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. A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline. There is no slippage between the string and the pulley. The moment of inertia of the pulley is Mr2 . If m1 is 4.0 kg, m2 is 4.0 kg, and M is 4.0 kg, and the angle is 20°, then what is the acceleration of the masses?

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lublana

Answer:

[tex]2.2 m/s^2[/tex]

Explanation:

We are given that

Mass of pulley=M

[tex]m_1=4 kg[/tex]

[tex]m_2=4 kg[/tex]

[tex]M=4 kg[/tex]

[tex]\theta=20^{\circ}[/tex]

Moment of inertia,I=[tex]Mr^2[/tex]

According to question

[tex]T_2=m_2a+m_2gsin20[/tex]

[tex]T_1=m_1g-m_1a=m_1(g-a)[/tex]

[tex]T_1-T_2=I\alpha[/tex]

[tex]\alpha=\frac{a}{r^2}[/tex]

[tex]m_1g-m_1a-m_2a-m_2gsin20=Mr^2\times \frac{a}{r^2}=Ma[/tex]

[tex]4\times 9.8-4a-4a-4\times 9.8sin20=4a[/tex]

[tex]4a+4a+4a=4\times 9.8-4\times 9.8sin20[/tex]

[tex]12a=25.87[/tex]

[tex]a=\frac{25.87}{12}=2.2 m/s^2[/tex]

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