Work energy problem with damping?

In summary, the person is seeking help with part d of a problem and has worked out the damping constant correctly. They attempted to solve the problem using the work energy theorem and ended up with a quadratic equation, but the solutions do not match the answer key. They are questioning if the energy term for the damper is correct and mention the equation they have for rotational kinetic energy.
  • #1
theBEAST
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Homework Statement


I need help with part d.
dHyT2.png


The Attempt at a Solution


I worked out the damping constant and I am pretty sure it is correct. So I tried to solve this using work energy theorem. I ended up with a quadratic equation and solved for two solutions. None of them match the answer key which is -0.081rad/s. What am I doing wrong? Is the energy term for the damper correct?

Essentially I have:
Spring energy + Gravitational energy = Work done by damper + Rotational kinetic energy of the whole system
OcUIU.png
 
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  • #2
I solved for rotational kinetic energy and got a quadratic equation. I solved it and got two solutions which do not match the answer key.
 

FAQ: Work energy problem with damping?

What is the definition of work energy problem with damping?

The work energy problem with damping is a type of physics problem that involves calculating the work done on an object by a force, taking into account the effects of damping or friction on the object's motion.

What is the difference between work energy problem with damping and without damping?

The main difference between the two types of problems is the presence of damping or friction. In a work energy problem without damping, the object's motion is assumed to be frictionless, while in a work energy problem with damping, the effects of friction on the object's motion must be taken into account.

What are the key equations used in solving work energy problems with damping?

The key equations used in solving these types of problems include the work-energy theorem, which states that the work done on an object by a force is equal to the change in the object's kinetic energy, and the equations for calculating the force of friction and the work done by friction.

How can the coefficient of damping be determined in a work energy problem?

The coefficient of damping can be determined experimentally by measuring the velocity of the object at different points in its motion and using the data to calculate the damping force. It can also be estimated using theoretical models and assumptions about the object's motion.

What are some real-world applications of work energy problems with damping?

Work energy problems with damping can be applied to various real-world scenarios, such as calculating the force needed to stop a moving vehicle on a rough surface, determining the energy dissipated by a swinging pendulum due to air resistance, or analyzing the motion of a roller coaster with friction. These types of problems are also important in engineering fields, such as designing shock absorbers for vehicles or calculating the energy loss in mechanical systems due to friction.

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