Calculating G Using an Inclined Track

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Discussion Overview

The discussion revolves around the experimental determination of gravitational acceleration (g) using an inclined track setup in a high school mechanics lab. Participants explore the relationship between the measured acceleration of a cart on the track and the expected value of g, considering various factors such as angles and forces involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant questions whether they should obtain an acceleration of approximately 9.8 m/s² at different angles and seeks guidance on their calculations.
  • Another participant suggests providing a diagram and measurements for better assistance.
  • A participant describes their experimental setup, including the use of time measurements and height differences to calculate acceleration and angle, and questions the relationship between y-acceleration and g.
  • There is a query about whether other forces, aside from the weight component, affect the cart's motion down the track.
  • A participant clarifies that no external forces were applied to the cart, acknowledging friction and air resistance but indicating a focus on kinematics.
  • One participant states that if friction is negligible, the measured acceleration should equal g multiplied by the sine of the angle of the track.
  • A later reply indicates that this understanding leads to more consistent results in their calculations.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the relationship between the measured acceleration and gravitational acceleration, with some suggesting that the relationship is direct while others propose a proportional relationship dependent on the angle. The discussion remains unresolved regarding the exact nature of this relationship.

Contextual Notes

Participants acknowledge factors such as friction and air resistance but limit their analysis to kinematic principles. There is an implicit assumption that the experimental setup is idealized, which may not account for all real-world influences.

Who May Find This Useful

This discussion may be useful for high school students and educators involved in introductory mechanics experiments, particularly those exploring the principles of gravity and inclined planes.

jpm_iv
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I need to experimentally find gravity using information from a lab we finished last week. Should I not be getting 9.8 m/s² at each angle or am I doing something wrong? And if I should indeed be getting ≈9.8 m/s² as my y-acceleration, can you point me in the right direction?
 
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You can get more help if you give a diagram of the apparatus used and the measurements taken.
 
Sorry for being unspecific, I was looking more for a general answer. But we had a cart travel down a sloped track, had times recorded at A and B, along with a time taken to travel from A to B, all of which were known distances. This was used to calculate v1, v2, and a. Then we had taken two height measurements 60cm apart, and used this to find the angle of the track to the table. Then I multiplied the calculated acceleration by sine of the angle to get y-acceleration. Basically should this y-acceleration be ≈9.8 m/s/s or should it be proportionally related like y-acceleration/angle = g/90?
 
Were there any other forces parallel to the track besides a component of the weight of the cart?
 
Nothing was applied to the cart directly, it was just set at the top and then released. Obviously there are factors of friction and air resistance, but this is the third week of a high school mechanics course and we're limiting everything to kinematics.
 
If friction is negligible (eg air track) then the measured acc will be gsin(angle between track and horizontal)
 
Okay, that gives me more consistent results. I had been solving for g by g=asin.
 

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