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A small 250-g collar C can slide on a semicircular rod which is made to rotate about the vertical AB at a constant rate of 7.5 rad/s. Knowing that the coefficients of friction are us
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Vector Mechanics For Engineers
- A thin circular rod is supported in a vertical plane by a bracket at A. Attached to the bracket and loosely wound around the rod is a spring of constant k= 3 lb/ft and undeformed length equal to the arc of circle AB. An 8-oz collar C , not attached to the spring, can slide without friction along the rod. Knowing that the collar is released from rest at an angle 0 with the vertical, determine (a) the smallest value of 0 for which the collar will pass through D and reach point A, (b) the velocity of the collar as it reaches point A.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_forwardA spring AB of constant k is attached to a support at A and to a collar of mass m. The unstretched length of the spring is 1 . Knowing that the collar is released from rest at x=x0 and neglecting friction between the collar and the horizontal rod, determine the magnitude of the velocity of the collar as it passes through point C.arrow_forward
- A baggage conveyor is used to unload luggage from an airplane. The 10-kg duffel bag A is sitting on top of the 20-kg suitcase B . The conveyor is moving the bags down at a constant speed of 0.5 m/s when the belt suddenly stops. Knowing that the coefficient of friction between the belt and B is 0.3 and that bag A does not slip on suitcase B, determine the smallest allowable coefficient of static friction between the bags.arrow_forwardA truck is traveling down a road with a 4-percent grade at a speed of 60 mi/h when its brakes are applied to slow it down to 20 mi/h. An antiskid braking system limits the braking force to a value at which the wheels of the truck are just about to slide. Knowing that the coefficient of static friction between the road and the wheels is 0.60, determine the shortest time needed for the truck to slow down.arrow_forwardPlease answer this NEATLY, COMPLETELY, and CORRECTLY for an UPVOTE. In the system shown, a 150 N collar-pulley assembly slides on a horizontal shaft with coefficient of kinetic friction μk = 0.10 between the collar and the shaft, and is acted upon by a force P with a magnitude of P = 253.5 N at an angle θ = 30.35° as shown. Knowing that the assembly is initially at rest, what is the time when the velocity reaches to 3 m/s? Also, at this instant, find the tension in the cord and the velocity of block A.arrow_forward
- In the braking test of a sports car its velocity is reduced from 70 mi/h to zero in a distance of 170 ft with slipping impending. Knowing that the coefficient of kinetic friction is 80 percent of the coefficient of static friction, determine (a) the coefficient of static friction, (b) the stopping distance for the same initial velocity if the car skids. Ignore air resistance and rolling resistance.arrow_forwardDetermine the maximum theoretical speed that may be achieved over a distance of 70 m by a car starting from rest, knowing that the coefficient of static friction is 0.80 between the tires and the pavement and that 60 percent of the weight of the car is distributed over its front wheels and 40 percent over its rear wheels. Assume a four-wheel drive car. The maximum theoretical speed that may be achieved is ____ km/h.arrow_forwardA spring AB of constant k=200kn/m is attached to a support at A and to a collar of mass m=200 gm. The unstretched length of the spring is I=0.6m. Knowing that the collar is released from rest at x0 = 80 cm and neglecting friction between the collar and the horizontal rod, determine :the magnitude of the velocity of the collar as it passes through point C.arrow_forward
- Three packages each of weight m = 9 kg A, B, and C are placed on a conveyor belt that is at rest. Between the belt and both packages A and C, the coefficients of friction are Ms = 0.30 and Mk = 0.20; between package B and the belt, the coefficients are Ms = 0.10 and Mk = 0.08. The packages are placed on the belt so that they are in contact with each other and at rest. Determine which, if any, of the packages will move and the friction force acting on each package. The frictional force acting on A is N The frictional force acting on B is N The frictional force acting on C is N Note: please show correct step by step working out. And double check final answers. Also for frictional force A, B & C show their directions as well. Thanks!arrow_forwardSHOW COMPLETE SOLUTION A spring is used to stop 50kg block moving down a 20 degrees inclined plane. The spring has a constant K= 30KN/M and is held by the cables so that it is initially compressed 50mm. Knowing that the velocity of the package is 2m/s when it is 8m from the spring and assuming the kinetic coefficient of friction between the package and the incline is 0.20. Determine: A. Final kinetic energy B. Maximum additional deformation of spring in bringing the block to rest C. Frictional forcearrow_forwardSolve Prob. 13.68 assuming the kinetic coefficient of friction between the package and the incline is 0.2.Reference to Problem 13.68:A spring is used to stop a 50-kg package that is moving down a 20° incline. The spring has a constant k = 30 kN/m and is held by cables so that it is initially compressed 50 mm. Knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.arrow_forward
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