Determine the magnitude of the acceleration of the block?
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Determine the magnitude of the acceleration of the block?
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- A slender rod CDE of length L of Mass m is attached to a pin support at its midpoint D. A second and identical rod AB is rotating about a pin support at A with an angular velocity w1 when its end B strikes end of rod CDE. The coefficient of restitution between the rods is e. Draw the impulse–momentum diagrams that are needed to determine the angular velocity of each rod immediately after the impact.The slender rod AB of length L = 1 m forms an angle β = 30° with the vertical as it strikes the frictionless surface shown with a vertical velocity v1=2 m/s and no angular velocity. Knowing that the coefficient of restitution between the rod and the ground is e = 0.8, determine the angular velocity of the rod immediately after the impact.An 80-Mg railroad engine A coasting at 6.5 km/h strikes a 20-Mg flatcar C carrying a 30-Mg load B which can slide along the floor of the car (μk= 0.25). The flatcar was at rest with its brakes released. Instead of A and C coupling as expected, it is observed that A rebounds with a speed of 2 km/h after the impact. Draw impulse-momentum diagrams that can be used to determine (a) the coefficient of restitution and the speed of the flatcar immediately after impact, (b) the time it takes the load to slide to a stop relative to the car.
- Instead of a traditional cue, Rodrigow used a spring-powered cue in his game of billiards. When the constraints on the spring (k = 100 kN/m) are removed, the launching mechanism of the cue is triggered, and the 170-g cue ball A is launched forward. Ball A is separated from the plate when the spring becomes fully unstretched. Ball A is launched at an angle a with the horizontal, making it rebound off the cushion at an angle ß. When the cue ball A hits the initially stationary 9-ball B (ma= 160 g), the latter goes snuggly into the lower left pocket. Determine the amount of compression (mm) on the spring so that the speed of ball B is exactly 5.XYZ m/s, where XYZ is the last three digits of your student number (Ball B may bounce off the table if its velocity is> 5.XYZ m/s and may not reach the pocket if < 5.XYZ m/s). The coefficient of restitution between ball A and the cushion is 0.6 while between balls A and B is 0.95. Neglect the effect of friction and the size of the balls.Direct central impact occurs between a 100lbs body moving to the right at 5 ft per second and a body of weight W moving to the left at 3 ft per sec. The coefficient of restitution e = 0.5. After impact the 100lb body rebounds to the left at 2ft/s. Determine the weight W of the other body. (lbs)Disk A has a mass of 250 g and is sliding on a smooth horizontal surface with an initial velocity (vA)1 = 2 m/s. It makes a direct collision with disk B, which has a mass of 175 g and is originally at rest. If both disks are of the same size and the collision is perfectly elastic (e = 1), determine the velocity of each disk just after collision. Show that the kinetic energy of the disks before and after collision is the same.
- The two spheres shown collide. the weight of the first sphere (W1) is 40 N while that of the second is (W2) is 30N. assuming that the second sphere's velocity (v2) is 14 m/s and the first sphere's velocity (v1) is 16 m/s along the their respective angles. theta 1(θ1)=30 degrees and theta 2(θ2)=60 degrees. Assume velocities along y will be equal before and after impact. The coefficient of restitution is 0.57. A.) Determine the velocity of the 30N sphere after impact (m/s) B.) Determine the Velocity of the 40N sphere after impact (m/s) C.) Determine the angle of the velocity after impact of the 40N sphere with the horizontal (degrees) D.) Determine the angle of the velocity after impact for the 30N sphere with the vertical (degrees)Instead of a traditional cue, Rodrigo used a spring-powered cue in his game of billiards.When the constraints on the spring (k = 100 kN/m) are removed, the launchingmechanism of the cue is triggered, and the 170-g cue ball A is launched forward. Ball A isseparated from the plate when the spring becomes fully unstretched. Ball A is launched atan angle α with the horizontal, making it rebound off the cushion at an angle β. When thecue ball A hits the initially stationary 9-ball B (mB = 160 g), the latter goes snuggly into thelower left pocket. Determine the amount of compression (mm) on the spring so that thespeed of ball B is exactly 5. XYZ m/s, where XYZ is the last three digits of your studentnumber (Ball B may bounce off the table if its velocity is > 5. XYZ m/s and may not reachthe pocket if < 5.XYZ m/s). The coefficient of restitution between ball A and the cushion is0.6 while between balls A and B is 0.95. Neglect the effect of friction and the size of theballs. PLEASE…The 7-kg sphere is projected horizontally with a velocity of 18 m/s against the 38-kg carriage which is backed up by the spring with stiffness of 1650 N/m. The carriage is initially at rest with the spring uncompressed. If the coefficient of restitution is 0.64, calculate the rebound velocity v', the rebound angle 0, and the maximum travel S of the carriage after impact.
- Direct central impact occurs between a 300N body moving to the right with velocity of 6 m/s and 150 N body moving to the left with velocity of 10 m/s. Find the velocity of each body after impact if the coefficient of restitution is 0.8.Block A is released from rest and slides down the frictionless surface of B until it hits a bumper on the right end of B. block has a mass of 10 kg and object B has a mass of 30 kg and B can roll freely on the ground. Determine the velocities of A and B immediately after impact when (a) e= 0, (b) e= 0.7.The cylindrical plug A of mass ma = 3.3 kg is released from rest at B and slides down the smooth circular guide. The plug strikes the block C of mass mc = 3.7 kg and becomes embedded in it. Calculate the distances which the block and plug slide before coming to rest. The coefficient of kinetic friction between the block and the horizontal surface is u = 0.42 and the distance r = 1.42 m.