Force & Velocity Homework: Ratios & Solutions

In summary, the conversation discusses the problem of finding the ratio of water flow speeds in two connected hoses of different lengths and diameters. The attempt at a solution initially assumes that velocity is proportional to area, but the correct equation is A1v1 = A2v2, which is based on conservation of mass.
  • #1
FauxNews
6
0

Homework Statement



A 1 meter long hose of 8 cm diameter is conneted to a faucet. The end of this hose is connected to a second hose which is 4 meters long and 4 cm in diameter. At the open end of the second hose water flows out at a rate of 8 cm cubed/s.

What is the ratio of the speed of the water flowing in the second hose to the speed of the water flowing in the first hose?


Homework Equations



P = F/A Not sure what other equations I could be using!


The Attempt at a Solution



At first I assumed v1/A1 = v2/A2, so (8 cm cubed/s)/(4pi) = (x)/(16pi), and thus the answer ought to be 1/4, but that is incorrect. I also tried to use squares, since I reasoned that a = (v^2)/r, but this gave me the equally incorrect ratio of 1/8. Help!
 
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  • #2
Welcome to PF!

Hi FauxNews! Welcome to PF! :wink:
FauxNews said:
At first I assumed v1/A1 = v2/A2 …

hmm … so you think velocity is proportional to area?

why? :smile:​
 
  • #3
Thank you for the welcome!

Well, I know that F1/A1 = F2/A2...correct? But I suppose that would not hold true for velocity, now that I think about it! I'm completely confused. :(
 
  • #4
tiny-tim's question is a hint to guide you on your way. The fact that A1v1 = A2v2 is only true because of the way the rate of flow of a fluid "works."

So, go back and figure out why A1v1 = A2v2, and see if that helps you find the solution.

Good luck!
 
  • #5
FauxNews said:
Thank you for the welcome!

Well, I know that F1/A1 = F2/A2...correct? But I suppose that would not hold true for velocity, now that I think about it! I'm completely confused. :(

Hi FauxNews! :smile:

(just got up :zzz: …)

Hint: conservation of mass. :wink:​
 

1. What is the relationship between force and velocity?

The relationship between force and velocity is defined by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. In other words, the greater the force applied to an object, the greater its acceleration will be, and the smaller its mass, the greater its acceleration will be.

2. How do you calculate the force-velocity ratio?

The force-velocity ratio, also known as the mechanical advantage, can be calculated by dividing the output force (the force applied to the object) by the input force (the force applied by the object). In mathematical terms, it can be expressed as: mechanical advantage = output force / input force.

3. What is the difference between force and velocity?

Force and velocity are two different physical quantities. Force is a vector quantity that describes the strength or intensity of an applied push or pull, while velocity is a vector quantity that describes the speed and direction of an object's motion.

4. How does the mass of an object affect its velocity?

The mass of an object does not directly affect its velocity. According to Newton's Second Law of Motion, the acceleration of an object is inversely proportional to its mass, meaning that an object with a smaller mass will experience a greater acceleration for the same amount of force applied. However, the velocity of an object is determined by its acceleration and the time it has been accelerating, not its mass alone.

5. Can force and velocity be negative quantities?

Yes, both force and velocity can be negative quantities. In physics, negative values indicate the direction of the quantity, not its magnitude. For example, a negative force means that the force is acting in the opposite direction of the positive force. Similarly, a negative velocity means that the object is moving in the opposite direction of the positive velocity.

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