Introductory Work due to Friction equals Change in Mechanical Energy Problem
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Introductory Work due to Friction equals Change in Mechanical Energy Problem

November 11, 2019


– Good morning. Bo, could you please read the problem, and Bobby, could you please translate? ♫ Flipping Physics ♫ – On a level surface, a street hockey puck is given an initial velocity of -3.2 meters per second and slides to a stop. – Please stop. Velocity initial equals
-3.2 meters per second, and velocity final equals zero. – Bo, please continue. – If the coefficient of kinetic friction between the puck and the surface is 0.60, how far did the puck slide? – Mu k equals 0.60, and delta x equals question mark; although, it’s just how
far, so just the magnitude of the displacement. – I want my two dollars. – Correct. Bobby, why is the initial
velocity of the puck negative? – Because the puck is moving to the left? – Yes, the initial velocity is negative, because the puck is moving to the left. Now we have solved
problems like this before using Newton’s Second Law and the Uniformly Accelerated Motion equations; however, today we are
going to use the equation work due to friction equals
change in mechanical energy to solve this problem. Billy, how do we know
we can use this equation to solve this problem? – Because there is work done
by the force of friction; however, there is no work
done by a force applied. – Yes, we can use the work due to friction equals change in
mechanical energy equation when there is work done by friction, however, there is no work
done by the force applied. Bo, could you please expand the work due to friction equation? – Okay. Work due to friction equals force of kinetic friction
times displacement times cosine theta, and the
change in mechanical energy equals mechanical energy final minus mechanical energy initial. – Billy, before we can use this equation– – You cut your hair. – [Bo] Nope
– Yes you did, Bo! You cut your hair! – No, I did not. – Bo did not cut his hair. Bo got his hair cut. – (laughs) So did I. Can we get back to the physics please? (laughing) Billy, before
we can use this equation, what do we need to do? – We need to identify the locations of the initial and final points and the horizontal zero line. – Then could you all
please identify those? – Okay, let’s set the initial point where the puck leaves your hand. – And the final point
where the puck stops. – And let’s set the horizontal zero line at the height of the
center of mass of the puck. – Great, now we can
work with the equation. Bobby, what can we do
with the left-hand side? – We can substitute the
coefficient of kinetic friction times force normal for the
force of kinetic friction, and the displacement
of puck is to the left, and the force of kinetic friction is to the right, and the angle between those two directions is 180 degrees, so theta equals 180 degrees. – All right, now, the
right-hand side of this equation is very similar to conservation
of mechanical energy. And we have worked a lot by now with conservation of mechanical energy. We’ve even taken a quiz on conservation of mechanical energy,
which means, at this point, I’m going to say we can graduate. And rather than listing all the energies which could possibly be there, we are only going to list the energies which actually are there. Is everybody okay with that? – [Billy] I’m okay with that.
– [Bo] About time. – Can we still list all the energies if we feel more comfortable
doing it that way? – Absolutely, Bobby. If you would like to, you may
still list all the energies which could possibly be
there, but you do not have to. Billy, could you please tell
me, initially and finally, which energies are there
and are not there, and why? – Okay, there is no spring, so
no elastic potential energy, initial or final. The height of the puck is zero,
both initially and finally, so there is no gravitational
potential energy at all. The final velocity of the puck is zero, so the kinetic energy final is zero; however, the initial velocity
of the puck is not zero, so the initial kinetic energy is not zero. Is that really true? There is no final mechanical energy, and the only energy initial
is the kinetic energy? – Yes, that is true, there is
zero final mechanical energy, and the only initial mechanical
energy is kinetic energy, so zero minus one half mass
times velocity initial squared. But where did all that
initial kinetic energy go? (sliding puck) – Oh you can hear it. Some of the kinetic energy becomes sound. – And some of the kinetic
energy becomes heat. The puck is warmer after
sliding along the table, just like your hands heat up
when you rub them together. – [mr.p] Yes, all that initial
kinetic energy is dissipated as heat and sound. So let’s put that equation
in our equation holster. And Bo, please go through the
equation from left to right, and tell me which variables
we do and do not know. – We know the coefficient
of kinetic friction. We don’t know the force
normal or the displacement. The cosine of 180 degrees is negative one. We don’t know the mass of the puck. We do know the velocity initial. Oh (laughs), we need to
draw a free body diagram and sum the forces to solve
for the force normal, right? – Correct. Bobby, could you please do that? – Sure. The force normal is up, the force of gravity is down, the force of kinetic
friction is to the right, and the force applied by
your hand is to the left. – [Mr. P] So you’re talking
about the force applied by your hand? – Right, sorry, your hand
is not touching the puck while it is sliding to a stop,
so there is no force applied in the free body diagram, sorry. – [Mr. P] Bobby, you don’t need to apologize. That happens all the time. – Okay, we can sum the
forces in the y direction. The net force in the y direction equals force normal minus force of gravity, and the net force in the
y direction also equals mass times acceleration
in the y direction. Because the puck does not move up or down, the acceleration in the
y direction is zero. Therefore, the force normal
equals the force of gravity, which equals mass times the
acceleration due to gravity. – Bo, please keep going. – Using the equation from
the equation holster, we can substitute mass times
acceleration due to gravity for force normal, and, wait for it, everybody brought negative
mass to the party. (techno music) ♫ Everybody brought mass, mass ♫ – (laughs) And we are
left with the coefficient of kinetic friction times the
acceleration due to gravity times displacement is
equal to one half times the initial velocity squared. Bo, please keep going. – Divide both sides by
acceleration due to gravity and the coefficient of kinetic friction to get displacement equals
velocity initial squared divided by the quantity
two times acceleration due to gravity times the
coefficient of kinetic friction. With numbers, that is the quantity negative 3.2 squared divided by the quantity two times 9.81 times 0.60, which works out to be 0.869861, or with two significant digits, 0.87 meters. – Yes, thank you very much for– – Wait a second, the
puck moves to the left. The displacement should be negative. Our answer should be negative. I give up, why does this always happen? Why can’t we just get the right answer? – Bobby, chill out. We got the right answer. – That is true, Bo, please explain. – When using the work equation, you only use magnitudes of the
force and the displacement. So if you solve for the
force or the displacement in the work equation, you will only get the magnitude of that variable. – Right, so our answer is the magnitude of the displacement of the puck, which is the answer to how far the puck slid. Our answer is correct. – Absolutely. Thank you very much for
learning with me today. I enjoyed learning with you. – [Bobby] Does anybody
know where my pencil is?

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  1. I had to pause at 7:14 to make sense of an equation. Upon looking at your paused faces in the excitement of a mass party, I felt like bobby, bo and billy where all three unique people with their own reactions to the situation.

    Nice acting.

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