Calculating Drop Locations: The Physics of Water Dripping from a Shower Nozzle

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In summary, there is a shower nozzle dripping water onto a stall floor 81 inches below. The drops fall at regular intervals of time, with the first drop hitting the floor at the same time the fourth drop begins to fall. To find the location of the individual drops, a position function is needed. However, since there is no initial velocity, the time each drop starts to fall must be calculated first. This time is 1/3 of the time it takes for the first drop to hit the floor, and each successive drop starts falling at this interval.
  • #1
courtrigrad
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Water drips from the nozzle of a shower onto the stall floor 81 in. below. The drops fall at regular intervals of time, the first drop striking the floor at the instant the fourth drop begins to fall. Find the location of the individual drops when a drop strikes the floor.

So we are given a distance the drop falls 81 inches . When it says to find the location of the individual drops, I need a position function. Should I use [itex] y = v_{y}_{0}t + \frac{1}{2}a_{y}t^{2} [/itex]?

Thanks
 
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  • #2
Right, but there's no initial velocity. And first you need to find the time each drop starts falling.
 
  • #3
Or, more correctly, the initial velocity is 0! Calculate the time it takes the first drop to hit the floor. According to the problem, that is exactly the time the fourth drop starts to fall. So, since the drops fall "at regular intervals of time", that "regular intervals of time" is 1/3 the time the first drop takes to hit the floor (do you see why it is 1/3 and not 1/4?). Now you know when each successive drop starts!
 
  • #4
yes that's what i was thinking. its 1/3 and not 1/4, because the first drop hits the ground only when the fourth drop starts to fall, not when it hits the ground.
 

1. How does the shape of the shower nozzle affect the drop location?

The shape of the shower nozzle can greatly affect the drop location. A narrow nozzle will produce a concentrated stream of water, leading to smaller and more consistent drop locations. A wider nozzle will produce a wider and more dispersed stream of water, leading to larger and more varied drop locations.

2. What role does water pressure play in determining drop location?

Water pressure plays a significant role in determining drop location. Higher water pressure will result in a stronger and more forceful stream of water, leading to drops that are more spread out and closer to the nozzle. Lower water pressure will result in a weaker and gentler stream of water, leading to drops that are more focused and farther from the nozzle.

3. How does the height of the nozzle affect the drop location?

The height of the nozzle can also impact the drop location. The higher the nozzle is placed, the longer the distance the water droplets have to travel before reaching the ground. This can lead to smaller and more concentrated drops, as well as a longer and more dispersed path for the drops to follow.

4. What other factors besides water flow can affect drop location?

Besides water flow, other factors that can impact drop location include air resistance, surface tension of the water, and the presence of any obstacles in the path of the drops. Air resistance can cause the drops to slow down and change direction, while surface tension can cause the drops to stick together or break apart. Obstacles such as shower curtains or objects in the shower can also alter the trajectory of the drops.

5. Is there a way to accurately predict the drop location from a shower nozzle?

While there are many factors that can influence drop location, there are mathematical equations and simulations that can help predict the general pattern of drops from a shower nozzle. However, due to the complex and unpredictable nature of dripping water, it is difficult to accurately predict the exact drop location every time.

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