Cameron Romano Lab 5-2

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. The theory for this experiment is that when extending 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. This theory will be tested by the experiment in order to prove it as this trend should be demonstrated by the data recorded. Formulas: Force is dependent upon linear momentum as defined by: 𝐹⃗ = ?𝑝⃗ ?𝑡 Impulse momentum theorem defines J as Impulse: 𝐽⃗ ∆ 𝑝⃗ ≡ 𝑡 𝑖 𝑡 ? ∫ 𝐹⃗ ?𝑡 = 𝑡 𝑖 𝑡 ? ∫ ?𝑝⃗ = The relationship between force and impulse is described as 𝐽⃗ = ∆t =∆ 𝑝⃗ 𝐹⃗ 𝑎𝑣?𝑟𝑎??

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 2. Velocity versus time and force versus time graphs (Light Spring) Fig 3. Velocity versus time and force versus time graphs (Air Bag)

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. However, for the trials with the air bag we had much higher percent difference which can be attributed to the fact that these recordings were much less precise compared to those with or without the spring as in those instances we could more accurately measure the force applied by the spring whereas with the airbag it was much more erratic and as it was not held in place constantly as the spring was this led to innacurresies in our measurements and recordings.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 our data. Some measurements took a few attempts to collect our data but we were able to get acceptable data for each trial.

Fig 5. Spring System Diagram Conclusion From this experiment we were able to determine that increasing the time of the impact results in a decrease in the force. Therefore if t is increased, for a constant change in momentum, the force on the body is reduced. This relationship was observed and recorded through this experiment as the data demonstrated an increase in the interval of time resulted in a smaller force being experienced. This is proven by the formula for impulse as, , which demonstrates this relationship between time, force and ∆𝑝 = 𝐹∆𝑡 impulse as since the impulse experienced in a collision is constant, when we increase the time experienced in the collision it decreases the force experienced and vice versa. Questions 1. Compare and contrast the results from collisions with the light spring and those with the airbag. What differences did you observe in terms of impulse and force? Explain the possible reasons behind these differences.