Finding Mass of Wooden Block Without Masing It

[Riogho]

Homework Statement

Okay, my chemistry teacher has given each of us an object, my object is a wooden block. We are required to find the mass of this object, WITHOUT massing the object. He has given us no procedure as we must go on simply our knowledge. Or yours :D

Homework Equations

Possibly F=ma

The Attempt at a Solution

The only solution I can come up with, is to drop the wood block from a certain height and and measure how long it takes to fall to the ground, find the acceleration, and use the graviational constant as the force. Unfortunately, unless I drop this from a great height, and have awesome reflexes, getting any accuracy will be difficult with my wristwatch. I was wondering if anyone else had any ideas.

 

[kplooksafterme]

How about putting the object in a liquid of known density (i.e., water)? From this you can measure the amount of the object that's submerged, or if it's all submerged, how far below the surface the object floats, and consequently the mass of the object.

 

[chickendude]

What ARE you allowed to measure?

You can weigh the object on a scale (not a balance). Technically, that is not massing the object since you are measuring weight (the force of gravity) rather than mass. Weight also depends on gravity. A scale wouldn't work the same on the moon, but a triple-beam-balance would.

It may not be what your teacher had in mind, but it is a valid solution to the exact problem your teacher gave

 

[nicksauce]

Dropping the block from a certain height is a poor solution, since the time it takes to reach the ground is INDEPENDENT of mass (unless you count for air resistance, and know the aerodynamic properties of wood and how they relate to mass)

 

[kplooksafterme]

What ARE you allowed to measure?

You can weigh the object on a scale (not a balance). Technically, that is not massing the object since you are measuring weight (the force of gravity) rather than mass. Weight also depends on gravity. A scale wouldn't work the same on the moon, but a triple-beam-balance would.

It may not be what your teacher had in mind, but it is a valid solution to the exact problem your teacher gave

Using a scale with predetermined masses on one side is the same as using a balance...

 

[Riogho]

We can't mass the object :P

We have to use something else to find it. I don't know the equations for density to find mass though :P

 

[kplooksafterme]

Density = mass/volume... Have you done buoyant forces yet?

 

[Riogho]

Nope :P

How would I go about checking how far it is submerged and how will that tell me what the wood blocks density is?

Because I'll need an exact density to find the mass, volume will not be hard though.

 

[kplooksafterme]

There's also the option of attaching the block to a spring and measuring how far from the equilibrium position the block stretches it...

To use the water method you'll have to either a)measure how much of the block is underwater (just measure how high up on the block the water level reaches) or b) if the block is completely submerged measure how far from the surface the bottom of the object is.

When the object is at rest, either fully or partially submerged, we know that the net-force acting on the object is zero. The only 2 vertical forces acting on the object is the buoyant force of the water and gravity; therefore, if we know the magnitude of the buoyant force, we know the weight of the object.
For an object completely submerged, use Archimedes' principle that the buoyant force acting on an object at a specific depth is a force of magnitude equal to the weight of the water that has been displaced by the object; that is
Buoyant Force = (mass of water displaced) x g = (volume of water displaced) x (density of water) x g

Once you've calculated the buoyant force acting on the object, the weight, and therefore mass, are easily found.

 

[Riogho]

But my idea wouldn't work?

I always thought you could find the graviational mass = intertial mass, and wala- you got mass

 

[kplooksafterme]

What was your idea? Measuring the object's speed? in free-fall won't tell you anything about the mass of the object.

 

[Riogho]

Why not?

 

[kplooksafterme]

If you do use the water method, don't forget to include the atm pressure in the room and, if the object is submerged, the water pressure pushing down on the object from the top (which is found using the same method as finding the buoyant force).

 

[kplooksafterme]

Because acceleration due to gravity is independent of mass.

 

[Riogho]

But it has to do with inertia doesn't it?

 

[chickendude]

Why don't you simply weigh the object?

Weighing is not the same as massing. For example: use a spring scale. You are measuring the force of gravity by seeing how far it stretches the spring.and, dropping it wouldn't work because the acceleration of gravity is 9.8 m/s^2 regardless of the mass, so it wouldn't tell you anything about the mass.

 

[Inda House]

I guess the teacher has told you the answer already – but here goes anyway

Float your wooden object in a container full to the brim with water. Weigh the water which overflows. Bingo