Calculating magnitude of the acceleration of two ocean liners

AI Thread Summary
The discussion focuses on the calculation of acceleration for two ocean liners using gravitational force equations. The initial formula used was $$\frac{GMm}{r^2}$$, but confusion arose regarding the calculation leading to the result of ##6.6\times10^{-7}##. It was noted that the user incorrectly calculated the square of the mass term, leading to errors in their results. The correct application of the formula $$a=\frac{Gm}{r^2}$$ yielded an acceleration of ##3.31\times10^{-7}##, but the user mistakenly interpreted this as a force in Newtons. Overall, the discussion highlights the importance of careful algebraic manipulation in physics calculations.
naushaan
Messages
20
Reaction score
2
Homework Statement
Two ocean liners, each with a mass of 42,000 metric tons, are moving on parallel courses, 92 m apart. What is the magnitude of the acceleration of one of the liners toward the other due to their mutual gravitational attraction? Treat the ships as particles.

I've calculated the Force but I'm struggling to calculate acceleration.
Relevant Equations
F=GMm/r^2
F=ma
1583839005655.png


This is what I've done so far:

1583839127403.png
 
Physics news on Phys.org
It is difficult to deal with large pictures of hand-drawn equations rather than with typewritten equations. Let us try to see what you did.

You started with $$\frac{GMm}{r^2}$$ and substituted in numbers for M, m and r yielding $$\frac{G (42000\times1000)^2}{92^2}$$

But I cannot figure out how you arrived at ##6.6\times10^{-7}## as a result.

Then you go back and apply ##F=ma## to the algebraic formula ##F=\frac{GMm}{r^2}## to correctly decide that $$a=\frac{Gm}{r^2}$$ You then evaluate this with m=42000000 and r=92 to obtain ##3.31\times10^{-7}##. But for some reason you decide that this result is a force rather than an acceleration and give it units of Newtons.
 
jbriggs444 said:
But I cannot figure out how you arrived at 6.6×10−7 as a result.
He wrote and calculated (42000 x 1000) x2 instead of (42000 x 1000)^2
 
  • Like
Likes jbriggs444
mjc123 said:
He wrote and calculated (42000 x 1000) x2 instead of (42000 x 1000)^2
Thank you for that. I saw what I had expected to see rather than what was actually there.
 
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Back
Top