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Suppose that the position of a falling object is governed by the following
where
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EBK NUMERICAL METHODS FOR ENGINEERS
- The governing equation of motion for a base motion system is given by (assume the units are Newton) mä(t)+ci(t)+kx(t) =cY@, cos(@,t) +kY sin(@t) %3D Given that m = 180 kg, c = 30 kg/s, Y = 0.02 m, and о, — 3.5 rad/s %3| 1. Use Excel or Matlab to find the largest value of the stiffness, k that makes the transmissibility ratio less than 0.85 2. Using the value of the stiffness obtained in part (1), determine the transmitted force to the base motion system using Matlab or Excel. 3. Display and discuss your results.arrow_forwardAs shown in the following figure, vortices are shed from the rear of a bluff cylinder placed across a flow. The vortices alternately leave the top and bottom of the cylinder, causing an alternating force normal to the freestream velocity. The vortex shedding frequency, f, depends on the fluid density p, width of the cylinder d, freestream velocity V, and fluid viscosity u. (a) Use Buckingham Pi Theorem to develop a functional relationship for f. Use M, L, t as the primary dimensional. Use p, V, and d as the repeating parameters. (b) Vortex shedding occurs in standard air on two cylinders with a diameter ratio of 2. Determine the velocity ratio for dynamic similarity, and the ratio of vortex shedding frequencies. -Vortices Varrow_forwardThe left field wall at a baseball park is 320 feet down the third base line from home plate; the wall itself is 37 feet high. A batted ball must clear the wall to be a home run. Suppose a ball leaves the bat, 3 feet off the ground, at an angle of 45°. Use g = 32 ft/sec as the acceleration due to gravity and ignore any air resistance. Complete parts (a) through (d). (a) Find parametric equations that model the position of the ball as a function of time. Choose the correct answer below. x= (Vo cos 45) t, y = - 16t + (Vo sin 45) t+3 x= (Vo sin 45) t, y = 16t - (Vo cos 45) t+ 3 x= (Vo cos 45) t, y = - 32t + (Vo sin 45)t+3 x= (Vo sin 45) t, y = 32t - (vo cos 45)t+3 (b) What is the maximum height of the ball if it leaves the bat with a speed of 75 miles per hour? Give your answer in feet. The maximum height of the ball is feet. (Type an integer or decimal rounded to two decimal places as needed.) (c) What is the ball's horizontal distance from home plate at its maximum height? Give your…arrow_forward
- An object is shot upward from the ground with an initial velocity of 640 ft/sec, and experiencés a constant deceleration of 32 ft/sec² due to gravity as well as a deceleration of (v(t) / 10) ft/sec due to air resistance, where v(t) is the object's velocity in ft/sec. (a) Set up and solve an initial-value problem to determine the object's velocity v(t) at time t. (b) At what time does the object reach its highest point?arrow_forwardGiven: The plane accelerates in its current trajectory with a= 100 m/s^2 Farag Angle theta= 5° W=105 kips F_drag= 80 kips m= 1000 lbs Find: F_thrust, F_lift Please include the KD. Fthrust Futel t Fueight 000 BY NC SA 2013 Michael Swanbomarrow_forwardA student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 95 (m), and its student designers hope that it can travel fully submerged through water at 0.440 m/s. The water is freshwater (a lake) at T = 15°C. The design team builds a one-fifth scale model to test in their university’s wind tunnel. A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag. The air in the wind tunnel is at 25°C and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achievesimilarity?arrow_forward
- L. y X VA A VB PLANE OF CONTACT BY UBC Engineering On an air hockey table, two pucks of identical mass collide in the middle of the rink. Puck A had an initial m velocity vA 1.9? and puck B had an initial velocity vB = 3.2j The plane of contact can be thought of as a line angled 0 = 34° above the x-axis. If the coefficient of 0.5 between the pucks, what are the velocities of the pucks after the impact? || m according to the x-y axis shown. restitution is e =arrow_forward3.1 Two-dimensional incompressible flow can also be simulated using the vorticity w and streamfunction , instead of using the velocity and pressure variables. The vorticity field can be related to the velocity variables through the curl operation Əv ди Əx ду and the velocity field (u, v) can be related to the streamfunction with მს ду 11== v== Using the continuity equation, show that 2² 2² + əx² Əy² მს əx =-w. (3.252) (3.253)arrow_forwardQ.No.5: (a) Develop an equation by using pi-theorem for the shear stress in a fluid flowing in a pipe assuming that the stress is a function of the diameter and the roughness of the pipe, and the density, viscosity and velocity of the fluid. (b) A model of a torpedo is tested in a towing tank at a velocity of 24.4 m/s. The prototype is expected to attain a velocity of 246 m/min in 15.6°C water. (i) What model scale has been used? (ii) What would be the model speed it tested in a wind tunnel under a pressure of 290 psi and at constant temperature 26.77°C?arrow_forward
- #4 1.11 For a small particle of styrofoam (1 lbm/ft) (spherical, with diameter d = 0.3 mm) falling in standard air at speed V, the drag is given by FD-3mVd, where is the air viscosity. Find the maximum speed starting from rest, and the time it takes to reach 95 percent of this speed. Plot the speed as a function of time. s) Answer: (Vmax=0.0435",t=0.0133 Sarrow_forwardFIRST ORDER LINEAR EQUATIONS TO DYNAMICS A rocket that starts from rest is propelled by a constant thrust of 3000 pounds in a straight horizontal path for 40 seconds. Suppose that, as the propellant is burned, the mass of the rocket varies with time in accordance with m = 50 – t slugs, and that the drag force is numerically equal to four times the velocity. Please answer both parts: a) Find the velocity equation of the rocket (which includes finding C) b) What is the velocity of the rocket when t = 30 seconds?arrow_forwardApplying principles of dynamics, with step by step solutions pls (i give 5 stars) A usual football tryout involves a player running a 40-yard dash. If a particular player finishes the dash in 4.25 seconds while reaching his maximum speed at the first 16 yard mark with a constant acceleration and then maintains that speed for the remainder of the run, determine this person’s acceleration over the first 16 yard, his maximum speed and how long he accelerated. SET YOUR OWN VARIABLES AS YOU SEE FIT.arrow_forward
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