Convincing Features
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Question 1
a) In a room with no wind, a worker pushes a 10-kg trolley to a velocity of 1.5 m/s before letting go, as shown in Figure Q1a. Determine the distance traveled by the trolley before stopping, given that the coefficient of drag is 0.94 and the rolling (wheels) friction is 2 N. Assume that the density of air is 1.225 kg/m³
and that the frontal area is 0.4 m²
b) ) A tropical cyclone is a natural phenomenon on Earth, as shown in Figure Q1b. The wind speed of a cyclone can reach above 70 m/s, as measured on the eyewall or approximately 30 km from the center of the cyclone. Assume a cyclone with these numbers (maximum speed of 70 m/s at 30 km from the center) and the compound vortex model. Determine the angular velocity and the size of the cyclone. Take the size as the location when the wind speed drops below 2 m/s.
Question 2
Given the governing equations below, identify the equations on each line and sketch the domain
Question 3
(a) An airplane weighing 50,000 kg stalls at a high angle of attack of 105°. The engines produce a net thrust of 120 kN, but the flight is losing altitude at a constant speed, moving forward at 60° below the horizon. Using a free-body diagram, determine the drag force and the lift force of the plane.
(b) For compressible air flowing in a pipe, the diameter, pressure, velocity and temperature at the upstream section are 0.2 m, 50 kN/m², 30 m/s, and 50°C respectively. Given that the downstream section velocity is 50 m/s, determine the diameter of the pipe at the downstream section. Assume that the process is isothermal. Take ʏ = 1.4, R = 287 J/kg/K.
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