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**1. In this experiment, which we did in lab, we measured the diameter and length of 4 metal cylinders of different densities.**These cylinders were hung on a string and the force in Newtons was measured. Then the cylinder was submerged in water and the force was once again taken. These values were used to calculate the buoyant force. We were then supposed to graph the Buoyant Force vs the Volume. We entered these into the Graphical Analysis program and found the best fit line, the slope of which should have been ρg, or the density of water times g. This is where we encountered the problem. Our slope was way off.

**2. Homework Equations :**

**Volume of a cylinder:**V = L∏r^2 (length*pi*radius squared)

**Weight of cylinder in air:**F[itex]_{A}[/itex] = mg

**Weight in water:**F[itex]_{W}[/itex] = mg - F[itex]_{B}[/itex]

**Buoyant Force:**F[itex]_{B}[/itex] = F[itex]_{A}[/itex] - F[itex]_{W}[/itex]

**Diameters for the cylinders:**

1.) 1.909 * 10[itex]^{-2}[/itex] meters

2.) 1.902 * 10[itex]^{-2}[/itex] meters

3.) 1.909 * 10[itex]^{-2}[/itex] meters

4.) 1.904 * 10[itex]^{-2}[/itex] meters

**Lengths of the cylinders:**

1.) 2.538 * 10[itex]^{-2}[/itex] meters

2.) 3.184 * 10[itex]^{-2}[/itex] meters

3.) 7.633 * 10[itex]^{-2}[/itex] meters

4.) 3.356 * 10[itex]^{-2}[/itex] meters

**The volumes as I calculate them to be:**

1.) 7.264 * 10[itex]^{-6}[/itex] meters cubed

2.) 9.047 * 10[itex]^{-6}[/itex] meters cubed

3.) 2.185 * 10[itex]^{-5}[/itex] meters cubed

4.) 9.555 * 10[itex]^{-6}[/itex] meters cubed

**Weight in air:**

1.) 0.6251 N

2.) 0.6280 N

3.) 0.5869 N

4.) 0.2492 N

**Weight in water:**

1.) 0.5571 N

2.) 0.5368 N

3.) 0.3769 N

4.) 0.1584 N

**The buoyant forces are therefore:**

1.) 0.0680 N

2.) 0.0912 N

3.) 0.2100 N

4.) 0.0908 N

When I plot F[itex]_{B}[/itex] vs Volume and find the best fit line, the slope is 7.56. Cylinder 3 seems to be the outlier. However, even if I take it out of the graph, the slope is 85.8. From what I gather, it should be somewhere near 998. I'm not sure why it isn't. The forces and volumes are, as far as I can tell, correct. I even looked up the density of the different metals in order to make sure that the weight out of water was close to what it should be. Cylinder 1 is copper, #2 is zinc, and #4 is aluminum. I'm not sure what #3 was, as it wasn't marked. Hope all of this is clear. I'm not sure what went wrong unless the equipment wasn't actually measuring in Newtons or it was measuring kiloNewtons or something weird like that. Help is much appreciated. Thanks in advance! :-)

Oh yes. I did make sure to divide the diameters by 2 in order to get the radii before calculating the volume, so those (I think) should be correct.