Cameron Romano Lab 5-2

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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. 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??

Apparatus and Procedure Fig 1. Experimental Apparatus Setup 1. Determine the mass of the cart + force sensor. 2. Open the vernier graphical analysis software and open the program, “Impulse Momentum v2”. 3. Turn on the motion sensor on the cart and connect it to the computer. Data Collection 1. Screw the light spring into the bracket. The cart's track should be horizontal for this part of the experiment. 2. To record data zero the sensor, and then click the collect button. 3. Perform and record three collisions each with different initial velocities letting the cart collide with the spring. 4. This will create two graphs, velocity versus time and force versus time. 5. Press the ‘statistics’ button in the top menu. This will display the maximum (initial) and minimum (final) velocities. 6. From the ‘analyze’ menu, select ‘integral’ to obtain the impulse, compare this result with that for the change in momentum of the cart. 7. Record the maximum force experienced during each collision run. 8. Use these values to describe and analyze the relationship between the maximum force and the initial speed. 9. Copy the graphs from one of your trials to include in report. 10. Repeat this procedure for the recordings of data studying the collisions with an air bag and with nothing to slow down the collision.

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

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