Last Stretch of Junior Year Day 39 - AP Physics Studying

I was watching this A-team episode as a way to study for my physics quiz tomorrow:


This is an excerpt where Face and B.A. are basically coaching football, which is a rather amusing start to the episode.

Just so that this post is related to physics, I'll go ahead and blabber on about it, talking about this excerpt in terms of physics.

1.  So a football player tackles someone else.  Force is equal to change in momentum over time.  So we'll use 70 kg as the mass of football player number 1 and 70 kg as the mass of football player number 2.  Number 1 is running towards number 2 as shown in the diagram:

So let's say that player 1 is running at 4.5 m/s, which is about 10 mph.  He collides into number 2.  Newton's second law states that Force = mass x acceleration and Newton's third law states that every force has an equal and opposite reaction.  And by altering the equation F = ma, we get F = m(v/t), and then we get F = p/t.  We'll assume that if the football player didn't wear any padding, he would come to a stop in 2.0 ms.  That means a momentum of 70 kg x 4.5 m/s = 315 kg x m/s to 0 kg x m/s in 0.02 s.  That would be a force of 15750 N, or 3540 lbf.  And this is totally why football players need a whole lot of padding, and why it's a physically demanding sport. (Yeah, I know I simplified the example, typically you'd have x and y components, and thus it would be a collision in two dimensions problem, and football players tend to fall down, so the change in momentum would be less.)

2. The whistle that Face was blowing...so sound travels at a speed of Mach 1.  Yeah, like that says anything.  The speed of a wave traveling through air would be velocity = wavelength x frequency.  Thus by the Doppler effect, some football players will hear a higher pitched sound, some will hear a lower pitched sound, and others will hear the sound that Face is hearing.  That's because they are running away from Face, running towards Face, and staying in place, respectively.

3. We can see the grass as green, because light from the sun is reflected to our eyes by the blades of grass.    It is in the visible spectrum of electromagnetic waves.  It's wavelength is around 520–570 nm, and thus the frequency is around 5.504 x 10^14 Hz.  And thus the energy of a photon of green light (slightly off topic by I don't care), would be given by E = hf, so E = (6.63 x 10^-34 J s)(5.504 x 10^14 Hz), and 3.64 x 10-19 J.

4. All those gold chains B.A. is wearing is pretty heavy.  But it also will get pretty hot in the sun, and they will expand a bit because of thermal expansion.  That is given by the equation (change in length) = (coefficient of linear expansion) x (initial length) x (change in temperature).  The coefficient of linear expansion of gold is 14 x 10^-6 (C°)^-1.  We'll just say that initially B.A. had about 4 meters of gold, at 20°C.  And since he's in the sun, let's say the gold is now at 25°C.  That's a change of 5 C°.  So uh L = (14 x 10^-6 (C°)^-1) x (4 m) x (5 C°) = 0.28 mm.  So the gold doesn't expand too much.

5. Just for the heck of it, the A-team always gets into gun fights with bad guys.  Back in the day, people measured the speed of bullets using ballistic pendulums.  Basically this is would be a conservation of momentum problem - total momentum before = total momentum after.  Since the pendulum rises, we will also need conservation of energy - KE + PE before collision = KE + PE at pendulum's maximum height. then pugging in known quantities will give us 1/2(m + M)v^2 + 0 = 0 + (m + M)gh.

6. Also just for the heck of it, Murdock is the pilot for the team, even if B.A. ain't getin in no plane. So Bernoulli's equation gives us: P + 1/2pv^2 + pgy = constant.  And in a special case of Bernoulli's equation when afluid flows horizontally with no change in height, we get P sub 1 + 1/2 p sub 1 v sub 1 squared = P sub 2 + 1/2 p sub 1 v sub 1 squared, saying that when the speed is high when the pressure is low.  Because airfoils are designed to make air flow faster on the top of the airfoil than on the bottom, we get a net upwards force, and thus get dynamic lift.  This is probably too complicated for the AP test anyway, and I don't understand all of this anyway.

Alright, so I talked about Newtonian mechanics, sound, heat and fluids.  That's too much studying for one night.