I have been solving this problem:
A 5kg object on the table is linked to a 3kg object hanging from a massless rope in a pulley system as shown in the picture. Find the acceleration of a 5-kg objected. Ignore friction
So I drew up my free-body diagram and came up with these equations:
I assumed tension is the same on
$$m_1a = T$$
$$m_2a = W-T$$
After I got those two equations I replaced T this equation:
$$m_2a = m_2g – m_1a$$
Then I did some algebra to simply the equation, plugged in the masses and solved for acceleration:
$$a = \frac{m_2g}{m_2+m_1}$$
Acceleration equaled to around 3.68m/s^2
However, my friend was arguing that my calculations were incorrect because he said that tension equals to the weight of object 2, therefore he said
$$T = W_2$$
$$T = m_2g$$
$$T = 29.4N$$
After he obtained this tension he then solved for acceleration and got an acceleration of object 1 to be 5.88m/s^2
Is he correct to evaluate tension as the weight of object 2?
Best Answer
First of all common sense tells us that if the surface is smooth enough, then the system is definitely going move with certain acceleration.
If so, then mass 2 will also accelerate, this implies that net force on m2 is not zero. But if you put T = W for mass 2, then net force will become zero. Thus the assumption that T=W for m2 is wrong.
And yes your assumption that m2a = W - T and m1a = T, are correct.