8.10 A fixed pulley carries a weightless thread with masses \(m_{1\ }\)and \(m_{2\ }\)at its ends. There is friction between the thread and the pulley such that the thread starts slipping when \(m_2/m_1 = \eta_0\). Find: a) the friction coefficient; b) the acceleration of the masses when \(m_2/m_1 = \eta >\eta_0\).

8.11 A tree-trunk of diameter 20cm lies in a horizontal field. A lazy grasshopper wants to jump over the trunk. Find the minimum take-off speed of the grasshopper that will suffice.

8.12 A tanker full of liquid is parked at rest on a horizontal road as shown in Figure 6. The brake has not been applied, and it may be supposed that the tanker can move without friction. In which direction will the tanker move after the tap on the vertical outlet pipe, which is situated at the rear of the tanker, has been opened? Will the tanker continue to move in this direction?