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A system consists of three particles A, B, and C. We know that
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Vector Mechanics For Engineers
- A 20-kg base satellite deploys three sub-satellites, each which has its own thrust capabilities, to perform research on tether propulsion. The masses of sub-satellites A, B, and C are 4 kg, 6 kg, and 8 kg, respectively, and their velocities expressed in m/s are given by vA = 4i - 2j +2k, vB = i + 4j, vC = 2i + 2j +4k. At the instant shown, what is the angular momentum HO of the system about the base satellite?arrow_forwardA system consists of three identical 13.32-lb particles A, B, and C. The velocities of the particles are, respectively, vA = vA j, vB = vBi, and vC = vCk. The angular momentum of the system about O expressed in ft·lb·s is HO = -1.2k.a) Determine the velocities of the particles. b) Determine the angular momentum of the system about its mass center G.arrow_forwardA system consists of three identical 5-kg particles A, B, and C. Their position vectors (in meter) and velocity vectors (in m/s) are rA 0,0, 3 , v A v Aj , rB 2,2, 3 , vB v B i , and rC 1,4, 0 , vC v C k, respectively. Knowing that the angular momentum of the system about point O is HO 1.5k kg m 2s, determine (a) the velocities of the particles, (b) the angular momentum of the system about its center of mass G.arrow_forward
- A railroad car having a mass of 15 Mg is coasting at 1.5 m/s on a horizontal track. At the same time another car having a mass of 12 Mg is coasting at 0.75 m/s in the opposite direction. If the cars meet and couple together,determine the speed of both cars just after the coupling. Find the difference between the total kinetic energy before and after coupling has occurred, and explain qualitatively what happened to this energy.arrow_forwardA railroad car having a mass of 15 Mg is coasting at 1.5 m/s on a horizontal track. At the same time another car having a mass of 12Mg is coasting at 0.75 m/s in the opposite direction. If the cars meet and couple together, determine the speed of both cars just after the coupling. Find the difference between the total kinetic energy before and after coupling has occurred, and explain qualitatively what happened to this energyarrow_forwardTo apply Newton’s second law and the theorem of conservation of energy to solve kinetic problems. A bungee jumper wants to jump off the edge of a bridge that spans a river below. The jumper has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has lengthL when unstretched, will first straighten and then stretch as the jumper falls.Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch and has spring constant k. The jumper does not actually jump but simply steps off the edge of the bridge and falls straight downward. The jumper's height is negligible compared to the length of the bungee cord. Thus, the jumper can be treated as a point particle. Use g for the magnitude of the acceleration due to gravity. How far below the bridge, d, will the jumper eventually be hanging, once the jumper stops oscillating and comes finally to rest? Assume that the jumper does not touch the water. Express your answer in…arrow_forward
- A block of mass 0.25 kg travels down a frictionless surface with a velocity of 4.5 m/s to the left and collides with a second block of mass 1.5 kg with a velocity of 0.5 m/s to the right. The two carts stick together after the collision. (1) Find the total momentum of the two carts just before the collision. (2) Find the velocity of the two carts just after the collision.arrow_forwardA 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_forwardQ1/ Two balls of masses m; = 0.5 kg and my = 1.5 kg are sliding toward each other on a straight frictionless track. If they experience a head-on elastic collision and if the initial velocities of m; and m; are 0.6 m/s to the right and 3 m/s to the left, respectively, find the final velocities of two balls?arrow_forward
- at an amusement park there are 200 kg bumper cars A, B, and C that have riders with masses of 40kg, 60 kg, and 35 kg, respectively. Car A is moving to the right with a velocity Va=2m/s when it hits stationary car B. The coefficient of restitution between each car is 0.8. Determine the velocity of car C so that after car B collides with car C the velocity of car B is zero.arrow_forwardPrinciple of Angular Impulse and Momentum To apply the principle of angular impulse and momentum to find final speed and the time to reach a given speed. As shown, ball B, having a mass of 10.0 kg, is attached to the end of a rod whose mass can be neglected. Finding the final speed of the ball If the rod is 0.550 m long and subjected to a torque M=(1.95t2+3.75) N⋅m, where t is in seconds, determine the speed of the ball when t=4.80 s. The ball has a speed of v=2.25 m/s when t=0 Finding the time needed to reach a specific speed If the shaft is 0.250 m long, the ball has a speed of v=2.85 m/s when t=0, and the rod is subjected to a torque M=(3.40t+2.15) N⋅m, where t is in seconds, determine the time it will take for the ball to reach a speed of 5.80 m/s.arrow_forwardAn object with mass m is launched with initial kinetic energy E0 at an angle θ = 45° with respect to the horizontal (+x). At the peak of its trajectory the object explodes, breaking into two pieces. The explosion adds an additional mechanical energy E0 to the system. After the explosion, one piece (mass m1) travels straight downward(-y) with an unknown speed v1 while the second piece (mass m2) travels with an unknown velocity →v2. The total mass m1+m2 = m is the same as before the explosion, but the mass ratio of the two pieces q = m1/m2 is unknown. Assume that the motionof the two pieces is in the xy-plane. (a) Find the velocity →v2 of the second piece and the speed v1 of the first piece in terms of E0, m, and q.(b) What is the maximum mass m1 (as a fraction of m) that is physically permitted given that it is traveling straight down after the explosion?arrow_forward
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