All Problems The Fundamental Equation of Dynamics
Problem 1.71
A pulley fixed to the ceiling of an elevator car carries a thread whose ends are attached to the loads of masses \(m_{1}\) and \(m_{2}\). The car starts going up with an acceleration \(w_{0} .\) Assuming the masses of the pulley and the thread, as well as the friction, to be negligible find: (a) the acceleration of the load \(m_{1}\) relative to the elevator shaft and relative to the car; (b) the force exerted by the pulley on the ceiling of the car.
1.71. (a) \(\mathbf{w}_{1}=\frac{\left(m_{1}-m_{2}\right) \mathrm{g}+2 m_{2} \mathbf{w}_{0}}{m_{1}+m_{2}}, \quad \mathbf{w}_{1}^{\prime}=\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\left(\mathbf{g}-\mathbf{w}_{0}\right) ;\) (b) \(\mathbf{F}=\frac{4 m_{1} m_{2}}{m_{1}+m_{2}}\left(\mathbf{g}-\mathbf{w}_{0}\right)\)