(a) In Prob. 16.48 , determine the point of the rod A B at...

(a) In Prob. 16.48 , determine the point of the $\operatorname{rod} A B$ at which the force $\mathbf{P}$ should be applied if the acceleration of point $B$ is to be zero.
( b) Knowing that $P=0.75$ lb, determine the corresponding acceleration of point $A$.

Key Concepts

Force Application and Moment Effects

This concept involves understanding how the location of an applied force influences both the translational and rotational motion of a rigid body. By adjusting the point of application, the force can produce a torque that either enhances or diminishes the rotation, and finding the precise location can lead to special conditions, such as having zero acceleration at a given point.

Rigid Body Kinematics

This concept refers to the study of the motion of a body that is assumed not to deform, meaning that all points in the body experience the same rotational motion and related translation. It highlights the connection between linear motion and rotational motion, and it is crucial when analyzing how accelerations vary at different points along a rigid rod.

Angular and Translational Acceleration Relationship

This idea explains how the acceleration of any point on a rotating rigid body can be expressed as a combination of the acceleration of a reference point and a contribution from the angular acceleration multiplied by the distance from that point. This relationship is pivotal when setting conditions, such as achieving zero acceleration at a specific point on the rod.

Transcript

00:01 Hello everyone here it is given that determine the point of the rod a .b at which the force p should be applied to find a point if on which force p is to be applied is to be applied then acceleration of b is 0 if p is called to 0.

01:06 If p is called to point to 5 pound then acceleration of a let us start solving it this is the rod a b this is g center of mass so from here this distance is l y2 and this is also l y2 suppose here force is applied at c point which is h meter from here then submission of force along right direction to be taken positive so it could be p skull to m a and mass can be written as weight of the rot and divided by g into a so a will be p into g divided by w and if you write in vector form it will be towards right if we calculate moment of force about the center of mass so clockwise be a considering positive then it will be p into h equal to i into alpha so alpha can be written as p into h upon i i e a moment of inertia of the rod so you can write p p p into h i will be m square by 12 so 12 p h mass it weight weight upon g to l square so you will get 12 p h into omega l squared and in vector form it will be clock by direction a part acceleration of b point towards right to be taken positive a minus l y to alpha this is given zero a we have calculated p into g upon w and alpha we have calculated 12 p h upon w l square into g so on solving it you will get edge to be ly6 that is 36 inch upon 6 it will be 6 inch it will be 6 inch that is p point is located 12 inch from an a.

05:45 P point is located 12 inch from a.

06:04 So this is the answer of a part.

06:08 Now we have to find the acceleration of a in second part.

06:14 So b part we are solving...

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