Concept explainers
A sphere of radius r and mass m has a linear velocity v0 directed to the left and no angular velocity as it is placed on a belt moving to the right with a constant velocity v1. If after first sliding on the belt the sphere is to have no linear velocity relative to the ground as it starts rolling on the belt without sliding, determine in terms of v1 and the coefficient of kinetic friction μk between the sphere and the belt (a) the required value of v0, (b) the time t1 at which the sphere will start rolling on the belt, (c) the distance the sphere will have moved relative to the ground at time t1.
Fig. P16.74
Want to see the full answer?
Check out a sample textbook solutionChapter 16 Solutions
Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
Additional Engineering Textbook Solutions
Engineering Mechanics: Dynamics (14th Edition)
Machine Tool Practices (10th Edition)
Introduction to Heat Transfer
Statics and Mechanics of Materials
Fundamentals Of Thermodynamics
HEAT+MASS TRANSFER:FUND.+APPL.
- The spring-mounted 0.90-kg collar A oscillates along the horizontal rod, which is rotating at the constant angular rate 0 = 6.2 rad/s. At a certain instant, r is increasing at the rate of 790 mm/s. If the coefficient of kinetic friction between the collar and the rod is 0.68, calculate the friction force Fexerted by the rod on the collar at this instant. Vertical (ונננננ Answer: F = i Narrow_forwardThe 29-kg wheel is rolling under the constant moment of M = 85 N·m. The wheel has radius r = 0.57 m, has mass center at point G, and the radius of gyration is kg = 0.25 m. The coefficients of friction between the wheel and the ground is g = 0.37 and μk = 0.16. If the wheel rolls while slipping, determine the magnitude of the linear acceleration of point G (in m/s²). Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g = 9.81 m/s². M Your Answer: Answerarrow_forward3. A block of mass m = 2.00 kg rests on the left edge of a block of mass M= 8.00 kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00 kg block rests is frictionless. A constant horizontal force of magnitude F= 10.0N is applied to the 2.00-kg block, setting it in motion as shown in Figure. The distance L that the leading edge of the smaller block travels on the larger block is 3.00 m. F - m M M (a) Draw a separate free-body diagram for each block. (b) In what time interval will the smaller block make it to the right side of the 8.00-kg block? as (Note: Both blocks are set into motion when the force is applied.) (c) How far does the 8.00-kg block move in the process?arrow_forward
- A cylinder of mass M and radius R is rotated in a uniform V groovewith constant angular speed ω. The coefficient of friction betweenthe cylinder and each surface is μ. What torque must be applied tothe cylinder to keep it rotating?arrow_forwardQuestion 3 3.1. The 10 kg disk shown below is pin supported at its center. Determine the number of revolutions it must make to attain a speed of 150 rpm starting from rest. It is acted upon by the constant force F = 10 N, which is applied to the cord wrapped around its periphery, and a constant couple moment T = 5 Nm. Neglect the mass of the cord in the calculations. T= 3 Nm. 0.2 m F= 10N 3.2. The same disk is suddenly unbalanced and its axis passing through its mass center G. If it is released from rest, determine the horizontal and vertical components of reaction at the pin O as shown below. 100 0, 10 kgarrow_forward5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.arrow_forward
- The uniform rectangular plate is released from rest in the position shown. Determine the maximum angular velocity w during the ensuing motion. Friction at the pivot is negligible. b 2.4 b Answer: w - i | be|arrow_forward3. A block of mass m = 2.00 kg rests on the left edge of a block of mass M = 8.00 kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00 %3D kg block rests is frictionless. A constant horizontal force of magnitude F = 10.0 N is applied to the 2.00-kg block, setting it in motion as shown in Figure. The distance L that the leading edge of the smaller block travels on the larger block is 3.00 m. L M m M (a) Draw a separate free-body diagram for each block. (b) In what time interval will the smaller block make it to the right side of the 8.00-kg block? as (Note: Both blocks are set into motion when the force is applied.) (c) How far does the 8.00-kg block move in the process?arrow_forwardThe spool has a mass m, and a radius of gyration kG. An inextensible cord is attached to the wall at A. The cord is wound around the inner radius, R, and the outer radius is 2R. The coefficient of friction between the spool and the ground is mu. If instead of applying the force, F, at point B, the spool has an initial angular velocity given as omega naught. Use the work-energy principle to determine how far the center G will move before stopping.arrow_forward
- A spherical bowling ball with mass m = 4.6 kg and radius R = 0.105 m is thrown down the lane with an initial speed of v = 9.5 m/s. The coefficient of static friction between the ball and the ground is 0.35 and the coefficient for kinetic friction is μ = 0.3. Once the ball begins to roll without slipping it moves with a constant velocity down the lane. 1) What is the magnitude of the angular acceleration of the bowling ball as it slides down the lane? 2) What is magnitude of the linear acceleration of the bowling ball as it slides down the lane? 3) How long does it take the bowling ball to begin rolling without slipping? 4) Once it begins to roll without slipping, what is the force of friction on the ball?arrow_forward3. A 2-kg ball S is moved in the vertical plane by a robotic arm. When 0= 30°, the angular velocity of the arm about a horizontal axis through O is 50 deg/s clockwise, and the angular acceleration is 200 deg/s² counterclockwise. In addition, the hydraulic element is being shortened at the constant rate of 500 mm/s. Find the minimum gripping force needed to hold the ball is the coefficient of friction between the sphere and gripping surfaces is 0.5. Compare this force to the force needed to hold the sphere in static equilibrium.arrow_forwardThe disk with radius r is rolling (without slipping) with angular velocity through the bottom of the circular path of radius R. If @= 2 rad/sec, R = 0.5 m, r = 0.2 m, and the mass of the disk is 3 kg, calculate the magnitude of the normal force exerted by the path on the disk at that instant. Present your answer in Newtons using 3 significant figures. ໙arrow_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