Question

J 0.5kg-m2 that is initially rotating at an angular Figure P6.1 shows a flywheel with moment of inertia velocity 6o-40rad/s. The flywheel i subjected to friction, which is modeled by linear viscous friction torque bo, with friction coefficient b 0.06 N-m-s/rad. Use Simulink to obtain the dynamic response and plot the angular position θ(t) (in rad) and angular velocity θ(t) (in rad/s). In addition, use the simulation to integrate the rate of energy dissipation & and plot dissipated energy (in J) vs. time. Show that the total dissipated energy as computed by thc simulation is cqual to the system's initial energy 6.1 Flywheel, J Viscous friction, b Figure P6.1

pls solve
Mathematical model
Mathlab Simulink digram
Plot diagram

Answer 1

Given that: a fly wheel with moment of inertia J = 0.5 kg - at that is initially rotating at an angular velocity theta_1 = 40 rad/s. the fly wheel is subjected to friction, modeled by linear viscous friction coefficient b = 0.06 N - n S/rad. The fly wheel moment of inertia J = 0.5 kg/m Angular velocity theta_0 = 40 rad/s various for que = by tub = bw b = 0.06 uns/rad at a time 't'. \r\n let the angular velocity bw to trarque = g times dw/dt -bw = j times dw/dt -bx dt/g = dw/w integrating velocity bt/g = ln (w) + t Now, at t = 0/w = w_0 these, I_n (w_0) = -k So -bt/g = m(w) = ln (w_0) w = w_0 times e^^(-bt + g) the time given by w = 40 times e^^(-0.06t/0.5) w = 40^^(-0.12 t) Now power begin at this time P = torque