Suppose there is a small pond near your home. A measuringstick is mounted at the

Question

Suppose there is a small pond near your home. A measuringstick is mounted at the end of a pier in order to measure theheight of the water. Suppose the height of the water is 100 cm. Youare carrying a large boulder as you step into a small boat tied tothe pier. As you step into the boat the water’s height risesto 105 cm. Without making waves you paddle out to the middle of thepond. While floating there you decide to slowly drop the boulderinto the water. Initially there are some ripples on the surface ofthe water, but after a few minutes the water is calm. What is theheight of the water now? (a) Unchanged. (b) greater than 105 cm,(c) less than 105 cm but greater than 100 cm, or (d) less than 100cm. Explain
Suppose there is a small pond near your home. A measuringstick is mounted at the end of a pier in order to measure theheight of the water. Suppose the height of the water is 100 cm. Youare carrying a large boulder as you step into a small boat tied tothe pier. As you step into the boat the water’s height risesto 105 cm. Without making waves you paddle out to the middle of thepond. While floating there you decide to slowly drop the boulderinto the water. Initially there are some ripples on the surface ofthe water, but after a few minutes the water is calm. What is theheight of the water now? (a) Unchanged. (b) greater than 105 cm,(c) less than 105 cm but greater than 100 cm, or (d) less than 100cm. Explain

Explanation / Answer

The only difference at the end is whether the boulder is inthe boat or in the water. While in the boat, the boat willdisplace an amount of water equal to the weight of the boulder. Theboat can do this because it is large and can displace a largeamount of water. . When the boulder is dropped into the water, it will displacean amount of water equal to the VOLUME of the boulder. This is amuch smaller displacement. . Therefore... greatest displacement of water occurs when theboulder and you are in the boat. .          greatestdisplacement = 105 cm height . Less displacement of water occurs when the boulder is droppedinto the water. However, at least some water is displaced in thissituation. So... .       Final height of water is lessthan 105 cm but greater than 100 cm. The answer is (c)

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