Obtain the equation of motion for a particle falling vertically under the influence of gravity when frictional forces obtainable from a dissipation function 1/2kv2 are present. Integrate the equation to obtain the velocity as a function of time and show that the maximum possible velocity for a fall from rest is v = mg / k.

Given the following: Mass of the particle m=18.8 kg, ω=9.6 rad/s, α=8.3 rad/s^2, vrel=7.8 m/s, μs=0.6, μk=0.1, L=1.9 m, and h=2.9 m, What is the i^ component of the Normal force on particle P? What is the component of the friction force in the j^ direction on the particle?   What is the value (including sign) of (aP/O)rel?   What is the i^ component of the Acceleration of particle P?   What is the j^ component of acceleration of particle P?

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…

A certain lake is proposed as a landing area for large jet aircraft. The touchdown speed of 100 mph upon contact with the water is to be reduced to 20 mph  in a distance of 1500 ft. If the deceleration is proportional to the square of the velocity of the aircraft throug the water, a=-kv^2 , find the value of the design parameter k . This parameter serves as a measure of the size and shape of the landing gears vanes that plow through the water. Also, determine the time elapsed during the spedified interval. (1 mile=5280 ft)