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An airplane with a weight W and a total wing span b flies horizontally at a constant speed v. Use the airplane as a reference frame: that is, consider the airplane to be motionless and the air to flow past it with speed v. Suppose that a cylinder of air with diameter b is deflected downward by the wing (the cross section of the cylinder is the dashed circle in the figure). Show that the angle through which the cylinder stream is deflected (called the downwash angle) is determined by the formula sin
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Vector Mechanics For Engineers
- A block of wood with a weight of 30 N is held by a spring with a stiffness of 2 N/mm, as shown in the figure below. A bullet with a weight of 2 N is fired at a speed of 20 m/s into a speed of 20 m/s into the block and sinks into it. Assuming that all the momentum of the bullet is transferred to the block, the motion of the bullet is entirely transferred to the block at the moment of impact, we ask to calculate the maximum displacement of the block a) neglecting damping and b) assuming that the damping is 10% critical. ..arrow_forwardA small ball of mass m is placed on top of a large ball of mass 3m. Both balls are dropped simultaneously from a height h = 7 m as shown in the figure. Assuming the radius of the large ball and small are small and thus negligible in comparison to the height they are being dropped meaning the small ball has the same speed the large ball has when it hits the ground. If the large ball rebounds elastically from the floor, collides with the small ball, stops and then the small ball rebounds elastically from the large ball, find the maximum height the small reaches. Hint: Model all collisions as perfectly elasticarrow_forwardA non spinning ball having a mass of 3.5 oz is thrown vertically upward with a velocity of 100 mph and has zero velocity at a height of 210 ft above the release point. Assume that the air drag on the ball is constant and find this constant average" air drag. Neglect the buoyant force of air on the ball.arrow_forward
- An aircraft, of mass 2000 kg, is following a circular path in the vertical plane as shown inFigure 2. When the flight path of the aircraft is at an angle of 30 from the horizontal, theaircraft’s velocity is 150 m/sec, the radius of curvature of its trajectory is 1000 metres,and the net thrust (engine thrust minus drag) isT = 30kN and acts along the flight path.Assume that the lift force L is perpendicular to the flight path.Draw a free-body diagram showing all forces acting on the aircraft. Calculate the resultantacceleration and its angle from the flight path. Also calculate the lift force L.arrow_forwardA package is dropped from a height h. A high-speed camera is used to determine that the rebound height is ¼ of the drop height. If the impact velocity is 176 in/s, find the drop height, the coefficient of restitution, and the velocity change during the impact.arrow_forwardAn engineering student considers using a fan as a levitation demonstration. She plans to face the box-enclosed fan so the air blast is directed face down through a 3-ft-diameter blade span area. The system weighs 5 lbf, and the student will secure the system from rotating. By increasing the power to the fan, she plans to increase the blade rpm and air exit velocity until the exhaust provides sufficient upward force to cause the box fan to hover in the air. Determine (a) the air exit velocity to produce 5 lbf, (b) the volumetric flow rate needed, and (c) the minimum mechanical power that must be supplied to the airstream. Take the air density to be 0.078 lbm/ft3.arrow_forward
- An electric motor M is used to reel in cable and hoist a bicycle into the ceiling space of a garage. Pulleys are fastened to the bicycle frame with hooks at locations A and B, and the motor can reel in cable at a steady rate of 20 in./sec. At this rate, how long will it take to hoist the bicycle 7.9 feet into the air? Assume that the bicycle remains level.arrow_forwardAssuming that there are no heat effects and no frictional effects, find the kinetic energy and speed of a 3220‐lb body after it falls 778 ft from rest. Start with the steady flow equation, deleting energy terms which are irrelevant.arrow_forwardA 100-ft3 /s wáter jet hits a horizontally lying stationary splitter, such that half of the mass flow is diverted one way and the other half is diverted the other way, and both streams have a uniform velocity of 18 ft/s. The deflection angle of the splitter is 45 degrees as shown. Obtain (a) the cross-sectional area of the jet and (b) the horizontal (x-y) components of the force required to hold the splitter in place.arrow_forward
- Compare the total momentum before and total momentum after of elastic and perfectly inelastic collision. Compare the total KE before and total KE after of elastic and perfectly inelastic collision.arrow_forwardFind the total rebound distance of a ball that is dropped from height of 7 m,with each rebound three-fifths of the preceding one.arrow_forwardBlock A with a weight of 100N (mA=10kg) moves to the right (vA=1 m/s) at the moment shown in the figure. Since the kinetic friction coefficient between the surface and block A is μk=0.2, find the speed of block B when it moves 2 meters its weight is 200N (mB=20kg)arrow_forward
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