Amey
Last Activity: 9 Years ago
To find constraint eq. we use this

(Ti and ai are Tension in the string and acceleration of the block and are in vector form).
Eg : If there is a pulley with 3 kg block on left side and 5 kg block hanging on the other side.Assuming mass of the pulley and string be negligible,find the acceleration of the block?
To solve this question first find the equation using newton’s law. Assume 5 kg block is moving down with acc. a1 and 3 kg block is moving downward with acc. a2 . Tension will be same along the string as it’s massless. Choose one block let’s say 5 kg block and draw a fbd for that block and write down the equation. The 1st eq. should be like this : 5g-T=5a1
Now chose the 3 kg block and draw fbd. 2nd equation will be : 3g-T=3a1 . Now we have 3 variables but 2 equation so we have to get one more equation using constraint eq.. Using the above equation,for 5 kg and 3 kg block tension and acc. is acting in opposite direction therefore Ta1 cos 180 + Ta2cos 180=0. We used cos 180 because the angle between tension and acceleration is 180.Now we have got 3 equations and 3 unknowns and now we can solve the equation.