Concept explainers
The uniform rectangular block shown is moving along a frictionless surface with a velocity
Fig. P17.115
Find the magnitude of the velocity
Answer to Problem 17.115P
The magnitude of the velocity
Explanation of Solution
Given information:
The length
The width
Calculation:
Write the equation of centroidal moment of inertia
Find the one half of the diagonal distance
Substitute 200 mm for a and 100 mm for b.
Before impact, let
Here, magnitude of velocity of the rectangular block is
After impact, the rectangular block rotates about small obstruction at B. Therefore,
Let
Find the equation of velocity
Consider the principle of impulse and momentum.
Sketch the impulse and momentum diagram of the rectangular block as shown in Figure (1).
Take moment about B (positive sign in clockwise direction).
Substitute
Substitute
Sketch the free body diagram of the rectangular block after impact (position 2) and final position (position 3) as shown in Figure (2).
Write the equation of velocity
Refer Figure (2),
Find the angle
Substitute 200 mm for a and 100 mm for b.
Find the distance (h).
Substitute 0.1118 m for d and
At position 3, the angular velocity
Write the equation of the potential energy
Write the equation of the kinetic energy
Substitute
Substitute
Write the equation of the potential energy
The kinetic energy of the system at final position
Consider the conservation of energy.
Substitute
Substitute 200 mm for a, 100 mm for b, 0.1118 m for d,
Find the the magnitude of the velocity
Substitute 200 mm for a, 100 mm for b, and
Thus, the magnitude of the velocity
Want to see more full solutions like this?
Chapter 17 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Additional Engineering Textbook Solutions
Introduction to Heat Transfer
Engineering Mechanics: Statics
EBK FUNDAMENTALS OF THERMODYNAMICS, ENH
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Vector Mechanics for Engineers: Statics, 11th Edition
Engineering Mechanics: Statics
- The double pulley shown has a weight of 32.5 lb and a centroidal radius of gyration of 6.0 in. Cylinder A (35.0 lb) and block B (18 lb) are attached to cords that wrap around pulleys in the manner shown. The coefficient of kinetic friction between block B and the surface is 0.25. Knowing that the system is released from rest at the position shown (h = 3 ft), determine the total distance that block B moves before coming to rest. 6 in. A h 10 in. Barrow_forwardThe double pulley shown has a mass of 15 kg and a centroidal radius of gyration of 160 mm. Cylinder A and block B are attached to cords that are wrapped on the pulleys as shown. The coefficient of kinetic friction between block and the surface is 0.2. Knowing that the system is at rest in the position shown when a constant force P = 200 N is applied to cylinder A , determine (a ) the velocity of cylinder A as it strikes the ground, (b ) the total distance that block B moves before coming to rest.arrow_forwardA 1.6-kg tube AB can slide freely on rod DE which in turn can rotate freely in a horizontal plane. Initially the assembly is rotating with an angular velocity of magnitude w = 5 rad/s and the tube is held in position by a cord. The moment of inertia of the rod and bracket about the vertical axis of rotation is 0.30 kg.m2 and the centroidal moment of inertia of the tube about a vertical axis is 0.0025 kg.m2If the cord suddenly breaks, determine (a) the angular velocity of the assembly after the tube has moved to end E, (b) the energy lost during the plastic impact at E.arrow_forward
- PROBLEM 3 - In the system shown, a 150 N collar-pulley assembly slides on a horizontal shaft with coefficient of kinetic friction u = 0.10 between the collar and the shaft, and is acted upon by a force P with a magnitude of P 251.432 N at an angle 0 30.11° 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. Use g==9.81 m/s 32.2 ft/s %3D W-150 N WA 106. 54 N てarrow_forwardBlock A of Fig.(3) weighs 100N and block B weighs 300N. The coefficient of static friction between the blocks is 0.5, and the coefficient of kinetic friction between block B and the plane is 0.25. Determine the max. value of (P) that may be applied without causing block A to slide on block B when block B is moving to the left. (The gravitational acceleration is 10 m/s?) P. AT00 24 300 Fig.(3) m.ax Good Luck Pt N ray 2-2 B.arrow_forwardPROBLEM 3 - In the system shown, a 150 N collar-pulley assembly slides on a horizontal shaft with coefficient of kinetic friction u = 0.10 between the collar and the shaft, and is acted upon by a force P with a magnitude ofP= 251.432 N at an angle 0 = 30.11° 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. Use g== 9.81 m/s? = 32.2 ft/s? P W, - 150 N B C A WA = 106. 54 N %3Darrow_forward
- Problem (4) An 8-kg gear with a radius of 80 mm has a centroidal radius of gyration of 50 mm. A 5-kg slender rod AB is attached to the center of the gear while the pin at B is free to slide along the vertical slot (negligible friction). When 0 = 60°, the system is released from rest. Determine S0 mm (a) the velocity of the center of the gear when 6 = 15° (b) the velocity of pin B when 0 = 15°. 320 imm BOarrow_forwardThe mechanism shown is one of two identical mechanisms attached to the two sides of a 200-lb uniform rectangular door. Edge ABC of the door is guided by wheels of negligible mass that roll in horizontal and vertical tracks. A spring with a constant k is attached to wheel B in such a way that its tension is zero when 0 = 30°, Knowing that the door is released from rest in the position 0 = 45° and reaches the vertical position with an angular velocity of 0.6 rad/s, determine the spring constant k.arrow_forward196 A uniform slender rod AB is at rest on a frictionless horizontal table when end A of the rod is struck by a hammer which delivers an im- that is perpendicular to the rod. In the subsequent motion, determine distance b through which the rod will move each time it completes a full revolution. Fig. P17.96 Barrow_forward
- PROBLEM 5.17 A bowling ball of mass M1 = 6 kg is initially at rest on the sloped side of a wedge of mass M2 = 9 kg that is on a frictionless horizontal floor. The side of the wedge is sloped at an angle of 0 = 37° above the horizontal. MI M2 20. What is the magnitude of the horizontal force P that should be exerted to keep the ball at a constant height on the slope? a. 135.89 N b. 110.89 N с. 155.89 N d. 125.89 N 21. What is the magnitude of the acceleration of the wedge, if no external force is applied? 3.2433 m/s2 b. c. 3.1433 m/s? d. 7.8346 m/s? a. 7.5346 m/s?arrow_forwardThe ABC bar has a mass of 2.4 kg and is connected to a support on B. An 800 g D sphere reaches the end A of the bar with a vertical velocity v1 of 3 m / s. Knowing that L = 750 mm and that the coefficient of refund between the sphere and the ABC bar is equal to 0.5, determine immediately after the shock, the angular velocity of the ABC bar and the velocity of the sphere.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
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY