Find x: Solving a Spring Stretch Problem

[elunicornhunte]

Homework Statement

A relaxed spring is sitting on a horizontal surface. A block attached at one of its ends is kicked, with a horizontal velocity, v1, given to it. The block will move and stretch. Find the distance, x, the spring will stretch. See figure. Find x in meters.

http://i.imgur.com/tYyl3t4.png

Homework Equations

F=-kx

The Attempt at a Solution

I used the equation ω=v/r to find the angular velocity = 1 rad/sec. I then thought that the angular velocity produces a centripetal force, which is the driving force for the spring to stretch. This centripetal force can be found using a=(ω^2)*r which = 1 m/s^2. I however, do not know how to use this force to find how far a spring would stretch when said force is applied. Any help is appreciated!

 

[nasu]

You forgot the figure?

 

[elunicornhunte]

Fixed it, there's a link in the OP.

 

[nasu]

That angular speed is for un-stretched spring, right?
The centripetal force is the elastic force of the spring. And this happens when the spring is stretched. So you have to write the angular frequency for stretched spring (r>lo).

 

[HalfLostAndSearching]

Firstly, it is important to note that the given figure does not provide enough information to accurately solve for the distance x. We would need to know the spring constant and the mass of the block in order to use the equation F=-kx and solve for x.

However, assuming that these values are provided, your approach to finding the distance x is correct. The angular velocity, ω, is indeed related to the centripetal force, which is the force that causes the spring to stretch. However, the equation a=(ω^2)*r is not applicable in this scenario as it assumes a circular motion, which is not the case here.

Instead, we can use the equation F=ma to calculate the force acting on the spring. The mass, m, can be found using the given velocity, v1, and the spring constant, k, can be obtained from the given figure. Once we have the force, we can use the equation F=-kx and solve for x.

In summary, to find the distance x, we would need to use the equations F=ma and F=-kx, along with the given values of v1, k, and m, to solve for x. It is important to note that the values of v1, k, and m must be in consistent units (e.g. meters and kilograms) for the equations to work.