BLUE 42! HUT! HIKE! Football players know a lot about momentum, and so do students of physics. We look at the momentum of a linebacker and a quarterback throughout a play.
BLUE 42! HUT! HIKE! Football players know a lot about momentum, and so do students of physics. We look at the momentum of a linebacker and a quarterback throughout a play. (0:41) Different collision types are discussed. (2:35) We then look at the algebraic solution to a momentum problem. (4:31) Good ole’ Kinetic Energy has a cameo, and we look at how energy can change during a collision. (6:14) Graphs of velocity vs. time and momentum vs. time are also evaluated. (6:53)
The Question of the Day asks: (8:46) If a lab cart of mass “M” traveling at velocity “vo” collides inelastically with a stationary lab cart of mass “3M”, what will the velocity be after the collision?
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Hi and welcome to the APsolute RecAP: Physics 1 Edition. Today’s episode will focus on linear momentum, collisions, and the graphs associated.
Let’s Zoom out:
Unit 5 – Momentum
Topic 5.2-5.4
Big Idea – Force Interactions, Change, and Conservation
The linebacker on your school’s football team charges full speed at the opposing team’s quarterback, who happens to be half the mass of the linebacker. The linebacker jumps and wraps his arms around the quarterback while tackling him. Both players continue on in the same direction that the linebacker was initially running, with the quarterback now traveling backward. Why is this the case? Are the two players moving at the same speed as the linebacker was moving before tackling?
Let’s Zoom in:
Sometimes, in our everyday language, it is common to say that someone or something has a lot of momentum. But, what does that mean? Sure the linebacker has a lot of momentum, but why? What is it about the linebacker that gives him momentum? Momentum is the product of an object’s mass and velocity. A realistic mass for our linebacker would be 140 kg. A quarterback could have a mass of 70 kg. If the linebacker was running with a forward velocity of 10 m/s, then he would have had a momentum of 1400 kg*m/s. For the quarterback to match the momentum of the linebacker, he would have to run twice as fast, or 20 m/s, since he has half as much mass.
There is no cute name for the units of momentum, it is just kg*m/s. Who knows, maybe someday it will be renamed after our author Ryan, or maybe in your honor if your contributions to physics are great enough! Another thing that is very important to point out is that momentum is a vector, meaning that it has both magnitude and direction. In our linebacker example, the forward velocity causes the momentum to also be in the forward or positive direction. Meanwhile, our quarterback had a velocity of 0 m/s, therefore he had a momentum of 0 kg*m/s before the collision.
Collisions come in a few varieties. The two most important to know and to understand are perfectly elastic and perfectly inelastic collisions. Elastic collisions are when the objects involved move separately throughout the entire collision. Another telling sign that a collision is elastic is that the energy is conserved during the collision. An inelastic collision by contrast is a collision where energy changes throughout the collision, and the objects at some point are moving together with the same velocity. Regardless of the type of collision occurring, momentum is conserved throughout the interaction assuming there is no external force applied to the system. Similar to energy, it is important to define the system you are evaluating. In the case of our linebacker and quarterback example, it would make sense to look at the two players as the system. However, we could isolate just the linebacker and say that he is the system we are evaluating, or we could isolate the quarterback.
The most important thing for us to remember when looking at any situation involving more than one object, is that we need to account for all of the momentum before and after a collision. With our linebacker/quarterback example, the linebacker had +1400 kg*m/s of momentum before the collision, and the quarterback had 0 kg*m/s. The linebacker-quaterback system therefore had, and will continue to have +1400 kg*m/s after the collision. After colliding, the two players are wrapped together in a tackle and therefore must be moving with the same velocity (v). So, after the collision the linebacker has a momentum of 140kg*v and the quarterback has a momentum of 70kg*v. The system’s momentum is 210kg*v. With some division, we can find the final velocity of both players to be +6.67 m/s.
Knowing their final velocities, we can see that the linebacker slows down and loses momentum in the positive direction. His new momentum is +933.3 kg*m/s. The quarterback gains momentum, and his new momentum is +466.7 kg*m/s. WHOA! That’s the same amount that the linebacker lost! THAT is conservation of momentum. Although the momentum of the individuals changed, the momentum of the system was conserved. The system’s momentum is still +1400 kg*m/s.
Analyzing the kinetic energies of each player would result in finding that the linebacker had 7000 J initially before colliding with the quarterback. After the collision, the linebacker only had 3111 J of energy while the quarterback had 1556 J of energy. This means that 2333 J of energy was lost during the collision. Momentum is conserved during all types of collisions, while energy is not conserved during inelastic collisions. This is why momentum should always be your first choice when solving any problem, especially collisions.
Sometimes it makes sense to represent the momentum of objects not just algebraically, but graphically too. One way we could represent the motion of the two football players is on a velocity vs. time graph. The linebacker would have a horizontal line at +10 m/s until the time that the collision occurred, and then his velocity would abruptly (almost instantly, but not quite since all things take time) change to +6.67 m/s where it would remain - assuming no external forces slow the player down. The quarterback, by contrast, would start at rest and then rise abruptly at the time of the collision to +6.67 m/s. Of course, knowing the masses of each player would also allow us to graph their momentum vs. time. The shapes of these graphs would mimic the shape of each player’s velocity vs. time graphs since their masses are constant throughout the problem. The linebacker would have a negative slope during the collision, while the quarterback would have a positive slope. I wonder what units the slope of the momentum vs time graph would have? Graphing momentum on the vertical y-axis and time on the horizontal x-axis would create a slope (rise over run) of kg*m/s all over seconds or kg*(m/s^2)... or… NEWTONS?!?!? But, that leaves plenty to discuss during the next episode.
To Recap…
Momentum is the product of mass and velocity, and is measured in kg*m/s. Momentum is conserved for any closed system. There are two types of collisions, elastic and inelastic. Energy is only conserved in elastic collisions, while momentum is conserved in both collisions assuming there are no external forces applied.
Coming up next on the APsolute RecAP Physics 1 Edition, impulse and graphs showing momentum change.
Today’s Question of the Day focuses on conservation of momentum.
Question: If a lab cart of mass “M” traveling at velocity “vo” collides inelastically with a stationary lab cart of mass “3M”, what will the velocity be after the collision?
a) 4vo
b) ¼vo
c) ½vo