I am having trouble understanding the link between velocity 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 the static friction "locks" it to the metal surface.
Edit: Apologize if this is the wrong forum to post this kind of physics/math question. Not sure where it belongs. Thanks for reading!
Best Answer
While the puck is moving relative to the inclined plane, the coefficient of kinetic friction applies, regardless of how slow that relative motion is. At the highest point the puck has stopped moving and has lost all its KE. Using conservation of energy : initial KE of puck = increase in gravitational PE + work done against kinetic friction.
Static friction does not apply until the puck has stopped moving. The coefficient of static friction then determines whether the puck can start sliding again back down the plane. At this point you have to compare the force down the plane (the component of the weight of the puck down the plane) with the maximum force which static friction can apply up the plane. Sliding down the plane occurs when $\tan\theta > \mu_s$, where $\theta$ is the angle of inclination of the plane to the horizontal. This criterion applies regardless of the value of $\mu_k$, even if $\mu_k < \mu_s$.
If the puck does start sliding back down the plane, static friction no longer applies, only kinetic friction, as soon as there is relative motion, no matter how small. The 2 types of friction never apply at the same time between the same 2 surfaces.