Using Atwood's Machine to Measure Time Intervals

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SUMMARY

The discussion focuses on using an Atwood's machine to measure time intervals, specifically to achieve a vertical fall time of 10.0 seconds over a distance of 1.30 meters. The key formulas provided include acceleration calculation using \( a = \frac{2h}{t^2} \) and the relationship between masses \( g = a \times \frac{(2M+m)}{m} \). The acceleration must also satisfy the equation \( a = \frac{M-m}{M+m} \times g \), where \( g \) is assumed to be 9.80 m/s². The relationship between the masses \( M \) and \( m \) is critical to solving the problem.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with Atwood's machine mechanics
  • Knowledge of basic kinematics equations
  • Ability to manipulate algebraic equations
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  • Explore the derivation of acceleration in Atwood's machine scenarios
  • Study the effects of varying mass ratios on time intervals in Atwood's machine
  • Investigate practical applications of Atwood's machine in physics experiments
  • Learn about the impact of gravitational acceleration variations on timing accuracy
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Physics students, educators, and anyone interested in experimental mechanics or time measurement techniques using simple machines.

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Using this site as a reference: http://hyperphysics.phy-astr.gsu.edu/hbase/atwd.html

Can somebody show me how to solve this:

Suppose you don't have a watch, or a timer, and you want to use an Atwood's machine as a timer to give an accurate time interval (for the vertical fall) of t = 10.0s. Suppose the vertical fall, y, is 1.30m. Determine values of M and m which would make t - 10s.

Some formulas

a = (2h)/t2
g= a x ((2M+m)/m)/m
 
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Find the acceleration using the formula you have.

Then set this acceleration = [tex]\frac{M-m}{M+m}*g[/tex] (taking M as the heavier mass and m as the lighter mass of the atwood machine).

this will only give a relationship between M and m. is there any more information for the problem?
 
nope just that. I am guessing it might be sufficient just to have the relationship

i'm assuming g= 9.80
?
 

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