I am having trouble understanding the link between kinetic and static friction. Specifically how the force "locks down" or instantaneously stops an object before velocity is zero, after some time of kinetic friction slowing the object down.
In physics class, we were handed some problems to solve in which one of them was a hockey puck (117 grams) launched up an 34 degrees metal ramp. The coefficients of static and kinetic friction between the hockey puck and the metal ramp were $μ_s = 0,67$ and $μ_k = 0,22$. The puck's initial speed was $3,8 m/s$. What vertical height did the puck reach above its starting point?
I don't know how to determine the lowest speed of the puck before static friction "locks" it to the metal surface.
Edit: Apologies for posting this in /Mathematics, as it belongs in /Physics. Thanks for reading!
Kinetic friction acts till the object is in relative motion with the surface it is in contact with or has kinetic energy that is velocity(hence the name) and is always constant throughout the time it acts on the object. Whereas, static friction is the force that acts on the object when it is not in motion(or is at rest) and is self adjusting i.e. it adjusts its magnitude so as to be equal to the applied force till the limiting friction value.
As for the problem that is written in your post, its a fairly simple one but when you start Newton's Laws of Motion it might be very perturbing initially, so let me partially walk you though the problem so that you get a sens of how to interpret friction.
As the body has been projected with some velocity in the upward direction then static friction will not be acting on it, the one that will be acting is the kinetic friction which has a constant magnitude $f_{k}=\mu_{k}N$, where $N$ is the normal force exerted by the body on the surface on which it is moving, and acts til the object has "kinetic energy"(or velocity).
When the object has reached the farthest point on the ramp then its velocity will be zero. The moment the relative motion between the object and the ramp seizes static friction acts on the object. If the limiting value of the static friction is larger than the gravitational force along the ramp then there will no motion along the ramp and this point will be the highest point that the body reached.
As for the correct place to post this question I think it would be Physics Stack Exchange.