Initial Acceleration of Wood in Water

In summary, the problem involves a piece of balsa wood released under water and the task is to find its initial acceleration. The equation used is Fnet=Fbuoy-mg, where Fbuoy is the buoyant force, m is the mass, g is the acceleration due to gravity, and ρ is the density. The solution involves replacing the mass on both sides of the equation with its equivalent in terms of density and volume. The answer is positive because the balsa wood is less dense than water and can only rise, resulting in an upward acceleration. It is recommended to use a consistent sign convention and not to take shortcuts when solving equations.
  • #1
sona1177
173
1

Homework Statement


For the following problem:

A piece of balsa wood with density .50 g/cm^3 is released under water. What is its initial acceleration?

I have gotten this far:

Fnet=Fbuoy-mg
-ma=p(water)gV(displaced)- p(wood)g(Vdisplaced)
=(p(water)-p(wood))gV=-ma

where p="rho"

But in this equation I have three unknowns: mass of wood, Volume displaced, and the acceleration

How do I get around this? I've tried using equations involving Specific Gravity but that doesn't help, it leads be down an unproductive road of manipulating equations that don't have solutions because there are too many unknowns.

Homework Equations


The Attempt at a Solution

 
Physics news on Phys.org
  • #2
You replaced the mass on the right hand side with its equivalent in terms of density and volume. Do the same with the mass on the left hand side.
 
  • #3
Thank you! At first I had a negative sign in front of the m, which gave a negative acceleration of -9.8 m/s^2. But the answer is +9.8 m/s^2. Is this because the balsa wood is less dense than the water, so it can only rise, thereby giving + acceleration?
 
  • #4
sona1177 said:
Thank you! At first I had a negative sign in front of the m, which gave a negative acceleration of -9.8 m/s^2. But the answer is +9.8 m/s^2. Is this because the balsa wood is less dense than the water, so it can only rise, thereby giving + acceleration?
That's right. The net force is upward, thus the acceleration is upward. (You shouldn't have put a negative sign in front of the ma. Newton's law says ΣF = ma, not ΣF = -ma.)
 
  • #5
Doc Al said:
That's right. (You shouldn't have put a negative sign in front of the ma. Newton's law says ΣF = ma, not ΣF = -ma.)

But when I know the acceleration is negative, I usually just put the negative sign in there. Then all I have to do is work in terms of magnitudes.

For example if a block of metal was released in the water with a density larger than water, then I'd place the negative sign in front of acceleration and set the equation as

-ma=Fbuoy-mg

This way I can work in terms of magnitudes since signs are taken care of.

It's alright to put the negative sign if I know the object will sink right?
 
  • #6
Personally, I would not do that. Use a consistent sign convention (up = +) and let the equation do the work.

(It's ok to take shortcuts--as long as you know what you're doing. But you certainly don't want to show such an equation in work that's being marked.)
 
  • #7
Doc Al said:
Personally, I would not do that. Use a consistent sign convention (up = +) and let the equation do the work.

(It's ok to take shortcuts--as long as you know what you're doing. But you certainly don't want to show such an equation in work that's being marked.)

Thank you for the advice! :)
 

1. What is the initial acceleration of wood in water?

The initial acceleration of wood in water refers to the rate at which a wooden object starts to move when placed in water. It is influenced by factors such as the density and shape of the wood, as well as the properties of the water.

2. How does the initial acceleration of wood in water compare to other materials?

Wood typically has a lower initial acceleration in water compared to materials like metal or plastic. This is because wood is less dense than these materials and experiences more resistance from the water.

3. Can the initial acceleration of wood in water be changed?

Yes, the initial acceleration of wood in water can be changed by altering the shape or density of the wood, or by changing the properties of the water. For example, adding weight to the wood can increase its initial acceleration, while increasing the temperature of the water can decrease it.

4. Why is the initial acceleration of wood in water important to study?

The initial acceleration of wood in water is important to study because it can affect the performance and stability of wooden structures such as boats or docks. Understanding this phenomenon can help engineers and designers make more informed decisions when using wood in water-based applications.

5. How do scientists measure the initial acceleration of wood in water?

Scientists measure the initial acceleration of wood in water by conducting experiments using different types of wood and varying conditions, such as the shape of the wood and the properties of the water. They also use mathematical equations and models to analyze the data and determine the initial acceleration.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
5K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
758
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
993
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
8
Views
2K
  • Introductory Physics Homework Help
Replies
16
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
7K
Back
Top