Spring Force as Centripetal Force?

In summary, when the mass is set into motion on an air table connected to a spring with a constant k, the radius of the circle it travels is found to be 0.15 m.
  • #1
lavenderbaby
5
0

Homework Statement



A 2.1 kg mass is connected to a spring with spring constant k=150 N/m and unstretched length 0.18 m. The pair are mounted on a frictionless air table, with the free end of the spring attached to a frictionless pivot. The mass is set into circular motion at 1.4 m/s. Find the radius of its path.

Homework Equations



Fs= -kx
Fc= mv^2/r

The Attempt at a Solution



Since the centripetal force that keeps the mass moving in a circle is provided by the spring, I set Fs = Fc. However, I only equated their magnitudes. Thus, I have this equation:

mv^2/r = kx
r = mv^2 / kx
r = (2.1kg)(1.4m/s)^2 / (150N/m)(0.18m) = 0.15 m

What I am not sure about is the value for x in the equation Fs = -kx. Since the x in the equation is the change in spring length after the spring has been compressed/stretched, the x here should be zero for an unstretched spring. But then, what is the significance of the 0.18 m?

Please let me know if my solution is correct or if I need to change the x.
Thanks in advance!
 
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  • #2
The force in the spring is kx, where x is the stretched distance beyond the initial 0.18 m unstretched length. So what would be the radius of the path?
 
  • #3
PhanthomJay said:
The force in the spring is kx, where x is the stretched distance beyond the initial 0.18 m unstretched length. So what would be the radius of the path?

Since the question states that the spring is unstretched, wouldn't the radius of the path be the unstretched length of the spring, which is 0.18 m?
 
  • #4
The question states that the spring is unstretched before it is set into motion. That 0.18 m is just the length of the spring you bought off the shelf, with no loading on it. Once you set it into motion with the mass on it, it will stretch due to the centripetal force acting on it as caused by the centripetal acceleration. Draw a quick sketch to find the equation of the radius of the circle in terms of the unstretched length and x.
 
  • #5
PhanthomJay said:
The question states that the spring is unstretched before it is set into motion. That 0.18 m is just the length of the spring you bought off the shelf, with no loading on it. Once you set it into motion with the mass on it, it will stretch due to the centripetal force acting on it as caused by the centripetal acceleration. Draw a quick sketch to find the equation of the radius of the circle in terms of the unstretched length and x.

Ohhhhh, I get it now! the stretched length must be (radius of path - unstretched length) then! Thanks a lot!
 

Related to Spring Force as Centripetal Force?

1. What is spring force as centripetal force?

Spring force as centripetal force refers to the force exerted by a spring on a rotating object, which is necessary to keep the object moving in a circular path.

2. How is spring force related to centripetal force?

Spring force is directly related to centripetal force, as it is the force responsible for maintaining the circular motion of an object. Without the spring force, the object would move in a straight line due to inertia.

3. What factors affect the spring force as centripetal force?

The spring force as centripetal force is affected by the mass of the object, the speed of rotation, and the stiffness of the spring. As the mass or speed increases, the spring force must also increase to maintain the circular motion.

4. How is the direction of spring force as centripetal force determined?

The direction of the spring force as centripetal force is always towards the center of the circular motion. This is because the force must act in a direction perpendicular to the velocity of the object to keep it moving in a circular path.

5. Can spring force be used as centripetal force in all cases?

No, spring force can only act as centripetal force if the object is attached to the spring and the spring is stretched or compressed as the object moves in a circular path. In other cases, other forces such as friction or tension may act as the centripetal force.

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