Question

求解一道物理题目~~急急急。。英文的

An Atwood's machine consists of two masses, m1 and m2 (m2 > m1), which are
connected by a massless inelastic cord that passes over a pulley. Model the pulley as a cylinder of unknown radius R and known mass M. Noting that the tensions F1 and F2 are not equal, if the masses m1, m2 and M are known, find the acceleration of the system.

Answer 1

滑轮力矩，作用产生转动加速度
F1-M1G = M1a
M2G-F2 = M2a
F2-F1 = 滑轮受力F
转动惯量*角加速度 = F*R 动转惯量是=1/2MR2
角加速度*R = a

联立上面方程
（F2-F1）R=a/R *1/2MR2
F1=M1G+M1a
F2=M2G-M2a

则M2G-M2a-M1G-M1a =1/2Ma
a=（2M2G-2M1G）/（M+2M2+2M1)