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 v1and the coefficient of kinetic friction
(a)
The value of
Answer to Problem 16.74P
Value of
Explanation of Solution
Given information:
Mass
Radius
Belt velocity
Ball velocity
Friction coefficient
Concept used:
Following formula is used-
1. Sum of horizontal forces,
2. Sum of moments about mass center,
Calculation:
Friction force:
Sum of horizontal forces;
Sum of moments about mass center:
Velocity equation,
Angular velocity equation,
Velocity of contact point,
Conclusion:
Thus we get,
Value of
(b)
The time at which sphere starts rolling.
Answer to Problem 16.74P
Value of time
Explanation of Solution
Given information:
Mass
Radius
Belt velocity
Ball velocity
Friction coefficient
Concept used:
Following formula is used-
1. Sum of horizontal forces,
2. Sum of moments about mass center,
Calculation:
Friction force:
Sum of horizontal forces:
Sum of moments about mass center:
Velocity equation:
Angular velocity equation:
Velocity of contact point:
Conclusion:
Thus we get,
Value of time
(c)
The distance moved by sphere relative of ground.
Answer to Problem 16.74P
Distance moved
Explanation of Solution
Given information:
Mass
Radius
Belt velocity
Ball velocity
Friction coefficient
Concept used:
Following formula is used-
1. Sum of horizontal forces,
2. Sum of moments about mass center,
Calculation:
Friction force,
Sum of horizontal forces,
Sum of moments about mass center,
Velocity equation,
Angular velocity equation,
Velocity of contact point,
Distance moved,
Conclusion:
Thus we get,
Distance moved
Want to see more full solutions like this?
Chapter 16 Solutions
Vector Mechanics For Engineers
- A spool of mass 60 kg is supported on two rollers at A and B as shown in FigureQ1(c). Neglect the mass of the inelastic cable, friction and the mass of therollers at A and B. Knowing that a constant pulling force P is applied in order tounwind 6 m of cable in 3 s starting from rest. The radius of gyration for the spoolis (604) mm, Appendix Ashows the examples of identifying the radius of gyration using student ID.(i) Determine the angular acceleration of the spool. (ii) Determine the pulling force P. (iii) Explain with calculation on ways to increase the acceleration of cablebeing pulled. [arrow_forwardThe motion of the uniform rod AB is guided by small wheels of negligible mass that roll on the surface shown. If the rod is released from rest when 0 = 0, determine the velocities of A and B when 0= 30°.arrow_forwardFour pins slide in four separate slots cut in a horizontal circular plate as shown. When the plate is at rest, each pin has a velocity directed as shown and of the same constant magnitude u. Each pin has a mass m and maintains the same velocity relative to the plate when the plate rotates about O with a constant counterclockwise angular velocity w. Draw the FBDs and KDs to determine the forces on pins p1 and p2.arrow_forward
- Please 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_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 sphere of radius r and mass m is projected along a rough horizontal surface with the initial velocities shown. If the final velocity of the sphere is to be zero, express (a) the required magnitude of w0 in terms of and r, (b) the time required for the sphere to come to rest in terms of v0 and the coefficient of kinetic friction μk.arrow_forward
- The 2.00-kg slender rod shown is hanging in a vertical position and is pin-supported at point A. The slender rod is initially at rest until a 1.000-kg block C, strikes it at its end at point B.The block slides on a frictionless surface with a velocity of 3.50 m/s to the right. After the impact, it slides with a velocity of 1.250 m/s to the right, and the bar rotates with an angular velocity, ω'. 1. What gives the correct kinematic relationship relating the final velocity of the center of the rod, v' , and its angular velocity, ω'? 2. What is the coefficient of restitution, e, between the block and the slender rod? 3. What is the magnitude of the horizontal impulse at the support at point A?arrow_forwardThe drum, with radius R = 1.9 m, is given an initial counterclockwise angular velocity ω0. The drum is kept from rolling towards the left by a smooth vertical slot acting on a thin rod which passes through its centre. A vertical force (where C = 38, k = 1.7 and t denotes time in seconds) is being applied to a cord wrapped around the inner hub, with radius r = 0.7 m, of the drum. If the frictional coefficient is μk = 0.62 and the change in the angular momentum about O is ΔHO = 238 kg.m2/s (counterclockwise) during the first 2.3 seconds, determine the mass of the drum. (The mass of the cord and the thin rod may be regarded as negligible.) a)214.2 kg b)68.28 kg c)19.83 kg d)109.6 kg e)69.86 kgarrow_forwardA 5-m-long ladder has a mass of 15 kg and is placed against a house at an angle 0 = 20°. Knowing that the ladder is released from rest, determine the angular velocity of the ladder and the velocity of end A when 0 = 45°. Assume the ladder can slide freely on the horizontal ground and on the vertical wall.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_forwardA cylinder of radius r and weight W with an initial counterclockwise angular velocity w0 is placed in the corner formed by the floor and a vertical wall. Denoting by μk the coefficient of kinetic friction between the cylinder and the wall and the floor, derive an expression for the time required for the cylinder to come to rest.arrow_forwardThe 2.00-kg slender rod shown is hanging in a vertical position and is pin-supported at point A. The slender rod is initially at rest until a 1.000-kg block C, strikes it at its end at point B.The block slides on a frictionless surface with a velocity of 3.50 m/s to the right. After the impact, it slides with a velocity of 1.250 m/s to the right, and the bar rotates with an angular velocity, ω'. Sketch the moment-impulse diagram 1. Which of the following gives the correct kinematic relationship relating the final velocity of the center of the rod, v'G, and its angular velocity, ω'? 2. Which of the following gives the closest value of the coefficient of restitution, e, between the block and the slender rod? 3. Which of the following gives the closest value of the magnitude of the horizontal impulse at the support at point A?arrow_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