Finding Gravitational Acceleration with Atwood Machine Graphs

AI Thread Summary
To determine gravitational acceleration from the three graphs (acceleration vs. total mass, acceleration vs. mass difference, and acceleration vs. inverse total mass), the slope of each graph can be analyzed. The relationship between slope and gravitational acceleration is crucial, as acceleration is directly proportional to the mass difference and inversely proportional to the total mass in a two-mass pulley system. Specifically, the equation a = (m1 - m2)g / (m1 + m2) illustrates these relationships. By calculating the slopes, one can derive the gravitational acceleration from the graph data. Understanding these relationships is essential for completing the lab report accurately.
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Homework Statement



I have 3 graphs: accleration vs. total mass, acceleration vs. mass difference, and acceleration vs. inverse total mass.

How can I get the gravitational acceleration from these 3 graphs ?

I am doing a lab report on word and excel

Homework Equations



I don't think there is one, may be it will be the slope ??

The Attempt at a Solution



I think finding the slope of those graphs ? But what wil be the relationship between slope and gravitational acceleration ?
 
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Can anyone give some inputs. I really need help now. My lab is due tomorrow.
 
What do you guys think is the relationship between gravitational force and those 3 graphs ?
 
For a system with only two masses over a single pulley:

a = \frac{(m1 - m2)g}{m1 + m2}

so acceleration is directly proportional to mass difference (m1 - m2), and directly proportional to "inverse total mass" 1/(m1 + m2).
 
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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