# Multiple Pulleys and Masses with Friction

 P: 9 1. The problem statement, all variables and given/known data I have solved the question but I am still iffy as to whether my solution is correct or not. 2. Relevant equations Let m1 = 10kg. Let m2 = 20kg. (1) m1a1 = T1 - μm1g (2) m2aa = m2g - T2 (3) 2T1 = T2 (4) 2a2 = a1 3. The attempt at a solution T2 = m2g T2 = (20kg)(9.8m/s2) T2 = 196N T1 = $\frac{T_{2} + μm_{1}g}{2}$ T1 = $\frac{196N + (0.32)(10kg)(9.8m/s^{2})}{2}$ T1 = 113.68N Sub (3) and (4) into (2) m2a2 = m2g - T2 m2($\frac{a_{1}}{2}$) = m2g - 2T1 Called this new equation (5). (5) m2($\frac{a_{1}}{2}$) = m2g - 2T1 (1) m1a1 = T1 - μm1g (5) m2($\frac{a_{1}}{2}$) = m2g - 2T1 (1) + (5) m1a1 + m2($\frac{a_{1}}{2}$) = T1 - μm1g + m2g - 2T1 a1(m1 + m2($\frac{1}{2}$) = -μm1g + m2g - T1 a1(10kg + 20kg($\frac{1}{2}$) = -(0.32)(10kg)(9.8m/s2)+(20kg)(9.8m/s2)-113.68N a1 = 2.5448 m/s2 from (4) 2a2 = a1 a2 = $\frac{a_{1}}{2}$ a2 = $\frac{2.548m/s^{2}}{2}$ a2 = 1.274 m/s2 Therefore, T1 = 113.68N, T2 = 196N, a1 = 2.548 m/s2, and a2 = 1.274 m/s2. My question is if my solution is correct. Please check and reply back with suggestions or corrections. Thank you so much.