Solving for acceleration of two blocks with two pulleys

Thread starter Che8833
Start date Apr 1, 2019
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Acceleration Blocks Pulleys Two blocks

AI Thread Summary

The discussion focuses on solving for the acceleration of two blocks connected by pulleys using three key equations. The first equation relates tension to the mass and acceleration of one block, while the second equation balances forces on the second block. The third equation establishes a relationship between the accelerations of the two blocks. A participant confirms the correctness of the calculations, arriving at the final acceleration formula. The conclusion reached is a1 = mg / (4M + m), indicating agreement on the solution.

Apr 1, 2019

Che8833

Homework Statement: If block A has mass M and block b has mass m, find the acceleration of block B assuming that the acceleration of block A equals two times the acceleration of block B.

Relevant Equations: Equation 1: T = Ma1

Equation 2: mg - 2T = ma2

Equation 3: a1 = 2a2

Equation 1: T = Ma1

Equation 2: mg - 2T = ma2

Equation 3: a1 = 2a2

Since a1 = 2a for equation one I get T = 2Ma1

mg - 4Ma1 = ma1

mg = 4Ma1 + ma1

mg = 4a1(M+m)

a1= mg / 4M+m

Not sure if this is correct. Can someone please help to make sure I'm doing this right?
Thanx

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Apr 1, 2019

quinoa19

Looks correct, I got same answer,
##a_{\rm B}=\frac{mg}{m+4M} ##

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