Four small disks A, B, C, and D can slide freely on a frictionless horizontal surface. Disks B, C, and D are connected by light rods and are at rest in the position shown when disk B is struck squarely by disk A, which is moving to the right with a velocity
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Vector Mechanics For Engineers
- Three small spheres A, B, and C , each of mass m , are connected to a small ring D of negligible mass by means of three inextensible, inelastic cords of length I . The spheres can slide freely on a frictionless horizontal surface and are rotating initially at a speed v0 about ring D which is at rest. Suddenly the cord CD breaks. After the other two cords have again become taut, determine (C ) the speed of ring D, (b) the relative speed at which spheres A and B rotate about D , (c) the fraction of the original energy of spheres A and B that is dissipated when cords AD and BD again became taut.arrow_forwardThree spheres, each with a mass of m , can slide freely on a frictionless, horizontal surface. Spheres A and B are attached to an inextensible, inelastic cord with a length I and are at rest in the position shown when sphere B is struck squarely by sphere C , which is moving with a velocity v0 . Knowing that the cord is taut when sphere B is struck by sphere C and assuming perfectly elastic impact between B and C , and thus the conservation of energy for the entire system, determine the velocity of each sphere immediately after impact.arrow_forwardTwo identical giant flywheels are on 2 identical slopes at an angle alpha = 20 deg. One flywheel is rolling on its inside shaft of diameter d1 = 3 ft, and the second flywheel is rolling without slipping on its outside diameter d2 = 5 ft. They are both released from rest. The weight of the flywheel is W = 8 lbs Knowing that flywheel 1 attains a speed of v = 7.0 ft/s in t = [t] s, (if t doesn't show take any t between 5 and 10 sec) find the radius of gyration of the flywheels, following those steps: b. Find omega final c. Find the angular impulse at the point of contact between the shaft and the slope. d. Write the formula to find the final momentum. e. Solve for k, using the principle of angular impulse and momentumarrow_forward
- Two identical spheres A and B each of mass m , are attached to an inextensible inelastic cord of length L and are resting at a distance a from each other on a frictionless horizontal surface. Sphere B is given a velocity v0 in a direction perpendicular to line AB and moves it without friction until it reaches B ’ where the cord becomes taut. Draw the impulse-momentum diagram that can be used to determine the magnitude of the velocity of each sphere immediately after the cord has become taut.arrow_forwardTwo identical giant flywheels are on 2 identical slopes at an angle alpha = 20 deg. One flywheel is rolling on its inside shaft of diameter d1 = 3 ft, and the second flywheel is rolling without slipping on its outside diameter d2 = 5 ft. They are both released from rest. The weight of the flywheel is W = 8 lbs 1. Knowing that flywheel 1 attains a speed of v = 7.0 ft/s in t = [t] s, (if t doesn't show take any t between 5 and 10 sec) find the radius of gyration of the flywheels, following those steps: 3. What will be the distance between the 2 flywheels? Which one is in front? a. Explain your strategy to find the distance made by each wheel. b. Find the 3 distances made by each wheel. c. Find the distance between the 2 flywheels. d. Why one is in front? 4. Using flywheel 2, what is the coefficient of static friction between the outside diameter and the ground required to prevent slipping? a. Using the 3 previous diagrams, which impulse will you consider finding the force of…arrow_forwardA bowler projects an 8-in.-diameter ball weighing 12 lb along an alley with a forward velocity v0 of 15 ft/s and a backspin ω0 of 9 rad/s. Knowing that the coefficient of kinetic friction between the ball and the alley is 0.10, determine (a) the time t1 at which the ball will start rolling without sliding, (b) the speed of the ball at time t1, (c) the distance the ball will have traveled at time t1arrow_forward
- A small package of weight W is projected into a vertical return loop at A with a velocity v0 . The package travels without friction along a circle of radius r and is deposited on a horizontal surface at C. For each of the two loops shown, determine (a) the smallest velocity v0 for which the package will reach the horizontal surface at C, (b) the corresponding force exerted by the loop on the package as it passes point B.arrow_forwardThe W1= 69.01-lb block shown rests on a smooth plane (coefficient of kinetic friction = 0) with an angle of θ=34∘ from horizontal. It is connected by a flexible inextensible cord that passes around weightless, frictionless pulleys to a support. The W2 =134.93-lb weight is attached as shown. After the system is released from rest, in what distance will the block on the plain attain a speed of 10.0 ft/s?arrow_forwardTwo beads of mass m are initially at rest at the top of a frictionless hoop of mass M and radius R, which stands vertically on the ground. The beads, being strung on the hoop, are constrained to move along the hoop’s circular path. The beads are given tiny kicks, and they slide down the hoop, one to the right and one to the left. What is the largest value of m/M for which the hoop never rises up off the ground? (Given a sufficiently large ratio of m/M the normal force of the beads on the hoop can indeed cause it to jump off of the ground!) Some thoughts/hints about this problem:(a) It is important to think about the direction of the Normal force as the beads move around the hoop. The hoop is exerting a normal force on the beads which are constraining them to stay on the wire as they move around the hoop. The beads are also exerting a normal force on the hoop which is what will make the hoop jump.(b) What happens to the direction of the normal force exerted by the hoop on the beads as…arrow_forward
- A 300-g block is released from rest after a spring of constant k= 600 N/m has been compressed 160 mm. Determine the force exerted by the loop ABCD on the block as the block passes through (a) point A, (b) Point B, (c) . Assume no friction.arrow_forwardSolve Prob. 13.26, assuming that the 2-kg block is attached to the spring.Reference to Problem 13.26:A 3-kg block rests on top of a 2-kg block supported by, but not attached to, a spring of constant 40 N/m. The upper block is suddenly removed. Determine (a) the maximum speed reached by the 2-kg block, (b) the maximum height reached by the 2-kg block.arrow_forwardA series of small packages, each with a mass of 0.5 kg, are discharged from a conveyor belt as shown. Knowing that the coefficient of static friction between each package and the conveyor belt is 0.4, determine (a) the force exerted by the belt on the package just after it has passed point A, (b) the angle 0 defining the point B where the packages first slip relative to the belt.arrow_forward
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