A small ball swings in a horizontal circle at the end of a cord of length
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Vector Mechanics for Engineers: Dynamics
- If the rod AB rotates counterclockwise with angular velocity, ω AB =8rad / s Calculate the velocities of the blocks C and D at the moment shown in the figure below.arrow_forwardI Suppose an autonomous surface vessel (ASV) traveling with velocity TvG/O= vi₁ begins to make a turn by adjusting the thrust of its left and right thrusters, TA and TB, respectively. The center of mass of the ASV is located at G and the ASV is symmetric about its vertical axis. The ASV also experiences a drag force that is proportional to its speed and opposes its velocity. At the instant shown, the drag force is D = -kvi₁ where k is a drag coefficient. 1. To model the mass moment of inertia, approximate the ASV as consisting of three rigid bodies: a flat plate as a center body of mass 6m and two slender rods housing the propulsion assemblies, each of mass m, at the outboard sides of the vehicle. Determine the mass moment of inertia, IG, about the vertical axis passing through the center of mass G. (Hint: Use the parallel axis theorem.) 2. At the instant shown, determine the inertial acceleration vector ac/o = axi₁ + ayi2 of the center of mass and the angular acceleration a of the…arrow_forwardFind the magnitude and direction of the velocity at point B.arrow_forward
- Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 2.3 x 106 m through the center of a planet with radius 7.6 x 106 m. If the mass of the planet is 33.9 x 1015 kg, measure the displacement of the ball at time t = 9 s?arrow_forwardthere is a spring with k=0.9 N/m conected to arm AB which is 15 kg when angle 0 spring is uncompressed. if we release arm AB from rest when angle=0 what will its angular velocity when angle is 30 its moving on vertical planearrow_forwardTHE MOTION IS ON THE HORIZONTAL PLANE (NO GRAVITYarrow_forward
- A hollow, smooth cylindrical spool has inner radius R/ 2, outer radius R and mass M. The roller is frictionally M mounted so that it can rotate around a fixed horizontal shaft. The mass m is attached to the end of the rope wrapped around the reel. When this mass m is released, it drops by y in time t. The moment of the friction force between the pulley and the shaft, m R/2 7 = R[m(g – 2y/t²) – M(5y/41²)] R/2 prove that it is. (The moment of inertia of a hollow cylinder with inner and outer radi, R1 and R2, with respect to the long axis through the center of mass.)arrow_forwardQ2/ The slotted arm revolves about a normal axis through point O with a constant angular velocity w.The path radius of the center of the pin A varies according to r = 20+ 2sin(nwt)where n is the number of lobes = 6 in this case. pin A If w=12 rad/s, and the spring compression varies from 11.5 N to 19.1 N, calculate the force R between the cam and the 0.1 kg pin A when it passes over the top of the lobe in the position shownarrow_forwardTwo flywheels are pinned to opposite ends of a metal bar. The smaller flywheel has a mass of 40 kg and a radius of 0.25 m. The larger flywheel has a mass of 275 kg and a radius of 1.75 m. The bar has a mass of 2 kg and a length of 3 m. A wooden plate acts as a ripcord by temporarily pressing it against the flywheels and rapidly translating it to the left at v = angular velocity of 25 rad/s and the large flywheel has an angular velocity of 3.5714285714286 rad/s. The flywheel-bar assembly is then set on frictionless ice such that the axes of rotation are perpendicular to the ice surface. 6.25 m/s. The plate is removed when the small flywheel has an The flywheel pins have Hk = 0.05, which eventually causes the flywheels to stop spinning relative to the metal bar. Angular momentum is conserved, so the whole assembly continues spinning as a rigid body about the center of mass. What is the final angular velocity of the assembly? rad/s. The flywheels and bar rotate about their combined center…arrow_forward
- People A and B are fixed on a frictionless disk with radius R= 4 (m) and rotating at an angular velocity o= 3 (rad/s) as shown in the figure. As shown in the figure, person A in the center throws the ball in his hand at v = 8 (m/s) so that the person B can catch the ball. Since the image given in the figure shows t=0 (s), after how many seconds should person A throw the ball so that pers on B can catch it? Take T=3. 1= 0 В A. v R A) 0.35 В) 0.55 С) 0.75 D) 1.2 E) 0.50arrow_forward3/218 A 0.4-kg particle is located at the position r, = 2i + 3j + k m and has the velocity v =i+j+ 2k m/s at time t = 0. If the particle is acted upon by a sin- gle force which has the moment Mo = (4 + 21)i + (3 -j + 5k N-m about the origin O of the Coordinate system in use, determine the angular momentum about O of the particle when t = 4 s.arrow_forwardI need a simple solutionarrow_forward
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