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Phy 231
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A ball falls freely from rest at a height of 2 meters. Observations indicate that the ball reaches the ground in .64 seconds.
• Based on this information what is its acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
a = `dv / `dt; a = (vf – v0) / `dt
vf = 2m / 0.64 s = 3.125 m/s
this is v_Ave, not v_f
v0 = 0 m / 0.64s = 0 m/s
a = (3.125 m/s – 0 m/s) / (0.64 s) = (3.125 m/s) / (0.64 s) = 4.8828 m/s^2
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• Is this consistent with an observation which concludes that a ball dropped from a height of 5 meters reaches the ground in 1.05 seconds?
answer/question/discussion: ->->->->->->->->->->->-> :
a = `dv / `dt; a = (vf – v0) / `dt
vf = 5m / 1.05 s = 4.762 m/s
v0 = 0 m / 1.05s = 0 m/s
a = (4.762 m/s – 0 m/s) / (1.05 s) = (4.762 m/s) / (1.05 s) = 4.535 m/s^2
When you round 4.8828 m/s^2 and 4.535 m/s^2 to the nearest whole number they both round to 5 m/s^2. Therefore, this is and is not consistent. If you are basing consistency on the nearest whole number then yes. If not then the two numbers will be different.
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• Are these observations consistent with the accepted value of the acceleration of gravity, which is 9.8 m / s^2?
answer/question/discussion: ->->->->->->->->->->->-> :
No because the acceleration of gravity is 9.8 m/s^2 and the acceleration for the previous question rounds to 5 m/s^2. Therefore these observations are not consistent.
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15 min
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Acceleration is `dv / `dt, not v_Ave / `dt. You can easily correct your calculations.
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