# A ship going upstream and experiences a frictional force

• fara0815
In summary, the conversation discusses a problem involving a ship moving upstream with a constant power P and overcoming a frictional force caused by the water. The participants briefly discuss the necessary power for the ship to stay in the same place and continue upstream, with different opinions on how to calculate it. There is also a suggestion to use F_rU as the necessary power.
fara0815
Hello there!

This problem is giving me a hard time and I thought maybe one of you could give me a hint:

"A ship is going upstream with a constant power P. Its speed $$V$$ is relative to the water and the water's speed $$U$$ is relative to the shore. The ship needs tp overcome a frictional force of $$F_r=cv^2$$ caused by the water which depends on its relativ speed. How big does v have to be so that the ship goes from A to B with the lowest energy consumption?"

Where I would start is that the ship needs at least the power which is neccesary to stay in the same place. Which would be
$$P=F_r x U = cU^2U=cU^3$$ and than in addition some extra power to go upstream. That would be $$P=F_r x (v-u)=c(V-U)^2 x (V-U)$$. But from here, if it's really correct, I do not know how to continue :(

I assume the "x" in your formula is a multiplication sign. Don't do that, it's confusing. Just $P= F_rU$ would be sufficient.
I don't believe you can or should distinguish between the power necessary to "stand still" and the power necessary to move forward against the current. They are the same. Note also that U is speed of the boat relative to the water so it makes no sense to use V-U (which would be negative: if the boat is moving forward against the current, U> V).

I can definitely understand how this problem is giving you a hard time. It seems like a complex and multi-dimensional problem. To start, we can break down the forces acting on the ship into two components: the driving force (P) and the resisting force (F_r). The driving force is responsible for propelling the ship forward, while the resisting force is caused by the friction between the ship and the water.

To determine the minimum energy consumption for the ship to travel from point A to point B, we need to consider the work done by the driving and resisting forces. The work done by the driving force is simply P x distance traveled, while the work done by the resisting force is F_r x distance traveled.

Since we want to minimize the energy consumption, we want to minimize the total work done. This means that the ratio of work done by the driving force to the work done by the resisting force should be as low as possible.

Using this information, we can set up an equation: P x distance traveled / F_r x distance traveled = P / F_r. This represents the ratio of the work done by the driving force to the work done by the resisting force.

To minimize this ratio, we can take the derivative with respect to v (the speed of the ship) and set it equal to 0. This will give us the optimal speed (v) for the ship to travel from A to B with the lowest energy consumption.

I hope this helps give you a starting point for solving this problem. Remember, as a scientist, it's important to break down complex problems into smaller, more manageable parts and use equations and principles to guide your thinking. Good luck!

## 1. What is a ship going upstream?

A ship going upstream refers to a situation in which a boat or ship is traveling against the direction of a current or river flow.

## 2. What is frictional force?

Frictional force is a resistive force that occurs when two surfaces come into contact and move against each other. In the case of a ship going upstream, the frictional force acts in the opposite direction to the boat's movement, making it more difficult to travel upstream.

## 3. How does frictional force affect a ship going upstream?

Frictional force can significantly affect a ship going upstream by slowing down its speed and making it more difficult to navigate against the current. It also requires the ship to use more energy to overcome the resistance of the water.

## 4. Can the frictional force on a ship going upstream be reduced?

Yes, the frictional force on a ship going upstream can be reduced by using methods such as reducing the surface area of the ship that comes into contact with the water, using lubricants, or altering the shape of the ship's hull to minimize resistance.

## 5. How does the weight of the ship affect the frictional force when going upstream?

The weight of the ship does not directly affect the frictional force when going upstream. However, a heavier ship may require more energy and power to overcome the resistance of the water, making it more difficult to travel upstream.

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