Ahoy! In this episode we take a look at the change in momentum for a vehicle made by a crazy physics teacher.
Ahoy! In this episode we take a look at the change in momentum for a vehicle made by a crazy physics teacher. (0:42) We quickly shift gears to look at a graph of your physics teacher’s vehicle. (4:06) It’s then game, set, match while we look at the momentum change for a tennis ball. (4:37) Of course, what description of impulse would be complete without looking at the graph of force vs. time for the tennis ball. (5:38)
The Question of the Day asks: (6:45)
If a force of +20 N is applied for 5 seconds to a 10 kg lab cart initially at rest, how fast will the cart now be traveling?
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Hi and welcome to the APsolute RecAP: Physics 1 Edition. Today’s episode will focus on impulse and graphs you can expect to see related to impulse.
Let’s Zoom out:
Unit 5 – Momentum
Topic 5.1-5.4
Big Idea – Force Interactions, Change, and Conservation
While sitting in a desk chair with wheels, your crazy physics teacher decides to propel himself forward with a fire extinguisher. He aims the extinguisher nozzle backwards and he begins gaining speed forward. Is his momentum conserved? If not, why not? How can we create a graph of your teacher’s maiden voyage that is useful? We will be answering these questions and more in this episode.
Let’s Zoom in:
Most people have heard the saying that momentum is conserved, or the phrase “conservation of momentum”. That is only part of the story however. Yes, momentum is conserved in a system if there is no external force acting, but… if there is an external force on the system there will be a change in momentum. That is impulse, a change in momentum. Your daring teacher was at rest initially, but then after the compressed gas was allowed to rush out of the nozzle, your teacher’s speed increased. As a result, your teacher gained momentum because there was an impulse. Imagine a fire extinguisher with an infinite amount of gas inside. It would be able to just keep moving the teacher along faster, and faster, and faster. So, somehow time must be involved.
Another way you can find impulse is to multiply the force being applied to the system by the duration of time the force was applied. Or, if we know that the teacher has a mass of 50 kg, and eventually speeds up to 10 m/s in the forward direction using the extinguisher for 5 s, then we can determine the average force of the gas expelled pushing on your teacher. We can determine the change in momentum for the teacher and set it equal to the force applied times the elapsed time. Your teacher had a final momentum of 50 kg times 10 m/s or 500 kg*m/s. Their initial momentum was 0 kg*m/s and therefore their change in momentum or impulse was +500 kg*m/s. If we set that equal to the other equation for impulse, force times time, and then divide the time on both sides, we see that there was an average force applied of 100 N in the positive or forward direction.
Notice, momentum, velocity, and force are all vectors, so signs matter! A LOT!
Another way to analyze your teacher’s motion is to create a graph of Force vs. time, and then using the area of that graph which is equal to the change in momentum, or the impulse. Our particular graph would have a horizontal line at +100 N for 5 seconds, which would have an area of +500 kg*m/s. For a fire extinguisher with fairly steady force that is great, but for an applied force that varies over time the shape would look different.
Let’s look at what happens when a 0.05 kg tennis ball is served with a velocity of +50 m/s and hits the opponents racquet and then bounces backward at the same speed that it was initially served. These collisions don’t occur instantaneously. It takes a bit of time for the ball to slow to rest as the ball deforms and then rebounds off the racquet with velocity of -50 m/s. Think Slow Mo. (makes slow motion noises) If the ball was in contact with the racquet for just 1/20 of a second, then the force exerted by the racquet on the tennis ball would be -100 N. Final momentum (-2.5 kg*m/s) minus initial momentum (+2.5 kg*m/s) is a momentum changed of -5 kg*m/s. Dividing the change in momentum by time yields a force of -100 N.
As a force vs time graph, the tennis ball would look quite different from your teacher. The springiness of the tennis ball and racquet would make a shape more triangular that would be 0.05 seconds wide along the horizontal axis and with a negative peak of approximately -200 N vertically. The area of that triangle would be half the base times the height. Or, half of -200 N times 0.05 seconds… -5 kg*m/s, the momentum change.
To Recap…
Momentum of a system is conserved as long as there is not a net external force applied. Impulse is the average force applied multiplied by the duration of time it is applied. And, impulse can be set equal to the change in a system’s momentum. Momentum, velocity and force are all vectors, so pay attention to your positive and negative signs to indicate direction.
Coming up next on the APsolute RecAP Physics 1 Edition, reading and using the data graphed with regards to velocity vs. time, momentum vs. time, and force vs. time.
Today’s Question of the Day focuses on momentum and impulse.
Question: If a force of +20 N is applied for 5 seconds to a 10 kg lab cart initially at rest, how fast will the cart now be traveling?
a) 1 m/s
b) 10 m/s
c) 100 m/s