Find Magnitude of Buoyant Force on Boat in Water

In summary: The total buoyant force is equal to the weight of the water displaced by the bubble multiplied by the surface area of the bubble.
  • #1
XodoX
203
0
Hello, I am having with this ( actually) kinda easy problem. I don't know how to approach it.



There's a worker poling a boat. He pushes parallel to the length of the light pole, exerting on the bottom of the lake a force of 240 N. Assume the pole lies in the vertical plane containing the boat's keel.
At one moment, the pole makes an angle of 35 degrees with the vertical and the water exerts a horizontal drag force of 47.5 N on the boat, opposite to its forward velocity magnitude 0.857 m/s. Total mass of the boat is 370 kg.

The water exerts a buoyant force vertically upward on the boat. Find the magnitude of this force.



I've been trying to find an equation to get started, but I have no idea.
 
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  • #2
Resolve the force provided by the pole into x,y components.

Then look at the forces on the boat. How will the vertical component of the poleman's force affect the buoyant force provided by the water?
 
  • #3
LowlyPion said:
Resolve the force provided by the pole into x,y components.

Then look at the forces on the boat. How will the vertical component of the poleman's force affect the buoyant force provided by the water?

I thought about that too, but can't find the right answer.

Vertical would be the 240 N ( cos, I think) and horizontal would be the drag force of 47.N ( sin). Is that what you mean?
 
  • #4
XodoX said:
I thought about that too, but can't find the right answer.

Vertical would be the 240 N ( cos, I think) and horizontal would be the drag force of 47.N ( sin). Is that what you mean?

Cos35 is the correct vertical component of the 240 N force. So how many N is the boat? And then what is the net?
 
  • #5
Ok, I think I used a slightly different approach. Now I just need to calculate the buoyant force. I don't know how to do this for this problem. The book deals with the buoyant force several chapters after the one we are doing right now.
 
  • #6
XodoX said:
Ok, I think I used a slightly different approach. Now I just need to calculate the buoyant force. I don't know how to do this for this problem. The book deals with the buoyant force several chapters after the one we are doing right now.

Look they don't give you displacement to figure the weight of the water displaced. It's not needed. No need to get chapters ahead.

Make a diagram of the boat. There are 2 forces holding the boat up. The water (aka buoyant force) and the pole (the vertical component of the 240 N the guy is pushing down with.)

Like I said before, just figure the net ... weight - vertical component.
 
  • #7
I still don't get that. Originally I thought I could do it like this...

Vertical component of the 240 N force (up) - Weight of boat (down) + Buoyancy force (up) = 0

But this all will not get me the right result. It's supposed to be 3.43 KN...
 
  • #8
Why don't you show your calculation then for that equation?
 
  • #9
I don't understand why is doesn't work for you since it works really well for me...

But my answer in part b isn't the same as in the book and I'm wondering why.

The question is: Model the forces as constant over a short interval of time to find the velocity of the boat 0.450 s after the moment described.

First, I used my x components to find the acceleration.
After, I used the formula Vf=Vi+at.

My answer is 0.914 and the real answer is 0.967.

According to me, my mistake must be in my calculation of the acceleration.

Here is what I've done:

F=ma
Fwater/horizontal=ma

Is that right?
 
  • #10
What is the equation for total buoyant force for a volume that changes as it ascends to the surface, like an air bubble?
 

1. What is buoyancy and how does it affect a boat in water?

Buoyancy is the upward force exerted by a fluid on an object immersed in it. It is a result of the difference in pressure on the top and bottom of the object. For a boat in water, the buoyant force pushes upwards, counteracting the weight of the boat and allowing it to float.

2. What factors affect the magnitude of the buoyant force on a boat in water?

The magnitude of the buoyant force on a boat in water depends on the density of the fluid, the volume of the boat that is submerged, and the acceleration due to gravity. The denser the fluid, the more buoyant force it exerts. The more of the boat that is submerged, the greater the buoyant force. And the stronger the gravitational pull, the greater the buoyant force.

3. How can I calculate the magnitude of the buoyant force on a boat in water?

The magnitude of the buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid that is displaced by the object. This can be represented by the equation Fb = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

4. Does the shape and size of the boat affect the magnitude of the buoyant force?

Yes, the shape and size of the boat can affect the magnitude of the buoyant force. A wider and more curved boat will displace more water and therefore experience a greater buoyant force. Additionally, the shape of the boat can also affect how it sits in the water, which can impact the volume of the boat that is submerged and thus the magnitude of the buoyant force.

5. How does the buoyant force on a boat in water compare to the weight of the boat?

According to Archimedes' principle, the buoyant force on a boat in water is equal to the weight of the displaced fluid. This means that the buoyant force can be equal to or greater than the weight of the boat. If the buoyant force is greater, the boat will float; if it is equal, the boat will remain at equilibrium; and if it is less, the boat will sink.

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