How Do You Calculate Oscillation Periods and Forces on a Dam?

Just integrate the pressure function to find the total force acting on the dam.In summary, the conversation includes questions about finding the time for one period/oscillation of a massless spring attached to a solid cylinder, and finding the total force acting on a dam with a certain height of water. The total mechanical energy is equal to the sum of kinetic and potential energies, and for the first question, the moment of inertia must be taken into account. For the second question, the pressure function can be integrated to find the total force.
  • #1
blackbody
5
0
Hi, I have a couple general (pretty much abstract) mechanics questions, and I'm not sure I'm going the right way about doing them. Any help would be appreciated.

1)On a flat surface with friction, you have a massless spring with a spring constant (k) attached to a wall on one end, and on the other end to a solid cylinder of radius R, which can roll back and forth, due to oscillation. How can you find the time for one period/oscillation?

Ok, so the total mechanical energy is the sum of the kinetic (translational and rotational) and potential energies:
E = [tex]\frac{1}{2}[/tex]m[tex]v^2[/tex] + [tex]\frac{1}{2}[/tex]I[tex]\omega^2[/tex]+ [tex]\frac{1}{2}[/tex]k[tex]x^2[/tex]

I don't know whether to consider this SHM...how would I go about doing this?

2) You have a dam with a certain height of water against it. The pressure of the water can be given as a function of the height of the water p(h). What is the total force acting on the dam?

I'm thinking you just integrate the pressure function from 0 to the height?
 
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  • #2
blackbody said:
Hi, I have a couple general (pretty much abstract) mechanics questions, and I'm not sure I'm going the right way about doing them. Any help would be appreciated.

1)On a flat surface with friction, you have a massless spring with a spring constant (k) attached to a wall on one end, and on the other end to a solid cylinder of radius R, which can roll back and forth, due to oscillation. How can you find the time for one period/oscillation?

Ok, so the total mechanical energy is the sum of the kinetic (translational and rotational) and potential energies:
E = [tex]\frac{1}{2}[/tex]m[tex]v^2[/tex] + [tex]\frac{1}{2}[/tex]I[tex]\omega^2[/tex]+ [tex]\frac{1}{2}[/tex]k[tex]x^2[/tex]

I don't know whether to consider this SHM...how would I go about doing this?

2) You have a dam with a certain height of water against it. The pressure of the water can be given as a function of the height of the water p(h). What is the total force acting on the dam?

I'm thinking you just integrate the pressure function from 0 to the height?
As long as you are rolling without slipping, [itex]\omega[/itex] is proportional to v. Combine the first two terms to get something that looks like [itex]\frac{1}{2}Mv^2[/itex]
where M is a constant that is made up of the mass and moment of inertia. You should be able to take it from there.

You have the right idea about the dam
 
  • #3


For the first question, it seems like you are on the right track. The system can be considered as simple harmonic motion (SHM) since the restoring force (from the spring) is proportional to the displacement (from equilibrium position). To find the time for one period, you can use the equation T = 2π√(m/k) where m is the mass attached to the spring and k is the spring constant.

For the second question, you are correct in thinking that you can integrate the pressure function from 0 to the height to find the total force acting on the dam. This is because the total force is equal to the pressure multiplied by the area (F = pA), and the area in this case is just the height of the water times the width of the dam. So the integral would be ∫p(h)dh from 0 to the height.
 

Related to How Do You Calculate Oscillation Periods and Forces on a Dam?

1. What are couple mechanics problems?

Couple mechanics problems involve the study of the motion and forces of two objects that are connected together by a rigid body. This can include problems related to rotational motion, torque, and angular momentum.

2. What is the difference between a couple and a force?

A couple is a pair of equal and opposite forces that act on different points of an object, causing it to rotate. A force, on the other hand, is a push or pull that can cause an object to move in a linear direction.

3. How do you calculate the torque of a couple?

The torque of a couple can be calculated by multiplying one of the forces in the couple by the distance between the two forces, known as the lever arm. The direction of the torque is perpendicular to the plane formed by the two forces.

4. What are some real-world applications of couple mechanics?

Couple mechanics problems can be applied to various real-world scenarios, such as the motion of a seesaw, the rotation of a bicycle wheel, the movement of a door on its hinges, or the stability of a building's foundation.

5. How can couple mechanics problems be solved?

To solve a couple mechanics problem, you need to first identify the forces involved and their respective magnitudes and directions. Then, use the principles of rotational motion and equilibrium to calculate the torque and determine if the system is in static equilibrium. This can involve using equations such as Στ = 0 and ΣF = 0.

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