Momentum

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Mercyhurst University *

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101

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Physics

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Apr 3, 2024

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docx

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Uploaded by SuperNeutronOtter36

Momentum: Video Analysis Background When we talk about momentum , it can be first helpful to define another quantity: impulse . Impulse is a vector (direction matters) represented by There are two different ways to define impulse: The first is that impulse equals the change in momentum, or . The second is using the net force on the object and time, or . Combining these, we get and if you divide both sides by time, This means that if there is no net force on the body or system of bodies ( ⃗ F net = 0 ), then Δ ⃗ p Δt = 0 . Time cannot be zero, so there must be no change of momentum within the system with time. This is known as conservation of momentum . Let’s take conservation of momentum one step farther. Since the change in momentum has to be zero, or Since we are talking about the whole system, remember that the final momentum is the sum of the final momentum of the parts, and the initial momentum is the sum of the initial momentum of the parts. In today’s lab, you’ll be examining collisions. There are two types of collisions that will be examined. Perfectly inelastic collisions are collisions that hit, stick together, and move with a constant velocity after the collision. Elastic collisions are those where the objects do not stick together, but rather move separately from each other after the collision. (Elastic collisions also conserve kinetic energy.) Goal: The purpose of this experiment is to use LoggerPro to measure the momentum in various collisions and determine whether conservation of momentum applies. Case I - Perfectly Inelastic Collision with Equal Masses  Open LoggerPro  Insert Movie  Logger Files (on Desktop)  Collision Videos  Colliding_Carts_37-mmi.mov. Go to Page  Auto Arrange to put your movie

in the top left-hand corner. Set your scale and note the masses of the two carts from the first slide.  Plot the location of the left cart by using the Add Point button. Click on a certain part of the cart (front, middle, back…) and the movie will advance to the next frame. Be consistent, plot the same part of the cart for every frame, and continue plotting the points until the end of the movie.  Rewind the movie to the beginning. Press the Set Active Point button and select Add Point Series and plot the location of the cart on the right. You will notice that the dot is a different color. Start at the first slide and continue plotting the location, even if the cart is not moving.  Use LoggerPro to determine the velocity of each cart by taking the slope of the position v. time graph before and after the collision. Record these values in the table below.  Determine the momentum of each cart by going to Data  New Calculated Column. Name your new quantity “cart 1 p” or something similar. You will create an equation with constants and known variables. Note: to use a variable from your data, choose it from the Variables column. (For example, “ X Velocity ”) can be used to calculate the momentum in the x-direction. o Plot a “cart 1 p” v. time graph. Shade the part of the data that is a flat line before the collision and find the mean value by going to Analyze  Statistics. Do the same for after the collision. Record these values in the table below. Mass (kg) v i (m/s) p i (Ns) Σ p i (Ns) Cart left 0.524 0.5743 0.3009 0.3009 Cart right 0.524 0 0 Mass (kg) v f (m/s) p f (Ns) p Σ f (Ns) p Δ (Ns) Two carts together 1.048 0.283 0.296 0.296 -0.0049 3 Phys 103 - Principles of Physics I Labs Momentum: Collision Carts

Case II - Perfectly Inelastic Collisions with Unequal Masses  Repeat the experiment above, this time using the Colliding_Carts_32-mMi.mov file. Mass (kg) v i (m/s) p i (Ns) Σ p i (Ns) Cart left 0.524 0.5459 0.286 0.286 Cart right 1.048 0 0 Mass (kg) v f (m/s) p f (Ns) p Σ f (Ns) p Δ (Ns) Two carts together 1.576 0.1756 0.276 0.276 -0.01  Repeat the experiment above, this time using the Colliding_Carts_34-Mmi.mov file. Mass (kg) v i (m/s) p i (Ns) Σ p i (Ns) Cart left 1.048 0.3913 0.4100 0.4100 Cart right 0.524 0 0 Mass (kg) v f (m/s) p f (Ns) p Σ f (Ns) p Δ (Ns) Two carts together 0.572 0.251 0.395 0.395 -0.02 4 Phys 103 - Principles of Physics I Labs Momentum: Collision Carts

Case III - Perfectly Elastic Collisions with Equal Masses  Repeat the experiment above, this time using the Colliding_Carts_41-mme.mov file. Mass (kg) v i (m/s) p i (Ns) Σ p i (Ns) Cart left 0.524 0.4860 0.2546 0.2546 Cart right 0.524 0 0 Mass (kg) v f (m/s) p f (Ns) p Σ f (Ns) p Δ (Ns) Cart left 0.524 0 0 0.2496 -0.005 Cart right 0.524 0.4762 0.2496 Case IV - Perfectly Elastic Collisions with Unequal Masses  Repeat the experiment above, this time using the Colliding_Carts_45-mMe.mov file. Mass (kg) v i (m/s) p i (Ns) Σ p i (Ns) Cart left 0.524 -0.4832 -0.2531 -0.2531 Cart right 1.048 0 0 Mass (kg) v f (m/s) p f (Ns) p Σ f (Ns) p Δ (Ns) Cart left 0.524 -0.1386 -0.0726 0.2553 0.002 Cart right 1.048 0.3129 0.3279  Repeat the experiment above, this time using the Colliding_Carts_31-Mme.mov file. Mass (kg) v i (m/s) p i (Ns) Σ p i (Ns) Cart left 1.048 0.5099 0.5343 0.5343 Cart right 0.524 0 0 Mass (kg) v f (m/s) p f (Ns) p Σ f (Ns) p Δ (Ns) Cart left 1.048 0.6968 0.7302 0.0610 -0.4733 5 Phys 103 - Principles of Physics I Labs Momentum: Collision Carts

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