Cameron Romano Lab 5

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Apr 3, 2024

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Cameron Romano Physics 1410 Lab Jack Shannon 10/7/2023 Luke Shomphe and Matt Favreau Experiment #5 Impulse and Collisions Objectives: Identify the principles of impulse and momentum in the context of collisions between objects and determine the relationship between impulse, time, and force.

Introduction This experiment will study collisions as collisions can be used to study the details of forces. Typical analysis of collisions involves using the principle of conservation of linear momentum as this is one of the most useful conservation laws in physics. Alternatively, the details of the force during a collision can be measured directly and compared to the change in the linear momentum, which is the approach taken in this experiment. In this experiment the direct measurement of the forces involved during the collision between a spring and a cart will result in the time-dependence of the force and will demonstrate the Impulse- Momentum Theorem. We will examine the variables that contribute to a collisions, and how these factors effect impulse. Through trials examining individual factors we can determine the relationships and dependence of these variables upon impulse. By manipulating the time that a collision occurs over we can evaluate how it affects the impulse of the collision if at all and in relation how it effects the force experienced in the collision. My theory for this experiment is that when we apply a variable to extend the time of which a collision occurs it lowers the maximum force experienced in the collision, as the force is experienced over a greater period of time the force is distributed throughout that period of time. Formulas: Newton’s second law of motion in its fundamental form relates the net external force acting on a point mass to its change in linear momentum ( 𝑝⃗ ): 𝐹⃗ = ?𝑝⃗ ?𝑡 Simple mathematical manipulation of this expression leads to the “Impulse-Momentum Theorem”, where 𝐽⃗ is the impulse:

𝐽⃗ ∆ 𝑝⃗ ≡ 𝑡 𝑖 𝑡 ? ∫ 𝐹⃗ ?𝑡 = 𝑡 𝑖 𝑡 ? ∫ ?𝑝⃗ = Hence, the impulse equals the area under the force versus time curve and is also equal to the change in linear momentum, i.e., the net effect of a force being applied for a given time interval is to change the linear momentum of the object acted on by the force. If the specific time dependence of the force is not known explicitly, the relationship can be approximated as: 𝐽⃗ = ∆t =∆ 𝑝⃗ 𝐹⃗ 𝑎𝑣?𝑟𝑎?? Apparatus and Procedure Fig 1. Experimental Apparatus a) Use a weighing balance to determine the mass of the cart with the force sensor attached. b) Turn on the motion cart power switch and the WDSS power switch (force sensor). c) Go to “Vernier” folder and open the program “Impulse Momentum v2” on a computer.

d) When the program indicates that the force sensor is not connected, press the ‘Scan for WDSS’ button. e) Choose the force sensor name that matches the name on your cart and select ‘OK’ connect. A) Data collection using the light spring. a) Screw the light spring into the bracket. The cart's track should be horizontal for this part of the experiment. b) Press the zero button (located next to the collect button on the top menu bar) to calibrate the force sensor. Ensure that the charging cord is disconnected from the force sensor and hold the end of the track during data runs to prevent it from moving when the cart strikes the spring. Three collisions, each with a different initial velocity, will be performed using the light spring, following the procedures described below: c) Hit the ‘collect’ button and then push the cart towards the spring, letting it hit the spring and rebound. Be sure to stop the cart before it hits the position sensor. Ensure that the cart does not hit the spring with enough force to fully compress it. Note: Data will be recorded for a time interval of 5 seconds after hitting the collect button. d) Two graphs will be displayed – velocity versus time and force versus time. Choose the velocity graph and press the “zoom in” button to expand the graphs to include the collision. e) Select a region that includes just the collision time interval and press the ‘statistics’ button (refer to the icon below) in the top menu. This will display

the maximum (initial) and minimum (final) velocities. Use these velocities and your measured mass to calculate the change in momentum of the cart. f) Choose the force graph and again zoom in on the region containing the collision. g) From the ‘analyze’ menu, select ‘integral’ to obtain the impulse. h) Compare this result with that for the change in momentum of the cart. i) Record the maximum force experienced during each collision run. j) Describeandanalyzetherelationshipbetweenthemaximumforceandtheinitialsp eed. k) Print out graphs for velocity versus time and force versus time for one of your data runs. B) Data collection using an airbag. For a given change in momentum of an object, the maximum force applied to the object can be varied by changing the length of time the collision occurs (Eq. 3). This has important implications, as in a car crash, the maximum force one sustains relates to the severity of the injuries. Thus, by increasing the time during which this change in momentum takes place (bringing an accident victim to zero velocity), survivability is enhanced. This lengthening of the collision time can be achieved through airbags. In this part of the experiment, we will model an airbag using a zip-lock bag, and we will compare the maximum forces with and without the bag. Remove the spring and use a zip-lock bag as an airbag. Inflate it using a straw, leaving the opening approximately 3 cm wide. Tape the bag to the bracket of the track. The goal is to ensure that the cart's final velocity is zero without striking the bracket. To achieve this, you will need to adjust the bag's opening and the cart's speed.

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