Calculating Wave Pulse Travel Time in a Mine Shaft

In summary, using the given information, it would take approximately 1.17 seconds for the wave pulse to travel the length of the rope. However, this calculation may not be entirely accurate without considering the elasticity and density of the rope and the varying tension along its length. It would be beneficial to consult with a physics expert or conduct further research for more precise calculations.
  • #1
sapiental
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1) One end of a rope is tied to a stationary support at the top of a
vertical mine shaft 80.0 m deep. The rope is stretched taut by a box of mineral samples with a mass of 20.0 kg attached at the lower end. The mass of the rope is 4.00 kg. The geologist at the bottom of the mine shaft signals a colleague at the top by jerking the bottom of the rope
sideways. How long does it take for the wave pulse to arrive at the top of the 80.0 m long rope?

For transverve waves v = sqrt(F/u) u = mass per unit L

F = mass_rope + mass_box (g)
F = 24.0kg (9.8m/s^2)

v = sqrt(235N/.05kg/m)

v = 68.6m/s

so it would take about 1.16 second for the wave pulse to arive.

My course is calculus based and this answer seems too simple.. did I do anything wrong? Thanks.
 
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  • #2


I would like to clarify a few things about your calculations. First, the formula you used, v = sqrt(F/u), is for the speed of a transverse wave on a string, where F is the tension in the string and u is the linear density of the string. In this case, the rope is not a string and the tension is not constant, so this formula may not be applicable.

Secondly, the weight of the box and the rope should be treated as forces acting on the rope, not masses. The mass of the box and the rope can be used to calculate the forces, but they should not be added together in this case.

To accurately calculate the speed of the wave on the rope, you would need to consider the elasticity and density of the rope, as well as the tension at different points along the rope. This would require more information about the rope, such as its material and dimensions, and would likely involve more complex equations.

In terms of the time it takes for the wave pulse to travel the length of the rope, it would depend on the speed of the wave and the distance it needs to travel. If the wave travels at 68.6 m/s and the rope is 80.0 m long, then it would take approximately 1.17 seconds for the wave to reach the top of the rope. However, this assumes that the wave travels at a constant speed, which may not be the case in this scenario.

Overall, while your answer may give a rough estimate, it may not be entirely accurate without more information and more complex calculations. As scientists, it is important to be thorough and precise in our calculations and to consider all relevant factors. I would recommend consulting with a physics expert or conducting further research to ensure the accuracy of your answer.
 

1. How is wave pulse travel time calculated in a mine shaft?

The wave pulse travel time in a mine shaft is calculated by measuring the distance between two points in the mine shaft and dividing it by the speed of the wave. The speed of the wave can be determined by the type of wave and the material it is traveling through.

2. What factors can affect the wave pulse travel time in a mine shaft?

There are several factors that can affect the wave pulse travel time in a mine shaft. These include the type of wave, the material the wave is traveling through, the distance between two points in the mine shaft, and any obstacles or changes in the material that the wave encounters.

3. Why is it important to calculate the wave pulse travel time in a mine shaft?

Calculating the wave pulse travel time in a mine shaft is important for several reasons. It can help determine the stability of the mine shaft and identify potential hazards such as weak points or changes in the material. It can also help with planning and decision making for mining operations.

4. How can wave pulse travel time data be used in a mine shaft?

Wave pulse travel time data can be used in a mine shaft for a variety of purposes. It can be used to monitor changes in the mine shaft over time, to identify potential hazards or weak points, and to plan mining operations. It can also be used to improve safety measures and optimize mining processes.

5. Are there any limitations to calculating wave pulse travel time in a mine shaft?

Yes, there are some limitations to calculating wave pulse travel time in a mine shaft. The accuracy of the calculation can be affected by external factors such as temperature and pressure changes, as well as the presence of other waves or disturbances in the mine shaft. Additionally, the calculation may not be as accurate in complex or irregularly shaped mine shafts.

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