Given the following measurements of velocity for a falling object with m = 3kg: v, meters/seconds t, seconds 0 -1.424 0 0.05 0.10 0.15 0.20 0.25 0.30 Use 4th Order Runge-Kutta to approximate the coefficient of drag, k, given the model: -2.778 -4.068 -5.274 -6.426 -7.519 mv' = -mg - kv Approximate the terminal velocity and the time to reach terminal velocity of the falling
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- Data has been gathered from a lifting system used to transport engine parts. The system consists of a drum and cable. The following data was obtained when the drum lowers the load (assume constant acceleration). Drum diameter = 0.8m Mass of load = 3kg Initial velocitv = 0 m/s Time to descend = A secs 2. ( Distance travelled = 0.25m You have been asked to use this information to determine with 4 s.f. accuracy: Drum Cable a) The final linear velocity of the load b) The linear acceleration of the load Load c) The final angular velocity of the drum d) The angular acceleration of the drum e) The tension force in the cable f) The torque applied to the drum In determining the above quantities, you should clearly state the formulae used and apply dimensional analysis techniques to show that all values/units used are homogeneous.A skateboarder weighing 51.24 kg goes over a smooth circular hilI. If the skateboarder's speed at point A is 21.12 m/s, what is his speed at the top of the hill (point B)? B A 10 m 450 Paint X Ute Use g=9.8 m/s? . Derive first the working equation before you substitute the given data to avoid disparity from the correct answer. Round off answer up to two decimal places. Include the unit/s. Abbreviation only.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 =
- The following equation may be used to estimate the take-off ground run for an aircraft: Equation has been attached as an image. Calculate the take-off ground run, from a runway at ISA-SL conditions, for a twin engine aircraft for which the following data may be assumed Aircraft lift-off speed 155 knots Max take-off gross weight 220 tonnes Wing planform area (S) 358 m Wing CL (t/o flaps deployed, a = 0) 1.1 Wing span 53.18 m Oswald efficiency factor, e 0.7 KGE = CD(IGE) / Co(OGE) 0.4 Co sum (fuselage, wing, tailplane and nacelle) 0.015 Co for undercarriage 0.021 Co for flaps at taking-off setting 0.0073 Coefficient of rolling friction, u 0.02 Engine thrust (assumed constant) 310 kN per engine It may be assumed that 1knot = 0.51444 m/s It may be assumed that 1knot = 0.51444 m/s(b) A wind-tunnel experiment is performed on a small 1:5 linear-scale model of a car, in order to assess the drag force F on a new full-size car design. A dimensionless "drag coefficient" Ca is defined by C, =- pu'A where A is the maximum cross-sectional area of the car in the flow. With the model car, a force of 3 N was recorded at a flow velocity u of 6 m s. Assuming that flow conditions are comparable (i.e., at the same Reynolds number), calculate the expected drag force for the full-sized car when the flow velocity past it is 31 m s (equivalent to 70 miles per hour). [The density of air p= 1.2 kg m.]In the field of air pollution control, one often needs to sample the quality of a moving airstream. In such measurements a sampling probe is aligned with the flow as sketched in Fig. A suction pump draws air through the probe at volume flow rate V· as sketched. For accurate sampling, the air speed through the probe should be the same as that of the airstream (isokinetic sampling). However, if the applied suction is too large, as sketched in Fig, the air speed through the probe is greater than that of the airstream (super iso kinetic sampling). For simplicity consider a two-dimensional case in which the sampling probe height is h = 4.58 mm and its width is W = 39.5 mm. The values of the stream function corresponding to the lower and upper dividing streamlines are ?l = 0.093 m2/s and ?u = 0.150 m2/s, respectively. Calculate the volume flow rate through the probe (in units of m3/s) and the average speed of the air sucked through the probe.
- #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 S03:31 Given-Assign... External Problem 2: Dimensional analysis and similarity The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: PND? and a, = b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750 kg/m and the dynamic viscosity is 0.2 N.s/ m² . For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s / m². IN =1 kgmGiven: 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 Swanbom
- > | E9 docs.google.com/form تبديل الحساب Questions 7 نقاط Q1/ The power of 6-blade flat blade turbine agitator in a tank is a function of diameter of impeller, number of rotations of the impeller per unit time, viscosity and density of liquid. From a dimensional analysis, obtain a relation between the power and the four variables. 3. صفحة 2 منProblem Solving: )An object falls from rest in a medium offering a resistonce. The velocity of the object hefore the ohject reaches the ground is given by the differential egua- tion dv/t + V% = 32, t/sec. uhat is the veloaty of the okject one second after it falls ?(b) A new prototype rocket engine test shows that the distance covered by a rocket from t=8 sec to t= 30 sec is given by - 16 140000 (140000-2100r 2000 In 101)-9.81 ) di Comparing two and three points Gauss Quadrature, investigate which method gives the highest accuracy (in terms of relative error) in predicting the distance covered by a rocket from t = 8 sec to t = 30 sec.