What is the gravitational force homework

AI Thread Summary
To calculate the gravitational force exerted by a solid sphere on a particle located inside it, the standard formula F = M1*M2*G / r^2 is not applicable. Inside a uniform solid sphere, the gravitational force depends only on the mass enclosed within the radius at the particle's location, which is half the sphere's radius in this case. The gravitational field inside the sphere is not simply proportional to 1/r^2 due to Gauss' Law, which indicates that the gravitational force from the mass above the particle is zero. Therefore, only the mass beneath the particle contributes to the gravitational force. Understanding these principles is crucial for accurately solving the problem.
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Homework Statement



A solid sphere of uniform density has a mass of 3.0×10^4 kg and a radius of 1.0 m. What is the gravitational force due to the sphere on a particle of mass 1.0 kg located at a distance of 0.50 m from the center of the sphere?

Homework Equations



F = M1*M2*G / r^2

The Attempt at a Solution



F = (1*3E4*6.67E-11) / (0.5)^2

F = 8.00E-6 NAm I doing something wrong because the question is asking for the force of a particle inside the sphere?
 
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Yes, the gravitational field inside a solid sphere is not simply proportional to 1/r^2.
Do you know Gauss' Law?
 


The gravity inside a shell of uniform mass density will be 0.

So what you are interested in is how much mass remains in the sphere beneath you.

To calculate the effect of gravity at half the radius then you are only worried about the mass of attraction from a sphere of half the radius (since that's below the point of interest, with what is above having no effect).
 
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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