Checking a Problem: Speed of Bending Rod Tip

In summary, the conversation discusses a problem involving a thin rod bent into a quarter circle shape and rotated freely around the x-axis. The goal is to determine the speed of the tip of the rod when it reaches the bottom. The process involves calculating the potential energy and moment of inertia, then equating it to the kinetic energy. The final result is v=4[gR/pi]^(1/2). The conversation also clarifies that "thing rod" refers to a thin rod.
  • #1
225
0
I made up a problem and wanted to make sure that I did everything right.

A thing rod with mass M is bent into the shape of a quarter circle with radius R. It is positioned so that it looks like the arc made as theta moves from terminal position (+ x axis) to 90 degrees counterclockwise. I am going to let this arc rotate freely about the x-axis. My problem is to determine the speed of the tip of the wire when it has rotated all the way to the bottom.

First I calculated the potential energy of the rod using the x-axis as a refrence frame. I did this by integrating over the rod noting that the height of each piece is Rsin@

U=(2/pi)MgR.

Then I calculated the moment of inertia using the same integration techniques.

I=(1/2)MR^2

(Is that really true??!)

Finally I doubled the initial potential energy to get the kinetic when it has spun around and set that equal to (1/2)Iw^2

v=4[gR/pi]^(1/2)

If anyone would check this I would be very appreciative.
 
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  • #2
Should I perhaps move this question to a different forum?
 
  • #3
define "thing rod"
 
  • #4
403036387 said:
define "thing rod"
He means thin rod.
 

1. What is the purpose of checking the speed of a bending rod tip?

The purpose of checking the speed of a bending rod tip is to determine how quickly the rod is able to bend under a certain force or load. This can provide important information about the material properties of the rod and can help engineers and designers make decisions about its use in different applications.

2. How is the speed of a bending rod tip measured?

The speed of a bending rod tip can be measured using a variety of methods, including high-speed cameras, strain gauges, and accelerometers. These tools allow for precise measurement of the displacement and velocity of the rod tip as it bends under a load.

3. What factors can affect the speed of a bending rod tip?

Several factors can affect the speed of a bending rod tip, including the material properties of the rod (such as elasticity and strength), the magnitude and direction of the applied force, and any external factors such as temperature or humidity. Additionally, the shape and size of the rod can also impact its bending speed.

4. How does the speed of a bending rod tip relate to its strength and durability?

The speed of a bending rod tip can provide valuable information about its strength and durability. A faster bending speed may indicate that the rod is more prone to deformation and may have a lower strength. On the other hand, a slower bending speed may indicate a stronger and more durable rod.

5. What are some common applications for measuring the speed of a bending rod tip?

Measuring the speed of a bending rod tip is important in many industries and applications, such as structural engineering, material testing, and product design. It can also be used in fields such as sports science, where the bending speed of a golf club or tennis racket can impact its performance. Additionally, it is crucial in understanding the behavior of materials in critical structures, such as bridges and skyscrapers.

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