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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: Dynamics
- h=l m 1) A block of mass M is dropped from rest on the spring as shown in the figure. The spring compresses a maximum of 25 cm. Calculate the speed of the block when the compression of the spring is 15 cm. (M = 5 kg, h=1 m, k = 1000 N / m)arrow_forwardThe super-container vessel in the figure has a total mass displacement of 23000 long tons. This vessel towed by a tugboat with a=20° angle with horizontal. If a constant tension is applied as F=320 kN by the tugboat, please calculate the time to bring the vessel to a speed of 2 knot from the rest. At these low speeds, please neglect the hull resistance that created by the motion. Note: (1 long tons = 1016.05 kg, 1 knot=1.151 mi/hr= 0.5144 m/s) %3Darrow_forwardWe want to design a wagon system like the one below while filling the kiln with coal at the Coke factory inside Kardemir. In this system, we want the wagon to reach a speed of v= 1 m/s in t=2 seconds. It will then shoot at constant speed. How much engine power is required to tow a wagon with W= 500 kgf under these conditions P=? (Losses will be ignored). (The slope angle of the ramp is α= 25 degrees.)arrow_forward
- A spring of force constant K attached to the wall on a horizontal smooth plane. The spring is compressed by a block of mass 6 kg a distance x= 0.2 m. The speed of the block as it released and passes the equilibrium position is 5 m/s. Find the force constant k (in N/m). 100000000000 X=0arrow_forwardAn 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_forwardTwo objects m1 = 5.15 kg and m2 = 2.95 kg)are connected by a light string passing over a light, frictionless pulley as in the figure below. The 5.15-kg object is released from rest at a point h = 4.00 m above the table. (a) Determine the speed of each object when the two pass each other. m/s(b) Determine the speed of each object at the moment the 5.15-kg object hits the table. m/s(c) How much higher does the 2.95-kg object travel after the 5.15-kg object hits the table? marrow_forward
- The figure below shows a diver going through general motion. The diver's center of gravity can be assumed to undergo a projectile motion. Assume that the diver takes off from a diving board such that his center of gravity is a height ho = 11m above the water level and enters the water at a horizontal distance 1 = 4m from the end of the board. If the total time the diver remains in the air is t2 = 2.3s, calculate the speed, vo, and angle of takeoff ,O, of the diver's center of gravity. Also determine the height, hi, the diver reaches at the top of the dive. (Note that tr is NOT half of t2.)arrow_forwardA 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v2 = 1.9 m/s at the bottom. The track is frictionless between points A and %3D B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.28. The velocity of the block is v3 = 1.4 m/s at C. The block moves on to D, where it stops. The height h of the ramp is closest to elle V4 smooth Barough Carrow_forwardName-Lastname:. No . h =1 m 1) A block of mass M is dropped from rest on the spring as shown in the figure. The spring compresses a maximum of 25 cm. Calculate the speed of the block when the compression of the spring is 15 cm. (M = 5 kg, h=1 m, k = 1000 N / m)arrow_forward
- As seen in the figure, it has mass m1 and v isa bullet passes through a pendulum of mass m2 and its velocity v / 2exit with. Pendulum "L" long and mass negligibleIt is suspended on the end of a rope that can be carried. Your pendulum is a verticalminimum velocity v to move on the circlewhat should be min V?arrow_forwardA 67-kg fisherman in a 122 kg boat throws a package of mass mw 15 kg horizontally toward the right with a speed of v, 4.0 m/s as in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown m/s magnitude direction Seled Need Help? Roodarrow_forward3/186 A supertanker with a total displacement (weight) of 140(10') long tons (one long ton equals 2240 lb) is moving forward at a speed of 2 knots when the en- gines are reversed to produce a rearward propeller thrust of 90,000 lb. How long would it take the tanker to acquire a speed of 2 knots in the reverse direction? Can you justify neglecting the impulse of water resistance of the hull? (Recall 1 knot 1.151 mi/hr.)arrow_forward
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