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 m1m_{1} and m2m_{2}. The car starts going up with an acceleration w0.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 m1m_{1} relative to the elevator shaft and relative to the car; (b) the force exerted by the pulley on the ceiling of the car.

Reveal Answer
1.71. (a) w1=(m1−m2)g+2m2w0m1+m2,w1′=m1−m2m1+m2(g−w0);\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) F=4m1m2m1+m2(g−w0)\mathbf{F}=\frac{4 m_{1} m_{2}}{m_{1}+m_{2}}\left(\mathbf{g}-\mathbf{w}_{0}\right)
Prev
Next