1) Suppose you have two solid objects that have the same weight, one made of iro
ID: 1476711 • Letter: 1
Question
1) Suppose you have two solid objects that have the same weight, one made of iron with a large density and one made of aluminum with a smaller density. a) Which has the larger size? b) Which will weigh more when submerged in water? Explain
2) Suppose you have two solid objects that have the same weight, one made of wood that floats in water and one made of iron that sinks in water. a) Which has the larger size? b) Suppose you put them both in water. Will the buoyant force on the wood be (a) less than, (b) equal to, or (c) greater than its weight? c) Suppose you put them both in water. Will the buoyant force on the iron be (a) less than, (b) equal to, or (c) greater than its weight? d) Which will have a greater buoyant force when place in water, the wood or the iron?
3) While vacationing at the beach you find an old coin that looks like it is made of gold. Of course, you don’t believe that the coin is really authentic, but you pick it up anyway and take it home. It is hard to determine the density of the coin because you cannot easily calculate its volume. So you decide to use a method of determining the density without actually measuring the volume, similar to what Archimedes may have done. On a scale, you weigh the coin and find that it has a weight of 1.75 ounces (0.487 N). You then completely submerge the coin in water and weigh it again. While submerged in water it weighs 1.66 ounces (0.461 N). The density of water is w = 1000 kg/m3 . a) Draw a free body diagram of the situation when weighing the coin in air and write Newton’s 2nd law for this situation. You read the weight of the coin by observing the force with which the scale pushes up on the coin, call it the normal force, N. b) Draw a free body diagram of the situation when weighing the coin in water and write Newton’s 2nd law for this situation. You read the weight of the coin by observing the force with which the scale pushes up on the coin when the coin is in the water, call this normal force, N´. Remember there is a buoyant force from the water on the coin. c) From the equations in (a) and (b), find a numerical value for the buoyant force on the coin when weighing it in water. d) Using the definition of the buoyant force, find an equation for the volume of the coin in terms of the buoyant force, the density of water, and the acceleration of gravity. e) Write an equation for the density of the coin in terms of its weight in air, its volume and the acceleration of gravity. f) The two equations in (d) and (e) give two ways of writing the volume of the coin. Set them equal to each other to find a numerical value for the density of the coin. g) The density of gold is 1.9×104 kg/m3 . Should you get excited? Could this coin be gold?
Explanation / Answer
a ) weight is same so denser material will be smaller in size so aluminium is larger
b) when submerged in water wt = wt of body - buoyant force
buoyant force = wt of liquid displaced
as aluminium displaces larger volume of water it weighs less
2) wooden object will be larger in size
in floating condition one cant say which has highest buoyant force
but if both are completely inside water wooden object has more buoyant force than that of iron object
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