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Consider a rigid body initially at rest and subjected to an impulsive force F contained in the plane of the body. We define the center ofpercussionP as the point of intersection of the line of action of F with the perpendicular drawn from G. (a) Show that the instantaneous center of rotation C of the body is located on line GP at a distance
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Vector Mechanics For Engineers
- A 240-lb block is suspended from an inextensible cable which is wrapped around a drum of 1.25-ft radius rigidly attached to a flywheel. The drum and flywheel have a combined centroidal moment of intertia of 10.5 lb-ft-s^2. At the instant shown, the velocity of the block is 6 ft/s directed downward. The bearing at A as a frictional moment of 60 lb-ft. What is the kinetic energy of the system after the block moved after 4ft? (in ft-lb)arrow_forwardb 4 k m 36 4 A b 4 B The uniform slender bar of mass 3.0 kg pivots freely about a horizontal axis through O. If the bar is released from rest in the horizontal position shown where the spring is unstretched, it is observed to rotate a maximum of 42° clockwise. The spring constant k = 230 N/m and the distance b = 0.3 m. Determine the total work done on the bar.arrow_forwardQ4. A particle, of mass 2 kg, is attached to one end of a light inextensible string. The other end is fixed to the point O. The particle is set into motion, so that it describes a horizontal circle of radius 0.6 metres, with the string at an angle of 30° to the vertical. The centre of the circle is vertically below O. (a) Show that the tension in the string is 22.6 N, correct to three significant figures. (b) Find the speed of the particle. 30° 0.6m Iarrow_forward
- Bar AB in the figure rotates counterclockwise with a constant angular velocity of 2.5 rad/s. If all of the bars have a unit mass of 2 kg/m, determine the total kinetic energy of the system in the position shown.arrow_forwardA rotating shaft carries four masses A, B, C and D which are radially attached to it. The mass centres are30 mm, 38 mm, 40 mm and 35 mm respectively from the axis of rotation. The masses A, C and D are 7.5kg, 5 kg and 4 kg respectively. The axial distance between the planes of rotation of A and B is 400 mmand between B and C is 500 mm. The masses A and C are at right angles to each other. Find for acomplete balance; determine (a) the angles between the masses B and D from A, (b) the axial distancebetween the planes of rotation of C and D, (c) the magnitude of mass B.arrow_forwardRod OA rotates counterclockwise at a constant angular rate 0-4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r= (1.6 cos 6) m. Both collars have a mass of 0.65 kg. Motion is in the vertical plane. (Figure 1) Figure r=1.6 cos 9. 0-4 rad/s 0.8 m 1 of 1 Part A Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant 0=45 Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) F= Value Submit μÁ Part B Previous Answers Units X Incorrect; Try Again; 5 attempts remaining Determine the magnitude of the force that OA exerts on the other colar at the instant @-45. Express your answer to three significant figures and include the appropriate units. View Available Hint(s)arrow_forward
- 1) The figure below shows a system in which mass m2 is added to mass m1 (the spring is not stretched). Answer the following questions about the motion when mass m2 is released freely. However, the mass and moment of inertia of the movable pulley are ignored. M X1 mi m2 X2 1) Show the kinetic energy of the entire system using x1 and x2 (just the answer is enough). 2) Show the relationship between x1 and x2 (just the answer is enough). 3) Find the equivalent mass of the entire system. 4) Show the equation of motion of the system using this equivalent mass. However, assume that the damping is zero. 5) Find the natural frequencyarrow_forwardA 50-kg bar is subjected to a 100-N horizontal force, and two negligible-mass rods swing with a counterclockwise angular velocity of w = 5 rad/s. Determine the tension in Rod CD in N? w = 5 rad/s 1.5 m 100 N. B D •G 1 m 1 marrow_forwardThe forearm shown below is positioned at an angle θ with respect to the upper arm, and a 5.0-kg mass is held in the hand. The total mass of the forearm and hand is 3.0 kg, and their center of mass is 15.0 cm from the elbow. (a) What is the magnitude of the force that the biceps muscle exerts on the forearm for θ = 60°? (b) What is the magnitude of the force on the elbow joint for the same angle? (c) How do these forces depend on the angle θ ?arrow_forward
- 3. Figure 3 shows a system consisting of wedge A and block B connected by an inextensible cable that runs around three pulleys. The mass of A is 12 kg and the mass of B is 3 kg. Due to the application of the constant force P = 40 N, wedge A moves to the right causing block B to move up on the wedge. The friction between the wedge A and the horizontal surface is negligible. The kinetic coefficient of friction between A and B is μ = 0.25. If the system is originally at rest (before P was applied), determine the accelerations of wedge A and block B immediately after P is applied. Also, calculate the tension in the cable. Ans.: a=0.22 m/s² <; 20.3 N B A 30° P=40 N Figure 3arrow_forwardA body has mass 450 g .when it revolves in a circle of radius 2m.The body makes 2 revolution per second . the centripetal force is : *arrow_forward4. A six-pound weight hanging from the end of a spring is pulled 10 centimeters below its resting position and released; it takes 0.9 seconds to complete a cycle. Determine an equation for the motion of the weight, assuming that it is 10 centimeters below its resting position and rising at t = 0. 16165 -- below t=0 t=0.9arrow_forward
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