Point mass gravitational problem

AI Thread Summary
To find the point on the x-axis where the gravitational field g equals zero due to two point masses, the equation g1 + g2 = 0 is established, leading to a quadratic equation. The derived equation x^2 - 4x + 12 = 0 has no real solutions, indicating that there is no point on the x-axis where the gravitational fields from the two masses cancel each other out. The discussion raises questions about the meaning of g=0 in terms of gravitational fields and whether gravitational fields are vector fields. Clarification is sought on how to approach the problem correctly. Understanding the vector nature of gravitational fields is essential for solving such problems.
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Homework Statement


1. A point mass m1= 2kg is at the origin and a second point mass m2=4kg is on the x-axis at x=6m. Find the point on the x-axis for which g=0


Homework Equations



g= -Gm/r^2

The Attempt at a Solution



So g=0 means that g1+g2=0. I set up that 2(r2)^2= -4(r1)^2 and made r2=x-6 and r1=x.

Thus, I have a quadratic equation as x^2 -4x+12=0 which has no solution. I am wrong on this question. How should I fix this ??
 
Physics news on Phys.org
What would g=0 mean?
 
gravitational field.
 
Is the gravitational field a vector field?
 
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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