Rigid Body Kinetics Homework Solution

[9988776655]

Homework Statement

The problem is shown in the attachment.

Homework Equations

Mo = Ia
MgL/2 = moment of inertia of the bar
Io = Ig + md^2 parallel axis theorum

The Attempt at a Solution

I found the moment of inertia of the bar about its center of mass:
MgL/2 = (4.6*9.81*1.3)/2 = 29.3319
For the pulley, I tried:
(T2-T1)radius = Ialpha
acceleration = alpha*radius
For the mass:
T-mg = ma
There are too many unknowns for me unfortunately

 

[learningphysics]

There's probably multiple ways to do this problem... but the way that comes to mind for me is... first get the tension in the cable and get the angular acceleration of the rod about the pivot...

The moment of inertial of the bar is not MgL/2... The moment of inertia of a rod about it's end is (1/3)ML^2.

Use your torque equation for the rod... with the force equation for the hanging mass... to get alpha and tension...

Once you do that, you focus on the force equations for the rod...

What is the vertical acceleration of the center of mass of the rod? you can get this using your alpha...

What is the horizontal acceleration of the center of mass of the rod? you can get this using the v given for the mass (from this v you can get w, the angular velocity of the rod... then you can get the vertical velocity of the center of mass)...

from the vertical velocity of the center of mass, you can get the horizontal acceleration... think centripetal motion...

with the horizontal and vertical accelerations of the center of mass... you can solve for the forces at the A...

sum of all horizontal forces acting on the rod = (mass of the rod)*(acceleration of the center of mass of the rod)...

same thing vertically.

 

[ogb p]

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As a scientist, it is important to first understand the problem and its context before attempting to solve it. From the provided information, it appears that this is a problem involving rigid body kinetics and rotational motion. The equations listed are commonly used in such problems and it is good that the student has identified them as relevant.

However, it is important to also consider the physical principles and assumptions involved. For example, it is assumed that the bar and pulley are rigid bodies that do not deform under the applied forces. It is also important to clarify the coordinate system and direction of motion, as well as any other relevant parameters such as the mass and dimensions of the objects involved.

In terms of the solution attempt, the student has correctly calculated the moment of inertia for the bar. However, it is important to note that the moment of inertia for the pulley would depend on its shape and mass distribution, which are not provided in the problem. Therefore, it is not possible to solve for the tension or acceleration without this information.

In order to solve this problem, the student should first clarify any missing information and then apply the relevant equations, taking into account the physical principles involved. It may also be helpful to draw a free body diagram and consider the forces acting on each object. With a clear understanding of the problem and its context, the solution can be accurately determined.