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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.

Respuesta :

Answer:211.11 gm

Explanation:

Given

mass of lighter block [tex]m_1=100 gm[/tex]

mass of heavier  block is [tex]m_2[/tex]

acceleration of system [tex]a=3.5 m/s^2[/tex]

From diagram

for lighter block

[tex]T-m_1g=m_1a[/tex]

[tex]T=m_1(g+a)[/tex]

For heavier Block

[tex]m_2g-T=m_2a[/tex]

[tex]T=m_2(g-a)[/tex]

Equating Tension T

[tex]m_1(g+a)=m_2(g-a)[/tex]

[tex]m_2=m_1\cdot \frac{g+a}{g-a}[/tex]

[tex]m_2=m_1\cdot \frac{9.8+3.5}{9.8-3.5}[/tex]

[tex]m_2=0.1\cdot 2.11[/tex]

[tex]m_2=0.2111 kg[/tex]

[tex]m_2=211.11 gm[/tex]

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