question with the variables is as follows:

A mass (1.20 kg) is attached to a spring (k = 790 N/m) which is mounted onto a wall. This mass is on a frictionless horizontal surface. You apply a CONSTANT force to the mass while the spring is in the unstretched position and the mass comes to a momentary stop in 10 cm.
 
  • #5
gneill said:
Hi Raios168. Please use the entire formatting template when you post a problem.

What happens to the kinetic energy that the mass gains while the spring force is less than the applied force?

The kinetic energy becomes elastic potential energy doesn't it?
 
  • #6
Raios168 said:
This is not the entire question I just wanted to know if my thinking was correct.

It's impossible for us to tell that with only the information you've given us. We could guess, and if we guess wrong we do more damage than good.

Which is why you need to fill out the template.

Without the template we cannot help you.
 
  • #7
I think the key in the question is the "momentary stop". What provided the energy or (work) to get it to that point?
 
  • #8
Raios168 said:
The kinetic energy becomes elastic potential energy doesn't it?
It does. And the KE built up while the spring's force is less than the applied force allows the mass to pass the point where the two forces are equal. That's why mass-spring systems oscillate.
 

FAQ: Mass-Spring Systems and the Relationship Between Force, Displacement, and Energy

What is Hooke's Law?

Hooke's Law states that the force required to extend or compress a spring is directly proportional to the distance it is extended or compressed.

What is the equation for Hooke's Law?

The equation for Hooke's Law is F = -kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring.

How does the spring constant affect the force applied?

The spring constant, k, represents the stiffness of the spring. A higher spring constant means that more force is required to produce the same amount of displacement, while a lower spring constant requires less force.

What is the difference between a spring in tension and a spring in compression?

A spring in tension is when the force applied causes the spring to stretch, while a spring in compression is when the force applied causes the spring to compress. The direction of the force determines whether the spring is in tension or compression.

Can Hooke's Law be applied to other objects besides springs?

Yes, Hooke's Law can be applied to any object that exhibits elastic behavior, meaning it can be deformed and return to its original shape. This includes materials like rubber bands, metal wires, and even human bones and muscles.

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