Transcript The purpose of today`s lab is to investigate Archimedes` Principle
Physics 2015: Archimedes’ Principle Purpose
The purpose of today’s lab is to investigate Archimedes’ Principle and buoyant forces. First, we will determine the density of metal balls of the same substance, but different radii. Then, once this density is known, we will use a metal slug (made of the same metal) to find the buoyant force of 4 different liquids and determine the density of these liquids.
Physics 2015: Archimedes’ Principle Activity 1: Finding the density of the metal spheres • Force sensor • Metal tray (place the metal spheres into the tray) • Glass cylinder filled with water.
Please remember to only fill water into the glass cylinders and not any other type of liquid.
Physics 2015: Archimedes’ Principle • Activity 2: Finding Fluid Densities You will find 4 different plastic containers filled with the following liquids: • • • • Tap Water (get yourself) Salt Water Corn Syrup Vegetable oil • Attach the cylindrical metal mass to the end of the force sensor, and place it into the substances to measure force.
Cylindrical metal mass
Physics 2015: Archimedes’ Principle Notes: 1) In your lab manual we mention using isopropyl alcohol as one of the fluids. We have substituted vegetable oil for the isopropyl alcohol.
2) On page 104 a few equations were not printed correctly. There is a corrected version of that page on the website under Hints/Links in a pdf file. Please print out that pdf file and replace page 104.
Physics 2015: Archimedes’ Principle Archimedes’ Principle An object that is submerged in a liquid will experience an additional upward force (due to the submersion) that is equal to the weight of the amount of liquid that was displaced by the object. This force is called the “buoyant force”.
Translated into simpler language, this means: An extra force acts on an object when it is placed, for example, in water. This makes the object appear lighter than it really is.
Physics 2015: Archimedes’ Principle Example of a buoyant force A metal ball of volume 50cm 3 fully submerged in water will experience a buoyant force of the following magnitude: mass of displaced water density of water
F b
m w g
w V g
(
kg
0 .
001
cm
3 50
cm
3 9 .
8
m s
2 0 .
49
N
) volume of ball
Physics 2015: Archimedes’ Principle Free Body Diagram (3 forces) string
T
F b W
density of water
m w g
w V g
mg
m V g
volume of ball density of metal
Physics 2015: Archimedes’ Principle Using Newton’s Second Law… In this static situation there is no acceleration, therefore
T
w
V g
m
V g
0
F
0
T
V g
(
m
w
) By measuring T and V, and knowing the density of water and the acceleration of gravity, the density of the metal can be calculated.
Physics 2015: Archimedes’ Principle In Activity 1, we will use metal spheres in water:
V
sphere
4 3
r
3
T
4 3
r
3
g
m
w
In Activity 2, we will use a cylindrical metal object in a fluid:
V sphere
r
2
h
T
r
2
h g
m
fluid
Physics 2015: Archimedes’ Principle
There is one more idea you will want to consider before starting Activity 1
• Remember to “Tare” your force sensor in a clever way before any procedure. In this case, first hang the empty basket on the force sensor and into the water. THEN tare the force sensor.
This will negate both the weight of the basket and the buoyant force on the basket in your force measurement!
• Tared this way, when you graph the tension versus r 3 in Excel, you should expect the line to go through the origin. Why do you think this is?
Physics 2015: Archimedes’ Principle In Activity 1 (spheres)
V
4 3
r
3
T
4 3
r
3
g
(
w
m
) Measure T for different size spheres (different radii) and determine the density of the spheres.
measured calculated measured
T
r r
3
T
plot
What is the slope?
Get m from slope.
r
3
Physics 2015: Archimedes’ Principle Careful when doing the Excel Plot of T versus r 3 Plotting T versus r 3 and using m 3 as your unit results in a large number for the trendline slope.
When you display the trendline equation in the trendline label, not all digits of the slope may be displayed. So, your slope k result may be off by a factor of 10 or 100 etc.
Here is how to fix it: Right click on the trendline label (not on the trendline).
Choose “Format Trendline Label” Choose “Number” or Choose “Scientific” with 3 or 4 digits.
Physics 2015: Archimedes’ Principle For Activity 2 Step 1: Hang slug on force sensor Step 2: Tare the force sensor Step 3: Hang slug into Liquid. This way you measure only F buoyant Tare
Physics 2015: Archimedes’ Principle Then get the density of the liquid from the measured buoyant force using the equation:
F b
liquid V slug g
Note: You will need to figure out the volume of the slug somehow!.
Physics 2015: Archimedes’ Principle Activity 3 Determine the density of the fluids again by measuring mass and volume of the fluid:
density
mass volume
m V
This method of determining the density will give you a direct comparison to the density results obtained from the buoyancy measurement.
Note: It will be easiest to measure an empty plastic container first.
Physics 2015: Archimedes’ Principle Final Reminder • • • • DO NOT POUR ANYTHING BUT WATER down the drain (not even the salt water which we reuse)!
DO NOT POUR ANYTHING BUT WATER into the tall glass cylinders!
Clean up anything that spills IMMEDIATELY!
These can damage equipment in the lab!
Use a paper towel or a sponge Put the cardboard covers back on the plastic beakers containing the syrup before you leave.