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A system consists of three identical 19.32-lb particles A, B, and C. The velocities of the particles are, respectively
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Vector Mechanics For Engineers
- Show that the angular momentum HB of a rigid body about point B can be obtained by adding to the angular momentum HA of that body about point A the vector product of the vector rA/B drawn from B to A and the linear momentum of the body: Further show that when a rigid body rotates about a fixed axis, its angular momentum is the same about any two points A and B located on the fixed axis (HA=HB) if, and only if, the mass center G of the body is located on the fixed axis.arrow_forwardA system consists of three identical 14.32-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. Determine the velocities of the particles. (You must provide an answer before moving to the next part.) The velocity of particle A is ( ft/s)j. The velocity of particle B is ( ft/s)i. The velocity of particle C is ( ft/s)k.arrow_forwardTwo masses, m1 and m2, are each suspended on identical springs. They were displaced an equal distance from equilibrium position and were released simultaneously. They are both at position of initial displacement at the instant m1 has completed 5 cycles and m2 has completed 3 cycles. m1=3 kilograms, determine the mass of m2 in kgarrow_forward
- The platform swing consists of a 190-lb flat plate suspended by four rods of negligible weight. When the swing is at rest, the 170-lb man jumps off the platform when his center of gravity G is 10 ft from the pin at A. This is done with a horizontal velocity of 5 ft/s, measured relative to the swing at the level of G. (Eigure 1) Figure 1 of 1 10 ft 11 ft 4 ftarrow_forward4. Two blocks with the same mass are connected to a compressed spring at opposite ends. At first, the spring and blocks slide at the same velocity v on a frictionless surface to the right. The spring is released and at some later instant the left block is moving at v/2 to the left and the other block is moving to the right. What the speed of the center of mass of the system at that instant? (A) 5v/2 (B) 3v/2 (C) v (D) v/2arrow_forwarda 400-kg satellite was place in a circular orbit 1500 km above the surface of the earth at this elevation the acceleration of gravity is 6.43 m/s^2 determine the kinetic energy of the satellite in kJ knowing that its orbital speed is 25.6x10^3 km/harrow_forward
- Car A was traveling west at a speed of 15 m/s and car B was traveling north at an unknown speed when they slammed into each other at an intersection. Upon investigation it was found that after the crash the two cars got stuck and skidded off at an angle of 50° north of east. Knowing the masses of A and B are m mA and mB, respectively, draw the impulse-momentum diagram that can be used to determine the velocity of B before impact.arrow_forward14.11 A system consists of three identical 19.32-lb particles A, B, and C. The velocities of the particles are, respectively, VA = VAJ, VB = Üßi, and ock. Knowing that the angular momentum of the system about O, ex- pressed in ft lbs is Ho = -1.2k, determine (a) the velocities of the par- ticles, (b) the angular momentum of the system about its mass center G. A 2 ft 2 ft B of VB 1 ft 3 ft 4 ftarrow_forwardA 900 kg car travelling at 12 m/s due east collides with a 600 kg car travelling at 24 m/s due north. As a result of the collision, the two cars lock together and move in what final direction?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_forwardThe tube rotates in the horizontal plane at a constant rate of 0 = 4 rad/s as shown in (Figure 1). Figure Z = 4 rad/s 0.5 m 1 of 1 Part A If a 0.2-kg ball B starts at the origin O with an initial radial velocity of r = 1.5 m/s and moves outward through the tube, determine the radial and transverse components of the ball's velocity at the instant it leaves the outer end at C, r = 0.5 m. Hint: Show that the equation of motion in the direction is - 16r = 0. The solution is of the form r = Ae-4t+ Be¹t . Evaluate the integration constants A and B, and determine the time t when r = 0.5 m. Proceed to obtain vr and ve. Enter the components of the velocity separated by a comma. Express your answers in meters per second to three significant figures. Ur, υ θ = Submit Provide Feedback IVD ΑΣΦ Request Answer ↓1 vec ? m/s Next >arrow_forwardvehicles are approaching a road junction, both moving with speed (12.5 m/s). One vehicle has mass 1000 kg and the other mass kg, and the roads meet at an angle of 60° as shown. The vehicles collide and initially move as a single body. ss of Car A= 100 kg ss of Car B = 70 kg A 12.5 m/s B 60° 12.5 m/s culate the magnitude of the velocity of the two vehicles immediately after the collision (treating them as a gle body) (m/s) culate the linear momentum in the vector form of car B. (m/s) culate the linear momentum in the vector form of car A. (m/s) Choose... Choose... Choose... 4arrow_forward
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