Solve Mass of Glider with Harmonic Motion Help

AI Thread Summary
The discussion revolves around calculating the mass of a glider oscillating on a frictionless air track attached to a spring with a force constant of 2.20 N/cm. The user initially calculates the mass using the formula for the period of harmonic motion but struggles with determining the correct period of oscillation. After several attempts, they conclude that the period is 0.10 seconds, yet their final mass calculation yields an incorrect result of 5.43 kg. The user seeks clarification on their mathematical process and any potential errors in their calculations. Accurate determination of the period and subsequent calculations are crucial for finding the correct mass of the glider.
elsternj
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Homework Statement


On a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.20 N/cm . The graph in the figure shows the acceleration of the glider as a function of time.
Find the mass of the glider.

YF-13-31.jpg




Homework Equations


T= 2pi\sqrt{m/C}



The Attempt at a Solution


2.2 N/cm = 220 N/m
C=220

.4 = 2pi\sqrt{m/220}
m = 1389

I know I'm doing something wrong but what?
 
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How much is the period of the sine wave ?
 
would it be .2s? when it passes back through O and to where it started?
 
I tried .2 and .3. are any of these the right time for period? If so then my problem lies elsewhere. any insight? thanks
 
okay i see now. .10 is the time for a period.

so .10 = 2pi \sqrt{m/220}

multiply both sides by \sqrt{220}

1.48 = 2pi\sqrt{m}

divide both sides by 2pi

2.43 = \sqrt{m}

square both sides

m = 5.43 which is still the wrong answer.

is my math wrong? what exactly am i doing wrong?
 
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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