Webpage title: Calculating Acceleration and G for Two Isolated Spheres

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The discussion revolves around calculating the acceleration and gravitational constant G for two isolated spheres with significantly different masses. The smaller sphere, with a mass of 1.00 g, moves 0.534 mm towards the larger sphere, which has a mass of 100 kg, after one minute. Participants suggest starting with the law of gravity and the definition of force to derive the necessary calculations. The emphasis is on recognizing that the larger mass's influence on the smaller sphere's movement is the primary focus due to the mass disparity. This approach will lead to the determination of acceleration and G.
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Two spheres of masses m1 = 1.00 g and m2 = 1.00 *10^2
kg are isolated from all other bodies and are initially at
rest, with their centers a distance r = 15.0 cm apart. One
minute later, the smaller sphere has moved 0.534 mm
toward the larger sphere. Compute the acceleration and G.

Solution:

No idea where to being.. some hints please?
 
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To start the two masses are so greatly different the problem seems to only want you to consider the small ball as moving. I'd begin by writing down the law of gravity and the definition of a force. With those you can probably find a way to calculate acceleration.
 
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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