# Relationship between kinetic energy and static friction

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!

• I've never heard it described that way. I've always just heard static friction is when it's stationary, kinetic friction when it's moving. AFAIK there's no velocity threshold where it just stops. – JMac Mar 20 '17 at 17:10
• @JMac I thought that as well, it's just the way the problem is described. Why mention static friction at all, when the initial velocity is not zero. – E. l4d3 Mar 20 '17 at 17:14
• You can use static friction to make sure it doesn't slide back down the ramp. As far as I can tell that is why it is there. – JMac Mar 20 '17 at 17:15
• Obviously, the puck only gets 'locked' with static friction if its velocity is zero, so the lowest speed is zero. From an experimental perspective, this would be an aiming nightmare. From a pencil and paper perspective, it's the standard how steep can the ramp be question. – user121330 Mar 20 '17 at 17:20
• @user121330 I think his assumption was there was some cutoff velocity where static friction took over and forced the puck to stop. It's a weird assumption, but given the details of the question I can kinda see why he thought it was relevant during motion. – JMac Mar 20 '17 at 17:31

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.

• @user80556 The height reached, then, will be zero. Why? :) – Rafa Budría Mar 20 '17 at 18:17
• @RafaBudría The maximum height reached will not be zero, because the initial velocity is not zero. Static friction does not apply until the puck has stopped moving. – sammy gerbil Mar 20 '17 at 18:41
• @user80556 sammy: test the numbers into your inequality :) Not sure what "reach" means exactly in this context because the numbers in the problem are very fine tuned and, at the very least, if you don't touch anything, the block will be at height zero. I call this type of problems "a teachers joke", very serious problems, but with a funny surprise inside (jokes that rarely students appreciate :D – Rafa Budría Mar 20 '17 at 19:25
• @user80556 sammy: I'd like to know verbatim the problem's wording. – Rafa Budría Mar 20 '17 at 19:33
• @RafaBudría The joke is lost on me. Initial velocity is > 0 so the puck has to travel a distance > 0 before it loses any KE. You seem to be claiming that the puck does not move from its starting point. The problem seems clear enough to me. – sammy gerbil Mar 20 '17 at 20:27

Static friction would only applies when an object is stationary - so when it has not moved yet. Kinetic friction applies when an object is moving.

In your example, just kinetic friction would be acting on the object until it stopped, and then once the object has stopped just static friction acts on it. The time period when static friction takes over is infinitesimal, and for practical purposes you just work with kinetic friction when an object is in motion. Only work with static friction when you have a problem that involves an object starting at rest.

Philosophically, you could perhaps argue an object never really stops moving... heard of Zeno's paradox? :) But for mechanical physics that obviously doesn't apply, so you would just work with Kinetic Friction.