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Consider the frame of reference Ax'y'z' in translation with respect to the newtonian frame of reference Oxyz. We define the angular momentum
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Vector Mechanics For Engineers
- 1. Two mobile containers, A and B, carries raw materials for concrete batching plant. The containers' motions are defined by their velocity vectors: for container A, A = 6i + 4k (km/hr) and for container B, B = -4i +7k (km/hr). What is the angle between the line of action (path) of both containers? Express your answer in units of degree. 2. Two cables A and B are attached to a hook. Cable A exerts a pull with a magnitude and direction defined by the vector A = 6i + 4k (kN). Cable B is also attached to the same hook where cable A is attached, cable B exerts a pull with a magnitude and direction defined by the equation B = -4i +7k (kN). What should be the magnitude of pull exerted at cable B such that the line of action of resultant force is along the positive z-direction (the resultant lies along the positive z-axis)? Express your answer in unit of kN.arrow_forwardAn aircraft flying at a height of 800m with uniform horizontal velocity of 360km/hr releases abomb which hits a target on the ground. Find (a) the time required for the bomb to reach the target, (b) thehorizontal distance of the aircraft from the target when the bomb was released (c) direction and velocitywith which the bomb hits the targarrow_forwardIn a continuous printing process, paper is drawn into the presses at a constant speed v. Denoting by r the radius of the paper roll at any given time and by b the thickness of the paper, derive an expression for the angular acceleration of the paper roll.arrow_forward
- For the system of particles of Prob. 14.13, determine (a) the position vector r of the mass center G of the system, (b) the linear momentum mv of the system, (c) the angular momentum HG of the system about G . Also verify that the answers to this problem and to Problem 14.13 satisfy the equation given in Prob. 14.27.Reference to Problem 14.13:A system consists of three particles A, B, and C. We know that mA =3kg, mB =2kg, and mC = 4 kg and that the velocities of the particles expressed in m/s are, respectively, vA = 4i +2j +2k, vB = 4i + 3j, and vC = -2i + 4j +2k. Determine the angular momentum HO of the system about O.arrow_forwardTwo smooth disks A and B each have a mass of 0.5 kg. Both disks are moving with the velocities shown when they collide. Suppose that (vA)1 = 9 m/s , (vB)1 = 8 m/s. The figure shows two discs, A and B, moving toward the origin of a horizontal xy-plane, where they collide, so that their common tangent lies on y-axis. Disk A moves in negative x-direction with velocity left-parenthesis v subscript A right-parenthesis subscript 1. Block B moves from the third quarter with velocity left-parenthesis v subscript B right-parenthesis subscript 1, directed along an inclined line with a slope of four-thirds. Determine the coefficient of restitution between the disks if after collision B travels along a line, 30∘ counterclockwise from the y axis.arrow_forwardCollision at an Angle To apply conservation of linear momentum in an inelastic collision. Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2v, while the second was traveling in a southeastern direction at an angle ϕ with respect to the east-west direction and at a speed v. After the collision, the two-car system travels in a northeastern direction at an angle θ with respect to the north-south direction and at a speed v final. Find v final, the speed of the joined cars after the collision. Express your answer in terms of v and ϕ.arrow_forward
- Collision at an Angle To apply conservation of linear momentum in an inelastic collision. Two cars, both of mass m, collide and stick together. Prior to the collision, one car had been traveling north at a speed 2v, while the second was traveling in a southeastern direction at an angle ϕ with respect to the east-west direction and at a speed v. After the collision, the two-car system travels in a northeastern direction at an angle θ with respect to the north-south direction and at a speed v final. What is the angle θ (with respect to north) made by the velocity vector of the two cars after the collision? Express your answer in terms of ϕ. Your answer should contain an inverse trigonometric function.arrow_forwardA disk of radius r rolls to the right with a constant velocity v. Denoting by P the point of the rim in contact with the ground at t = 0, derive expressions for the horizontal and vertical components of the velocity of P at any time t.arrow_forwardAngular Momentum of a Particle Two identical spheres with m=3 kg each are rigidly attached to the rotating light rigid structure. The velocity of the spheres is v=2 m/s. Determine the angular momentum about the axis of rotation.arrow_forward
- for question 3 answer A and B 3. A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s. a. If the collision is perfectly elastic, what is the final speed of the 2.3-kg object? b. What is the change in Kinetic Energy of the 2.3 kg object?arrow_forwardA cylinder rolls without slipping between two moving plates C and D. The radius of the cylinder is r=4.0m. The velocity of the plate C is VC=6.0 m/s to the right. The velocity of the plate D is VD=2.0 m/s to the left. Using the instantaneous center of zero velocity (IC) to determine (1) The distance between point A and IC point, rA/IC=_____ marrow_forwardA basketball is bounced on the ground at point A and rebounds with a velocity vA of magnitude 2.5 m/s with 15º separation within the y axis. Determine the radius of curvature of the trajectory described by the ball (a) at point A, (b) at the highest point of the trajectory.arrow_forward
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