(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The figure shows two blocks suspended by a cord over a pulley. The mass of black B is twice the mass of black A, [tex]m_b = 2m_a = 2m[/tex]. The mass of the pulley is equal to the mass of black A, [tex]m_p = m_a = m[/tex], the radius of the pulley is [tex]R[/tex]. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cords are massless. The rotational inertia of the pulley is [tex]\frac{m_pR^2}{2}[/tex] about a perpendicular axis through the center. Find the magnitude of acceleration of the block B. Express your results in the simplest possible form in terms of any or all the following: m, g, R, and universal physical or mathematical constants.

2. Relevant equations

[tex]F_G = m * g[/tex] (force of gravity equals mass times gravitational acceleration)

[tex]\tau_net = I * \alpha[/tex] (torque equals moment of inertia times angular acceleration)

3. The attempt at a solution

[tex]\tau_{net} = I * \alpha = \frac{m * R^2}{2} * \alpha = \frac{m * R^3}{2} * a[/tex]

furthermore,

[tex]\tau_{net} = F_{G on B} * R + F_{G on A} * R = 2 * m * g * R - m * g * R = m * g * R[/tex]

so,

[tex]m * g * R = \frac{m * R^3}{2} * a[/tex]

which leads to the answer:

[tex]a = \frac{2 * g}{R^2} m/s^2[/tex]

Is this correct? Is there an easier way?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find acceleration of a Block within a simply pulley system.

**Physics Forums | Science Articles, Homework Help, Discussion**