Question

Two blocks of masses m1 and m2 are connected to each other on an Atwood machine (the blocks are connected by a string going over a light pulley with no friction in the bearing). A person holds one of the blocks with her hand. When the system is released, the heavier block moves down with an acceleration of 3.5 m/s2 and the lighter object moves up with an acceleration of the same magnitude. Suppose that the lighter block has a mass of m1 = 100 g. Determine the mass m2.

Answer 1

Answer:211.11 gm

Explanation:

Given

mass of lighter block $m_1=100 gm$

mass of heavier  block is $m_2$

acceleration of system $a=3.5 m/s^2$

From diagram

for lighter block

$T-m_1g=m_1a$

$T=m_1(g+a)$

For heavier Block

$m_2g-T=m_2a$

$T=m_2(g-a)$

Equating Tension T

$m_1(g+a)=m_2(g-a)$

$m_2=m_1\cdot \frac{g+a}{g-a}$

$m_2=m_1\cdot \frac{9.8+3.5}{9.8-3.5}$

$m_2=0.1\cdot 2.11$

$m_2=0.2111 kg$

$m_2=211.11 gm$