Pendulum acceleration homework

AI Thread Summary
To calculate the acceleration of gravity using a pendulum, the formula g = (4π²/T²)L is applied, where L is the length of the pendulum. The pendulum is 2.00 m long and completes 84.5 oscillations in 4.00 minutes, leading to a total time of 240 seconds. The mistake identified was using the total time as the period; instead, the period for one oscillation should be calculated by dividing the total time by the number of oscillations. After correcting this, the proper calculation yields a reasonable value for g. The discussion highlights the importance of accurately determining the period of oscillation in pendulum problems.
ahrog
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Homework Statement



A pendulum with is 2.00 m long makes 84.5 complete oscillations in 4.00 minutes. What is the acceleration of gravity at that spot?


Homework Equations



TG=(4pi^2/T^2)L


The Attempt at a Solution



g=(4pi^2/240s^2)2.00m
g= 0.0013707...

Which doesn't make sense, and it seems way to simple to be getting 8 marks for it. What am I missing?
 
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Find the time for one oscillation.
 


In your solution you seem to have just put in 240s for the period. This would certainly be true if the pendulum completed one oscillation in four minutes...
 


Oh geez *smacks head* Such an easy solution. Thanks!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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