While redesigning a medical fluid pump you notice that the drive wheel is made u
ID: 1631921 • Letter: W
Question
While redesigning a medical fluid pump you notice that the drive wheel is made up of a ring and a disk. The ring is fastened to the top of a heavy solid disk, "a flywheel," and that disk is attached to a shaft. You are interested in this configuration and decide to determine its moment of inertia. You have a friend who thinks you can add the moment of inertial by parts to get the moment of inertia of the system. To test this idea you decide to build a laboratory model described below to determine the moment of inertia of a similar system from the acceleration of the hanging weight.
1. Draw a side view of the equipment. Draw the velocity and acceleration vectors of the weight. Add the tangential velocity and tangential acceleration vectors of the outer edge of the spool. Also, show the angular acceleration of the spool. What are the relationships among the acceleration of the string, the acceleration of the weight, and the tangential acceleration of the outer edge of the spool if the string is taut?
2. To relate the moment of inertia of the system to the acceleration of the weight, you need to consider a dynamics approach (Newton’s 2nd) especially considering the torques exerted on the system. The relationships between rotational and linear kinematics will also be involved.
3. Draw a free-body diagram for the rotating system. Show the locations of the forces acting on the system. Label all the forces. Does this system accelerate? Is there an angular acceleration? Check to see if you have all the forces on your diagram. Which of these forces can exert a torque on the system? Identify the distance from the axis of rotation to the point where each force is exerted on the system. Write down an equation that gives the torque in terms of the distance and the force that causes it. Write down Newton's second law in its rotational form for this system. Remember that the moment of inertia includes everything in the system that will rotate.
4. Draw a free-body diagram for the hanging weight. Label all the forces acting on it. Does this weight accelerate? Is there an angular acceleration? Check to see if you have included all the forces on your diagram. Write down Newton's second law for the hanging weight. Is the force of the string on the hanging weight equal to the weight of the hanging weight?
5. Can you use Newton’s third law to relate pairs of forces shown in different force diagrams?
6. Is there a relationship between the angular acceleration of the rotating system and the acceleration of the hanging weight? To decide, examine the accelerations that you labeled in your drawing of the equipment.
7. Solve your equations for the moment of inertia of the rotating system as a function of the mass of the hanging weight, the acceleration of the hanging weight, and the radius of the spool. Start with the equation containing the quantity you want to know, the moment of inertia of the rotating system. Identify the unknowns in that equation and select equations for each of them from those you have collected. If those equations generate additional unknowns, search your collection for equations that contain them. Continue this process until all unknowns are accounted for. Now solve those equations for your target unknown.
EQUIPMENT ing. You also have a You have an apparatus that spins a horizontal disk and r stopwatch, meterstick, pulley, table clamp, mass set and the video analysis equipment. Pulley The disk and ring rotationa axis and represent the flywheel. A string has one end wrapped around the plastic spool (under the disk) and the other end passing over a vertical pulley lined up with the tangent to the spool. A mass is hung from the free end of the string so it can fall past the table, spinning the system. share the same Ring Disk Spool String Shaft Stand- MassExplanation / Answer
Q1. velocity and acceleration vectors of weight
the tangential velocity, tangential acceleration and angular acceleration of spool is as below
when string is taut, the acceleration of the string = the acceleration of the weight = the tangential acceleration of the outer edge of the spool
This is because if they have different acceleration, then system equilibrium will not be maintained and the tautness of string will not be there.
2. If a= acceleration of the weight
then mg-T =ma
so, T= m(g-a)
T x radius of the spool = moment of inertia x angular acceleration of the spool
so, m(g-a) x radius of the spool =moment of inertia x angular acceleration of the spool
so, m(g-a) x radius of the spool = moment of inertia x a / radius of the spool
3.The free body diagram and the relations between various variables are as below
4. the free- body diagram is same as in q1.
The forces are acting : tension in the string acting upwards
Weight acting vertically downward
the equation of motion as per Newton's second law = weight - tension= mass x acceleration
This system can not have any angular acceleration as it is not rotating.
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