Find Distance Compressed by Spring w/ Kinetic Friction

[senseandsanity]

How do you find the distance a spring is compressed by an object when kinetic friction is involved?

 

[dextercioby]

How do you find the distance a spring is compressed by an object when kinetic friction is involved?

Write Newton's second principle of dynamics in mathematical form including all the forces (they are only 2:the friction and the elastic force).To integrate the resulting ODE equation,your friction force must depend linearly on the speed (the example of viscous Stokes forces in fluids).From there,u'll find how the spring will oscilate.

The spring's compression understood as the amplitude of oscillation will decrease exponentially with time,so,eventually (for asymptotic times:t->+infinity),due to friction,the oscillations will stop and the body will stop as well.Where??That's impossible to tell,if u're in the "sin/cos" regime of oscillation.

 

[wais]

To find the distance a spring is compressed by an object when kinetic friction is involved, we can use the following equation:

x = (W - μkN) / k

where x is the distance the spring is compressed, W is the weight of the object, μk is the coefficient of kinetic friction, N is the normal force, and k is the spring constant.

First, we need to determine the normal force acting on the object. This can be done by using the equation N = mg, where m is the mass of the object and g is the acceleration due to gravity.

Next, we need to determine the weight of the object, which is simply the mass of the object multiplied by the acceleration due to gravity.

Once we have these values, we can plug them into the equation to find the distance the spring is compressed. The coefficient of kinetic friction, μk, can be found by conducting experiments or by looking it up in a table.

It is important to note that this equation only applies when the object is in motion and experiencing kinetic friction. If the object is at rest, then we need to use the equation for static friction to calculate the distance the spring is compressed.

In summary, to find the distance a spring is compressed by an object when kinetic friction is involved, we need to use the equation x = (W - μkN) / k, where W is the weight of the object, μk is the coefficient of kinetic friction, N is the normal force, and k is the spring constant.