Initial Acceleration of Wood in Water

Click For Summary

Homework Help Overview

The problem involves determining the initial acceleration of a piece of balsa wood with a density of 0.50 g/cm³ when released underwater. The discussion centers around the forces acting on the wood, including buoyancy and gravitational force, and how these relate to its acceleration.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to set up the equation of motion but encounters three unknowns: mass of wood, volume displaced, and acceleration. They express frustration with manipulating equations involving specific gravity without finding a solution.
  • Some participants suggest replacing mass with its equivalent in terms of density and volume to simplify the equation.
  • Questions arise regarding the sign of acceleration, particularly whether it should be positive or negative based on the density comparison between the wood and water.
  • There is a discussion about the consistency of sign conventions in equations, with differing opinions on whether to include negative signs when working with magnitudes.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem and offering guidance on handling signs in equations. There is no explicit consensus on the best approach to take regarding sign conventions, but participants are engaging with the concepts and reasoning behind the physics involved.

Contextual Notes

Participants are navigating the complexities of buoyancy and density, and there is an acknowledgment of the challenges posed by multiple unknowns in the problem setup. The original poster's mention of specific gravity indicates a potential constraint in their approach.

sona1177
Messages
171
Reaction score
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
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.
 
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?
 
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.)
 
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?
 
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.)
 
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! :)
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
6K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
6K
  • · Replies 16 ·
Replies
16
Views
4K
  • · Replies 1 ·
Replies
1
Views
7K
  • · Replies 1 ·
Replies
1
Views
3K