(3) A 300 N force is applied to the plate at A as shown. (a) Use the scalar components method to determine the moment of the 300 N force about D. (b) Determine the magnitude of the maximum moment about D that a 300 N force can create if it is applied at C. Ans: (a) 41.7 Nm CCW (b) 70.8 N·m 200 mm 100 mm- 200 mm 25° 300 N B 125 mm
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- A sheet of water of uniform thickness (h = 0.03 m) flows from the device shown in the figure below. The water enters vertically through the inlet pipe and exits horizontally with a speed that varies linearly from 0 to 11 m/s along the 0.2-m length of the slit. Determine the y component of anchoring force necessary to hold this device stationary. FAY = 0 m/s- i 0.2m 0.03m N 11m/sThe Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region 0.6x² and below the line 2 above the curve y y = 280. (Here, distances are measured in meters.) The water level is 34 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by kg m³ = water pressure. (Water has a density of 1000- and the acceleration of gravity is 9.8 m sec² .) " Note: Weight density of water is 1000 (9.8)=9800 N/m^3A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 3.25 ✕ 10−5 T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration. HINT (a) the magnitude (in N) of the magnetic force acting on the ion N (b) the magnitude (in m/s2) of the ion's acceleration m/s2
- The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y 0.3x² and below the line y 180. (Here, distances are measured in meters.) The water level is 36 meters below the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. (Water has a density of 1000kg/m³, and the acceleration of gravity is 9.8m/sec².) Answer:A helicopter flies over the arctic ice pack at a constant altitude, towing an airborne 147-kg laser sensor which measures the thickness of the ice (see the drawing). The helicopter and the sensor move only in the horizontal direction and have a horizontal acceleration of magnitude 2.54 m/s2. Ignoring air resistance, find the tension in the cable towing the sensor.(7) The effect of a slam dunk can be simulated by a force F = 47 lb acting at the front edge of the rim at point A shown. Use the scalar components approach to determine the moments of the force F about point O Mo and point B MB. Ans: Mo=81.5 lb-ft CCW, MB = 115.9 lb-ft CW -36"- B 12" 28" 10' F
- (5) The force F=80 N is applied to the crank OA through rod AB at point A as shown, with OA= 0.05 m, 0 = 55°, and ẞ= 15°. (a) Determine from geometry the moment arm d for the force about point O, and then (b) determine the moment of the force F about point O. Ans: (a) 0.0383 m (b) 3.06 N·m CCW F BAn inverted truncated pyramid-shaped tank with square cross section shown in the figure below is 8 m tall with 64 m² cross sectional area at the top and 16 m? cross sectional area at the bottom. The tank is full of oil of density p = 100 kg/m³. Find the work required to pump the oil in the tank 1 m above the top of the tank. (Note that the acceleration due to gravity is g = 9.8 m/s²). Include units in your answer. 8mA car travels over the hill having the shape of a parabola. When the car is at point A, it is traveling at 9 m/sec and increasing its speed at 3 m/sec2 . Determine the tangential and normal components of acceleration of the car at point A labeled below
- A 68 kg skydiver jumps out of an airplane. We assume that the forces acting on the body are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude cv² where c = 0.175 kg and v(t) is the velocity of the skydiver at time t (and upward is positive velocity). The gravitational constant is g = 9.8m/s². m a) Find a differential equation for the velocity v : dv dt b) Determine the terminal velocity in meters per second for free-fall (no parachute). terminal velocity= m/s Note: Answer should be negative for downward velocity.Use the concept of Particular Antiderivatives and Rectilinear Motion to answer the problem below: On the edge of an 8m building, Sam throws his toy vertically upwards at initial velocity = 28 m/s. If the only force that acts on the toy is accelerationdue to gravity (-32 ft/s), a. How many seconds will it take for the toy to reach its maximum height?b. What is the toy's speed when it hits the ground?A cable exerts a constant upward tension of magnitude 2.14 ✕ 104 N on a 2.00 ✕ 103 kg elevator as it rises through a vertical distance of 3.90 m. HINT (a) Find the work done by the tension force on the elevator (in J). J (b) Find the work done by the force of gravity on the elevator (in J). J
