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
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Chapter 15 Solutions
Loose Leaf for Vector Mechanics for Engineers: Statics and Dynamics
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