Question

Engineering dynamics

The wheel has an inner radius of 1 meter and an outer radius of 3 meters. It weighs 25 kilograms and has a radius of gyration about its mass center of 2 meters. The wheel rolls without slipping. Find the acceleration of block B which weighs 15 kilograms. ? 0.75 TO

Answer 1

A = r so T + F = m_A a S (TR + Fr) = m_A K^2 a/r S m_B g - 2T = m_B a/2 solving rightarrow F = (m_A a - T) S TR + (m_A a - T) r = m_A k^2 a/r rightarrow TR + (m_A a - T) r = m_A k^2 a/r rightarrow R (R- r) + m_A ar = m_A - k^2 a rightarrow T (rS) = m)A a (k^2/r - r)^r rightarrow T = m_A a (k^2 - e^2)/r (R - r) also m_B g - 2T = m_B a/2 rightarrow m_B g = [2 m_A (k^2 - r^2)/r (R - r) + m_B/) q rightarrow s a = m_B g m_B/2 + 2 m_A (k^2 - r^2)/r (R - r) Given r = 1 m R = 3m k = 2m m_A = 25 , m_B = 15 so a = 15 times 9.81 15/2 + 2 times 25 times 3/1 (3 - 1) = 66.9 N F = -22.35 N lessthanorequalto mu N also mu N = 0.75 times m_A 9 = 0.75 times 25 times 9.81