Constrained motion question (using moments of inertia/energy)

In summary, the conversation discusses the calculation of energy in a system consisting of a disc, an arm, and a collar. The initial energy of the system is calculated, and then the energy at a specific stage is determined. However, there is a discrepancy between the calculated and expected speed of the collar, indicating a potential error in the determination of kinetic energy of the arm. The request for hints on how to solve the problem is made.
  • #1
Mutant_Fruit
3
0
I've attached a screenshot of the question. This is what I've tried so far:

I've calculated the initial energy of the system (which is all potential energy):
Energy of disc:
0.5*I*w^2 + 0.5 *m*v^2 + m*g*h
= 0 + 0 + 0

Energy of arm:
0.5*m*v^2 + m*g*h
= 0 + 4*9.81*1.5Cos(45)
= 41.62 joules

Energy of collar:
0.5*m*v^2 + m*g*h
= 0 + 1*9.81*3Cos(45)
= 20.81 joules

Then i moved time on until the supporting arm BC was horizontal and calculated the energy at that stage (which would be all kinetic). When i do that, i end up calculating that the speed of the collar is 1.04 m/s. However, the answer is supposed to be 7.315 m/s.

I'm doing something wrong, but i can't figure out what it is. Any hints on how this is supposed to be solved would be great.

Thanks.

http://img127.imageshack.us/img127/3230/question8wo.th.jpg
 
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  • #2
In all probability, your flaw lies in determining the kinetic energy term of the arm. Specify what you did.
 

Related to Constrained motion question (using moments of inertia/energy)

1. What is constrained motion in physics?

Constrained motion in physics refers to the movement of an object that is not free to move in any direction, but rather is limited by certain constraints or restrictions. These constraints can be physical barriers, forces acting on the object, or other factors that restrict its motion.

2. How is the moment of inertia used in constrained motion?

The moment of inertia is a measure of an object's resistance to rotational motion. In constrained motion problems, the moment of inertia is used to calculate the torque or rotational force needed to overcome the constraints and cause the object to rotate.

3. What is the relationship between energy and constrained motion?

In constrained motion problems, the total energy of the system is conserved. This means that the initial energy of the system, which includes both kinetic and potential energy, will remain constant throughout the motion, even if the object is constrained.

4. How can we calculate the moment of inertia for a constrained object?

The moment of inertia for a constrained object can be calculated by breaking down the object into smaller, simpler parts and then using the parallel axis theorem to add their individual moments of inertia together. This takes into account the distance of each part from the axis of rotation, which may change due to the constraints.

5. What are some common examples of constrained motion in real life?

Some common examples of constrained motion in real life include a pendulum swinging back and forth, a car turning around a corner, or a planet orbiting around a star. In each of these cases, the motion is limited by certain constraints, such as gravity, friction, or physical barriers.

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