A block (mass = 2.0 kg) is hanging from a massless cord that is wrapped around a

Question

A block (mass = 2.0 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.1 10-3 kg

Explanation / Answer

Newtons Second says the force on the block is: F = m_b*g-T = m_b*a_y --> T = m_b*g-m_b*a_y Where m_b is the mass of the block. Now we know that ay = dv/dt = r dw/dt = r*alpha where alpha is angular acceleration So T = m_b*g-m_b*r*alpha now the torque on the pulley is tau = r T = I*alpha (I is moment of inertia of pulley). So m_b*g *r - m_b*r^2*alpha = I*alpha ---> alpha = m_b*g*r/(m*r^2+I) now T = I *m_b*g/(m*r^2 +I) from torque equaiton. Plugging in numbers alpha = 114.8 rad/s^2 and T = 5.601 N

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