Let us look back at this conceptual question again. Try it on a piece of a paper first. Answer again then look at the worked out answer in the video below (followed by a live demo to prove the point).
Here is a demo related to the last conceptual question with the turntable.
The wall of death
We can also analyse the "wall of death" situation in more details. Again this is the
situation where you spin against a wall and the static friction is the only
thing holding you up.(look back at previous page).
Applying Newton's Law in the z direction, we must have that
<span><span>&lt;span&gt;&amp;lt;span&amp;gt;&amp;amp;lt;span&amp;amp;gt;&amp;amp;amp;lt;span&amp;amp;amp;gt;&amp;amp;amp;amp;lt;span&amp;amp;amp;amp;gt; f_s = mg &amp;amp;amp;amp;lt;/span&amp;amp;amp;amp;gt;&amp;amp;amp;lt;/span&amp;amp;amp;gt;&amp;amp;lt;/span&amp;amp;gt;&amp;lt;/span&amp;gt;&lt;/span&gt;</span></span>
If the static friction is at its maximum it must be that
f_s = f_{s,max} =\mu_s n
.
Interestingly the normal force is what provide the centripetal acceleration.
Newton's law in the r direction gives.
<span><span>&lt;span&gt;&amp;lt;span&amp;gt;&amp;amp;lt;span&amp;amp;gt;&amp;amp;amp;lt;span&amp;amp;amp;gt;&amp;amp;amp;amp;lt;span&amp;amp;amp;amp;gt; n = mv^2/r &amp;amp;amp;amp;lt;/span&amp;amp;amp;amp;gt;&amp;amp;amp;lt;/span&amp;amp;amp;gt;&amp;amp;lt;/span&amp;amp;gt;&amp;lt;/span&amp;gt;&lt;/span&gt;</span></span>
As you increase the velocity of the "wall of death", the normal force pushes
harder on you. This also means that the max static friction increases and you
are less likely to fall. As you lower the velocity, the normal decreases and
the max static friction also decreases. If the max static friction is below
the force of gravity, you fall.
So in the wall of death, there is a minimum speed.
f_s = mg < f_{s,max} = \mu_s n = \mu_s m v^2/r
or v> \sqrt{\frac{gr}{\mu_s}}
.
Water in the Bucket or the Loop-the-Loop
This scenario will come back again and again. It is described in the book
section 8.4 and I discussed it in this short video.