Cameron Romano Lab 5

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:

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.

three trials at each velocity and calculate the average maximum force for each velocity. b)Analyze and compare the maximum forces obtained in these runs with those from the airbag-assisted experiments. Can you observe the benefits of the airbag in the collision? c) Print out graphs for velocity versus time and force versus time for one of your data runs. Turn off the motion cart power switch and the WDSS power switch (force sensor). Results and Analysis Results: V i (m/s) V f (m/s) ∆P (kg*m/s) J = F ∆t (N*S) % Difference Max force (N)

0.2082 -0.167 -0.29029 -0.3095 6.206785 -2.727 0.4747 -0.3813 -0.6674 -0.6247 -6.83528 -6.07 0.6044 -0.4975 -0.8625 -0.8736 1.270604 -12.33 Table 1. Light Spring Data V i (m/s) V f (m/s) ∆P (kg*m/s) J = F ∆t (N*S) % Difference Max force (N) 0.6472 -0.2236 -0.72433864 -0.7121 -1.7186687 -30.77 0.7014 -0.1951 -0.73777318 -0.7553 2.32051106 -36.2 0.5896 -0.1743 -0.63047352 -0.6137 -2.7331791 -25.72 Table 2. Air Bag Data V i (m/s) V f (m/s) ∆P (kg*m/s) J = F ∆t (N*S) % Difference Max force (N) 0.6507 -0.1424 -0.64585 -0.8984 28.11147 -44.83 0.709 -0.1507 -0.69925 -0.46 -52.0116 -44.09 0.7597 -0.1521 -0.73988 -0.916 19.22709 -45.81 Table 3. No Air Bag Data

Fig 4. Velocity versus time and force versus time graphs (No Air Bag) Analysis: This data demonstrates trends among the relationships between, velocity, force, and time. Notably the interval of time during the collision decreases with each recording. However, as the interval of time increases, the maximum force experienced at that time is increased. Our data displays the maximum forces were greatest from the recordings with no air bag while the least force were from the light spring. Notably throughout all of our trials it seems that with regard to velocity, the impulses experienced in each collision were consistent with each other. Another notable trend in our data is that of position and force as demonstrated in our provided graphs as I noticed that with consideration to the position, the force was not affected by what it was colliding with which implies that the maximum forces varied but that did not impact the magnitude of the force experienced, this would explain why the forces were experienced over greater periods of time. For example, the tests with the air bag and no air bag there were trials that had the same initial velocity with negligible difference, 0.7014 and 0.709 respectively and also had roughly the same impulse, 0.73777318 and 0.69925

respectively, however the test with no air bag displayed a greater force with 44.09 N while the air bag test displayed 36.2 N. Discussion From these results we are able to determine that when the interval of time experienced in a collision is increased it decreases the force of the impulse as it causes the force to be applied over a longer period of time therefore it is experienced as a weaker force. As expressed in the formula for impulse, ∆𝑝 = 𝐹∆𝑡 This would mean that to experience a lesser force we must experience it over a greater period of time allowing for the force to dissipate over the interval of time. This is demonstrated by our results as we tested 3 different scenarios each of which varied the interval of time at which the force was experienced, as the light spring experienced the greatest period while the trial with no spring or air bag experienced the shortest period. During a collision, an object always encounters an impulse and a change in momentum. During a collision, the impulse which an object experiences is equal to its velocity change. The velocity change of two respective objects involved in a collision will always be equal. This can be derived from our results as demonstrated by our data. From our graphs and the formula for impulse we can also derive that the area under a force-time graph is force multiplied by time, which is the quantity of impulse. For our measurements there are some experimental uncertainties that may have affected them as we did not account for forces such as friction, air resistance, and other unforeseen forces, all of which would have opposed the motion of the cart and thus decreased our measured force. There were some difficulties in performing this lab as we struggled with the procedure because it was somewhat difficult to collect accurate readings from the sensor and to avoid uncertainties from skewing

1) From collisions with the light spring and those with the airbag I noticed that the collisions with the light spring displayed lower forces than with the air bag and that the time of the collision occurring was longer the light spring, therefore the light spring displayed a lesser force over a longer period of time while the air bag displayed a greater force over a shorter period of time. 2. Explain how the concept of impulse can be used to minimize injuries during a car crash. What other safety measures are based on this principle? 2) The concept of impulse can be used to minimize injuries during a car crash because our seats have air bags for collisions which increase the time in which the force is experienced so that force less over that time. Other safety measures that are based on this principle are in car crashes we apply air bags so that we can expand the interval of time in which our bodies experience the collision, decreasing the force experienced on us, the same application is also used in sports when developing the padding in helmets or other protective gear. 3. Discuss the practical applications of the impulse-momentum theorem. How is this theorem relevant in real-life scenarios, such as car safety or sports? 3) Impulse-momentumtheorem provides many relevant in real-life scenarios and practical applications where it is tremendously important for example, in car crashes we apply air bags so that we can expand the interval of time in which our bodies experience the collision, decreasing the force experienced on us, the same application is also used in sports when developing the padding in helmets or other protective gear.