# Can't Seem To Understand This Tension Problem [closed]

I found this problem online while practicing and the answer is supposed to be D. I tried using the answer to solve for $$T$$ and I got $$T=\frac{gm_1m_2}{m_1+m_2}$$. The numerator is what's really confusing me, because I can't think of any situation where you would multiply the two masses together. My answer was $$\frac{T-gm_1}{g}$$.

My rationale was that the downward force of $$m_2$$ is $$gm_2$$, but $$m_1$$ is also exerting an upward force of $$gm_1$$. More rigorously, I found the net acceleration of the entire system to be $$\frac{gm_2}{m_1+m_2}$$ I then subtracted that from gravity to find the counteracting acceleration caused by $$m_1$$. Then I multiplied that by the mass of the system to find the counteracting force exerted by $$m_1$$:

$$(g-\frac{gm_2}{m_1+m_2})(m_1+m_2)$$Then I added that force to $$gm_2$$ to find the tension of the cord:

$$gm_2+(g-\frac{gm_2}{m_1+m_2})(m_1+m_2)=\\gm_2+g(m_1+m_2)-gm_2=\\g(m_1+m_2)$$

So we have $$T=g(m_1+m_2)$$

I've been spending days on this and can't find the mistake. Thank you in advance for any feedback.

## closed as off-topic by user191954, David Z♦Oct 27 '18 at 4:59

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I will tell you what to do. First find the net acceleration of $$m_2$$ using the free body diagram. The upward force is $$T$$ and downward force is $$m_2g$$. $$m_1$$ does not exert force $$m_1g$$ on $$m_2$$. Force on $$m_1$$ is only T. Find the acceleration of $$m_1$$. Then equate the values of acceleration and solve for $$m_2$$