Concept explainers
(a)
Find the velocity and acceleration of point B just before the power is turned off.
(a)
Answer to Problem 15.19P
The velocity and acceleration of point B just before the power is turned off are
Explanation of Solution
Given information:
The initial speed
The radius (r) of the wheel is
The time taken (t) by the wheel and the chain coast to come to rest is
Consider the motion as uniformly decelerated motion.
Calculation:
Show the position of point A and B as shown in Figure 1.
Calculate the velocity of the point B just before the power is turned off using the relation:
Substitute
Thus, the velocity of the point B just before the power is turned off is
Calculate the uniform angular acceleration
The value of angular velocity
Substitute 0 for
Consider just before power is turned off.
The angular acceleration
Consider the normal and tangential component of the acceleration at point B are denoted by
Calculate the tangential component of acceleration of the point B using the relation:
Substitute
Calculate the normal component of acceleration of the point B using the relation:
Substitute
Neglect the effect of tangential acceleration as it is small.
Thus, the acceleration of point B just before the power is turned off is
(b)
Find the velocity and acceleration of point B just after 2.5 s.
(b)
Answer to Problem 15.19P
The velocity and acceleration of point B just after 2.5 s are
Explanation of Solution
Given information:
Calculation:
Refer Part (a).
Calculate the uniform angular velocity
The value of angular velocity
Substitute
Consider the time
Calculate the velocity of the point B using the relation:
Substitute
Thus, the velocity of point B just after 2.5 s is
Show the components of acceleration as shown in Figure 2.
Refer Figure 2.
Consider the normal and tangential component of the acceleration at point B are denoted by
Calculate the tangential component of acceleration of the point B using the relation:
Substitute
Calculate the normal component of acceleration of the point B using the relation:
Substitute
Calculate the angle
Neglect the effect of tangential acceleration as it is small.
Thus, the acceleration of point B just after 2.5 s is
Want to see more full solutions like this?
Chapter 15 Solutions
VECTOR MECH...,STAT.+DYN.(LL)-W/ACCESS
- In order to uncoil electrical wire from a 0.6-m-radius spool fixed to a truck, a worker drives to the left with a speed of vA = 5 m/s. At the same time, a second worker holds the cable as he walks to the right with a speed of vB = 3 m/s. Knowing that at the instant shown the thickness of wire on the spool is 40 mm, determine (a) the instantaneous center of rotation of the spool, (b) the velocity of point D on the inside of the spool.arrow_forwardThe motion of an oscillating flywheel is defined by the relation 0=00e-3πtcos 4, πt where 0 is expressed in radians and t in seconds. Knowing that 00 = 0.5 rad, determine the angular coordinate, the angular velocity, and the angular acceleration of the flywheel when (a) t= 0, (b) t= 0.125 s.arrow_forwardThe motion of an oscillating flywheel is defined by the relation 0=00e- πtcos 4, πt where 0 is expressed in radians and t in seconds. Knowing that 00 = 0.5 rad, determine the angular coordinate, the angular velocity, and the angular acceleration of the flywheel when (a) t= 0, (b) t= 0.125 s.arrow_forward
- Consider that at the instant shown, bar AB of the mechanical system below has a angular velocity (wAB) counterclockwise at 5 rad/s and an angular acceleration (alphaAB)counterclockwise 2 rad/s².The length of bar AB is 0.4 m and the length of bar BC is 1 m. For the instant shown, and using a "Analysis of Relative Motion", determine: (a) the speed of point B (b) angular velocity of connecting bar BC (c) the speed of point C (d) the acceleration of point B (d) the acceleration of point Carrow_forwardA helicopter moves horizontally in the x direction at a speed of 120 mi/h. Knowing that the main blades rotate clockwise when viewed from above with an angular velocity of 180 rpm, determine the instantaneous axis of rotation of the main blades.arrow_forwardIn order to uncoil electrical wire from a spool fixed to a truck, a worker drives to the left with a speed of vA = 4 m/s. At the same time, a second worker holds the cable as he walks to the right. Knowing that at the instant shown the thickness of wire on the spool is 50 mm and that the 0.6-m-radius spool has an angular velocity of 8 rad/s, determine (a) the instantaneous center of rotation of the spool, (b) the velocity of point D on the spool, (c) the speed of the second worker B.arrow_forward
- The bucket of a backhoe is the element AB of the four-bar linkage system ABCD. Assume that the points A and D are fixed and that the bucket rotates with a constant angular velocity WAB = 0.25 rad/s. In addition, suppose that, at the instant shown, point B is aligned vertically with point A, and C is aligned horizontally with B. Determine the acceleration of point C at the instant shown along with the angular acceleration of the elements BC and CD. Let h= 0.66 ft, e= 0-46 ft, l= 0.9 ft, and w= 1.0 ft.arrow_forwardThe motion of an oscillating crank is defined by the relation u = u0 sin (π t/T) - (0.5u0) sin (2πt/T),where u is expressed in radians and t in seconds. Knowing that u0 = 6 rad and T = 4 s, determine theangular coordinate, the angular velocity, and the angular acceleration of the crank when (a) t = 0, (b)t = 2 s.arrow_forwardThe rectangular block shown rotates about the diagonal OA with an angular velocity of 3.38 rad/s that is decreasing at the rate of 5.07 rad/s2. Knowing that the rotation is counterclockwise as viewed from A , determine the velocity and acceleration of point B at the instant shown.arrow_forward
- A helicopter moves vertically in the y direction at a speed of 10 km/h. Knowing that the main blades rotate clockwise with an angular velocity of 180 rpm, and the assistive blades rotate counterclockwise with an angular velocity of 200 rpm, determine; a) the instantaneous axis of rotation of the main blades, b) the instantaneous axis of rotation of the assistive blades.arrow_forwardIn a four bar mechanism, the dimensions of the links are as given below:AB = 50 mm, BC = 66 mmCD = 56 mm and AD = 100 mmAt a given instant when | DAB=60°the angular velocity of link AB is 10.5rad/sec in CCW direction.Determine,i) Velocity of point Cii) Velocity of point E on link BC when BE = 40 mmiii) The angular velocity of link BC and CDiv) The velocity of an offset point F on link BC, if BF = 45 mm,CF = 30 mm and BCF is read clockwise.v) The velocity of an offset point G on link CD, if CG = 24mm, DG = 44 mm and DCG is read clockwise.vi) The velocity of rubbing of pins A, B, C and D. The ratios ofthe pins are 30 mm, 40 mm, 25 mm and 35 mmrespectively.arrow_forwardA radar system is used to track a new experimental space launch vehicle. Early in the vehicle’s flight trajectory, the azimuth angle β is increasing with the constant rate dβ/dt = 20°/s. The elevation angle γ is increasing at the rate dγ/dt = 40°/s, and this rate is increasing at 5°/s2 . Knowing that the distance between O and P is 2 m and that at this instant β = 0° and γ = 30°, determine (a) the angular velocity of the radar system, (b) the angular acceleration of the system, and (c) the velocity and acceleration of point P.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