Analyzing One-Dimensional Collisions (Physics Lab)

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SUMMARY

This discussion focuses on calculating the initial velocity of a cart in a one-dimensional collision experiment. The initial velocity should be measured as the cart leaves the hand, calculated using the formula Δd/Δt for the first two data points. However, for a more accurate approximation, it is recommended to use the formula (distance at collision - distance at start) / (time of collision - time of start) to account for any changes in velocity before the collision.

PREREQUISITES
  • Understanding of basic physics concepts, particularly momentum and velocity.
  • Familiarity with data collection and analysis in physics experiments.
  • Ability to interpret and manipulate data sets, including calculating averages and differences.
  • Knowledge of kinematic equations relevant to motion and collisions.
NEXT STEPS
  • Explore the principles of momentum conservation in collisions.
  • Learn how to apply kinematic equations to analyze motion in physics experiments.
  • Investigate the effects of friction and air resistance on cart motion.
  • Study advanced collision types, such as elastic and inelastic collisions.
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Students conducting physics experiments, educators teaching momentum and collision concepts, and anyone interested in practical applications of kinematics in physics labs.

toittoiger
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I am doing a Physics Lab where you have to measure initial and final velocities of two carts colliding in order to find the momentum. In this first category, you push a cart with a bumper into another cart with a bumper so that the first one completely stops right when it hits the second one. I am just wondering how you would calculate the initial velocity of the first cart I had to push off. Is the initial velocity right before it hits the cart or when it leaves my hand...etc. If you could please tell me what you think the initial velocity might be from this following data, that would be great. Here is the data:

t (s) d (m) ∆d (m) ∆t (s) v (m/s)
0 0
0.1 0.01 0.01 0.1 0.1
0.2 0.027 0.017 0.1 0.17
0.3 0.062 0.035 0.1 0.35
0.4 0.114 0.052 0.1 0.52
0.5 0.19 0.076 0.1 0.76
0.6 0.287 0.097 0.1 0.97
0.7 0.39 0.103 0.1 1.03
0.8 0.491 0.101 0.1 1.01
0.9 0.588 0.097 0.1 0.97
1 0.682 0.094 0.1 0.94
1.1 0.772 0.09 0.1 0.9
1.2 0.858 0.086 0.1 0.86
1.3 0.9431 0.0851 0.1 0.851
1.4 1.022 0.0789 0.1 0.789
1.5 1.097 0.075 0.1 0.75
1.6 1.16 0.063 0.1 0.63
1.7 1.227 0.067 0.1 0.67
1.8 1.244 0.017 0.1 0.17
 
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Strictly speaking, the initial velocity is just as it leaves your hand which would be
Δ d/Δ t for the first two times in your data list. However, that's really assuming that velocity remains constant until the collision. You might want to consider (distance at collision- distance at start)/(time of collision- time of start) as a better approximation.