Solving for acceleration of a piston

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SUMMARY

The discussion focuses on calculating the average acceleration of a piston with a displacement of 10 cm operating at 50 cycles per second. The key formulas used include d = 0.5a * t² and a = 2 * d / t². The correct calculation involves determining the time taken to travel 5 cm, which is 5 ms, leading to an acceleration of 40 m/s². The confusion arises from the interpretation of displacement and distance traveled during the cycle.

PREREQUISITES
  • Understanding of kinematic equations, specifically d = 0.5a * t² and a = 2 * d / t².
  • Basic knowledge of velocity calculations, including v = d / t.
  • Familiarity with the concept of cycles per second and its relation to time.
  • Ability to convert units, such as milliseconds to seconds.
NEXT STEPS
  • Review kinematic equations in physics to solidify understanding of motion principles.
  • Practice problems involving average acceleration and displacement in oscillatory systems.
  • Explore the relationship between frequency and time period in mechanical systems.
  • Investigate real-world applications of piston acceleration in automotive engineering.
USEFUL FOR

Students studying physics, mechanical engineers, and anyone interested in the dynamics of oscillatory motion and piston mechanisms.

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Homework Statement


The piston has a displacement of 10 cm and there are 50 cycles per second. Calculate the average acceleration that occurs between the start/stop point and the middle of the cycle. This value has to do with evenly accelerated movement. This can be described according to the formula d = .5a * t2.
To solve:
-Compute the average velocity using a full cycle.
-Calculate how long the piston needs to travel 5 cm from the top of the cycle to the middle, which will give us the value for t. Then use a = 2 * d / t2 to calculate the acceleration.

Homework Equations


d = .5a * t2
a = 2 * d / t2
v = d / t

The Attempt at a Solution


50 cycles per second = 1 cycle takes 20 milliseconds.
velocity = d / t
10 m/s = 20cm / 50 ms (total cycle distance is 20cm because the displacement is 10cm)
How long the piston takes to travel 5 cm: 5 ms (so t = .005s)
a = 2 * d / t2
a = 2 * .1m / .005s2 = 40 m/s2
But this isn't the right answer! Please help!
 
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Why are you using .1 m for d? d is the distance traveled in time t

AM
 

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