8.4 For the bar-spring-mass system in Fig. P8.4, assume that the bar is rigid but its mass is negiigibie, that the rotation of the bar remains small, and that gravity can be neglected. In parts (a) and (b), derive the equations of motion, and write the equations in matrix form. (a) Let coordinates u, and uz be the vertical displacements of the masses m, and m2, respectively. (b) Let coordinates u, and uz be the vertical displacements of points A and C where springs k, and k2, respectively, are connected to the rigid bar. (c) Briefly discuss how the equations of motion are coupled in each case.

A light parachute for military purposes is being designed. Its diameter is 7.3 m, test load, parachute and rig weight is 1023 N. For this weight, the limit descent speed Vt = 6.1 m / s, which is taken as a basis in the design of the parachute. The 1/12 scale model will be tested in the wind tunnel and the temperature and pressure of the tunnel are the same as that of the prototype. (15.5 ºC and standard atmospheric pressure) a) Calculate the resistance coefficient of the prototype. (Hint: At the limit descent speed, the weight is balanced by the aerodynamic resistance.) b) At what speed should the wind tunnel be run to achieve dynamic similarity? c) Calculate the aerodynamic resistance of the model parachute in the wind tunnel. Density of air at 15.5 ºC and standard atmospheric pressure ρ = 1.22 kg / m3 viscosity, µ = 8.16x10-6 kg / m.s will be taken.

This exercise is part of a series of problems aimed at modeling a situation by progressively refining our model to take into account more and more parameters. This progressive approach is very close to what professional scientists do! context We want to lower a suspended load in a controlled way so that it hits the ground with a speed whose modulus is not too great. To slow down the descent, a spring has been added behind the mass (A), The suspended load (B) is connected by a rope passing through a pulley to this mass (A), which slides on a horizontal surface with friction.   Information The masses of the charges A and B are known.The mass of the rope itself is negligible (very small compared to the loads).The pulley has negligible mass and can rotate without friction.The charge B is initially stationary and is at a known height h.The surface on which mass A sits is tilted upwards at a known angle theta from the horizontal.There is friction under mass A: the kinetic friction…

Expanded.3 deals with the conservation of momentum principle. Using the conservation of momentum principle to solve this problem is mandatory. Solution using other approaches will be automatically considered false. For the problem related to Expanded.3, sketches of the system showing: • the respective initial and final velocity and position coordinates and the frame of reference considered • the forces acting on the system of considered, in other words, a free body diagram (FBD) are mandatory. Their absences will automatically make the problem false. The automobile has a weight 3,158-lb and travels forward at 8ft/s when it crashes into the wall and stops. The impact occurs in 0.04 s. If the coefficient of kinetic friction between the wheels and the pavement is 0.42, and the brakes are applied, what is then the average impulsive force?