Episode 18 focuses on how to utilize graphs associated with momentum and impulse through three examples.
Episode 18 focuses on how to utilize graphs associated with momentum and impulse through three examples. Two railway cars collide in a velocity time graph. A fancy electric car accelerates (3:59) and a mischievous friend fires a slingshot in a force time graph (5:01). Momentum vs time graphs are less commonly used (6:16).
The Question of the Day asks: (7:06) A bullet of mass “m” is shot vertically at speed “v” into a wooden block of mass “10m.” After becoming embedded in the block, what height “h” does the bullet-block system reach?
Thank you for listening to The APsolute RecAP: Physics 1 Edition!
(AP is a registered trademark of the College Board and is not affiliated with The APsolute RecAP. Copyright 2021 - The APsolute RecAP, LLC. All rights reserved.)
Website:
EMAIL:
Follow Us:
Hi and welcome to the APsolute RecAP: Physics 1 Edition. Today’s episode will focus on how to utilize graphs associated with momentum and impulse.
Let’s Zoom out:
Unit 5 – Momentum
Topic 5.1-5.4
Big Idea – Force Interactions, Change, and Conservation
A 10,000 kg railroad car rolls along the tracks and attaches to another car of unknown mass that was initially at rest. A velocity vs time graph of the event captures the motion of the 10,000 kg car in great detail. How could you find the mass of the other car?
Let’s Zoom in:
The velocity vs time graph for an object in a collision is popular in physics lab activities. You will see that velocity is graphed on the y-axis with time on the x-axis. These graphs tend to have a horizontal bit followed by a sloped line (positive or negative) followed by another horizontal bit. The two portions that are horizontal show that the object, in this case a railroad car, is traveling at a constant velocity. The sloped bit shows that the car accelerated, or changed its velocity and therefore its momentum.
In the railroad car scenario presented, the graph includes a horizontal bit at +5 m/s and then a line with negative slope leading to another horizontal bit at +1.5 m/s. That is all of the relevant data taken from the v-t graph, with that, we know that the first car had a momentum of 10,000 kg times +5 m/s, or +50,000 kg*m/s. It later had a momentum of +15,000 kg*m/s. That is a change in momentum of -35,000 kg*m/s. If the first railroad car lost momentum, then you better believe that the initially stationary car gained that same amount, assuming no outside forces played a role. Finally, we know that the cars stick together, so we know that the initially stationary car had a change in momentum of +35,000 kg*m/s, had an initial velocity of 0 m/s, and a final velocity of +1.5 m/s. So, we find that the mass of the initially stationary boxcar was 23,333 kg by dividing the momentum change by the final velocity.
Let’s look at another type of graph, a force vs time graph. This particular graph shows a constant force of static friction responsible for allowing a particular model of Tesla car to increase its speed from rest in 2.3 seconds with a constant force of 26,000 N. You are asked to determine how fast the car is traveling after this increase in momentum from rest. As it turns out, the F-t graph can help a lot. The area bound by the graph of F-t is equal to the car’s change in momentum. Since that car started at rest, we will be able to quickly find the final momentum by multiplying the constant force of 26,000 N by the time, 2.3 s. This yields a momentum change of +59,800 kg*m/s, which is also the final momentum. Dividing by the car’s mass of 2,230 kg, we arrive at a velocity of 26.8 m/s or 60 mile per hour.
Constant force graphs are a treat, because the force applied is uniform and makes a nice rectangular area. But what about forces that change over time? That is essentially how most materials behave. They deform a bit. Springs are an example of a material that deforms quite a bit. A mischievous young boy has obtained a slingshot, and is tormenting some of his friends. He pulls a 0.05 kg stone back and releases it from rest in just 0.1 seconds. The rubberband sling had a maximum force of 50 N when fully pulled back. How fast does the stone leave the slingshot? The graph of force vs. time shows a force that starts at 50 N and drops to 0 N in a matter of 0.1 s. That is a right triangle with an area of ½ (50 N)(0.1 s), or a momentum change for the stone of 2.5 kg*m/s. That momentum change takes the stone from rest, 0 kg*m/s to its launch speed. Dividing the momentum change by the mass of the stone shows that the projectile will leave the slingshot at 50 m/s. Just over 110 miles per hour! Ouch
Those are the most prominent applications of graphs related to momentum, but certainly more can be thought up. Every once in a while, you will see a graph of momentum vs time in a question. These tend to be easier to solve since there is less calculation. You can jump right to identifying whether or not momentum was conserved in a particular interaction.
To Recap…
Velocity vs time, force vs time, and momentum vs time graphs can all help you to solve many varieties of problems. Usually, a good physics student knows a great deal about a scenario just by looking at the graph. Once they read a problem, it means so much more if you embrace the power of these graphs.
Coming up next on the APsolute RecAP Physics 1 Edition, we explain the concept of center of mass and take a look at how the velocity of the center of mass behaves during a collision.
Today’s Question of the Day focuses on momentum and impulse.
Question: A bullet of mass “m” is shot vertically at speed “v” into a wooden block of mass “10m.” After becoming embedded in the block, what height “h” does the bullet-block system reach?
a) (v2)/(22*g) b) (22*v2)/g c) (v2)/(11*g)