2. [25 pts] Consider the electro-hydraulic actuator system below in which an electric motor driven pump is used to control a linear actuator. The pump is assumed to be ideal.

Weight of the mass: W = Mg = 1e4 N Actuator piston area: Ap = 0.001 m? Pump displacement: D = 20cc/rev a) [10pts] Ignoring the needle valve, find i) pressure drop Ap[Pa], ii) ideal pump torque T ideal [N], and iii) ideal pump speed wheel [rad/sec] in order to raise the mass at a speed of v=0.1m/s. b) [15 pts] Consider now that the needle valve is in place representing leakage. It is known that the valve has these characteristics: \mathrm{Q}_{\text {leak }}=5 \mathrm{cc} / \mathrm{s} \text { when pressure drop is } \Delta p=5 \mathrm{MPa} Find i) the orifice flow Qleak, ii) the new pump torque T [Nm] and iii) new pump speed w[rad/sec] in order to raise the mass at a speed of v=0.1m/s. Determine also iv) the power loss at the needle valve.