This is the challenge question from the sample learning objects done during the tutorial.

1. Physics 101 Learning Object:
Buoyancy Explanation Question 2
Beaker 1 contains a wooden ball (which would normally float to the top) attached to a
massless string and Beaker 2 contains a metal ball (which would normally sink to the bottom)
that is suspended from the roof with a massless string. Both beakers are filled with water to
the same level, and put on a weighing scale.
Question 1: Compare the two beakers and determine which is heavier. Explain.
Question 2: What happens when you cut the string in beaker 1? Why?.
Question 3: What happens when you cut the string in beaker 2? Why?.
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Ceiling
1 2

2. Physics 101 Learning Object:
Buoyancy Explanation Question 2
Question: Compare the two beakers and determine which is heavier. Explain.
Answer: Beaker 2 (right) is heavier than Beaker 1 (left). The free body diagram on the beaker
is below (arrow lengths not to scale)
Observations:
- Both beakers have the same amount of water in them
- Both beakers are in an equilibrium situation - all the forces balance out in each case
- The diameter of the metal and wooden ball is the same
- The metal ball in beaker 2 weighs more than the wooden ball, and has a higher density (the
string is taut) but it’s not sinking because the ball is suspended from the ceiling. If the string
is cut, the wooden ball will sink down.
- The wooden ball in beaker 1 would normally float on the surface of the water because it has
a lower density than water but in this case, it’s held submerged by the string. If the string is
cut, the wooden ball will float up.
- The volume of water displaced in beaker 1 and 2 due to the wooden and metal balls
(respectively) is the same and consequently, the weight of this water is the same as well
Explanation (one of many): Think about the concept of ‘effective densities’. Both beakers
are identical and have the same amount of water in them. The only thing that’s different is a
certain percentage of the beaker contents have a different density. In the case of Beaker 1,
the wooden ball has a lower density than water (due to its tendency to float) and in the case
of Beaker 2, the metal ball has a higher density than water*.Ultimately, this results in the fact
that Beaker 1 has a LOWER effective density than Beaker 2. From the density = Mass /
Volume formula, we can see that if one object has a lower Density but the same Volume, then
the Mass must be lower.
*Intrepid learners will note that because of the string holding up the metal ball (i.e. buoyancy
force = apparent weight), the situation can be simplified as if the ball has the same effective
density as the water. However, this effective density is still HIGHER than the wooden ball, so
the subsequent logic still follows.
Ceiling
1 2
FB
FgT Fg
FBT