A bowling ball has a weight of 72 N and an apparent weight of 54 N when complete

Question

A bowling ball has a weight of 72 N and an apparent weight of 54 N when completely submerged in water. What is the average density of the bowling ball? 2500 kg/m^3 3000 kg/m^3 3500 kg/m^3 4000 kg/m^3 4500 kg/m^3 Find the density of the liquid 500 kg/m^3 1000 kg/m^3 1500 kg/m^3 2000 kg/m^3 2500 kg/m^3 An ice cube floats in a cup of water. When the ice cube has melted, the water level in the cup: (neglect changes in the density of water due to temperature) rises remains the same goes down more info is needed to determine A coin is dropped into a well filled with water with zero viscosity (no friction). The coin accelerates downward at 5 m/s^2. What is the density of the coin? 500 kg/m^3 1000 kg/m^3 1500 kg/m^3 2000 kg/m^3 2500 kg/m^3 Two 10 N blocks are completely submerged in water and a scale measures the apparent weight of block A to be 6 N, while the apparent weight of block B is measured to be 5 N. Which block has the greater average density? block A block B they have the same average density more info is needed to determine numbers 6-7 An ideal fluid moves through a cylindrical tube of varying diameter (cross-section shown). The fluid completely fills the tube - there are no pockets of air. Which point has a greater fluid speed? point A point B they have the same fluid speeding more info is needed to determine

Explanation / Answer

1)

fource of buoyancy (F) = (1000)(V)(g) = 72-54 = 18 ;

weight (W) = (d)(V)(g) = 72;

F/W = 18/72 = 1000/d;

=> d = 4000

2)

pressure (p) = dgh = 100000;

d = 100000/(10)(5);

=> d = 2000

3)

n the first state, we have an ice cube of mass m floating in the water. If it is floating (in equilibrium), it will have to displace enough water to support its weight. How much is that? It is just Volume = m/d , where m is the mass of the ice cube, and d is the density of water.

In the second state, where the ice has melted, it turns into water of volume.... Volume = m/d! exactly the same volume as it displaced before. So the added volume is the same, so the level of the water will not change.

As a matter of fact, as long as objects are floating (i.e. they don't rest on the bottom) they displace enough water to support their mass. Since by turning from solid to liquid, the mass of water does not change (well, maybe it does, due to mass-energy equivalence, but that's _really_ negligible) it will keep displacing the same amount of water.

However, note that this may not apply to everything. If you had solid alcohol floating in water, when it melts, the level would drop, because water and alcohol mix at the molecular level; i.e. water filling spaces among alcohol molecules.

4)

resultant accelerating force (R) = weight (W) - force of buoyancy (F)

R = (d)(V)(g) - (1000)(V)(g)

ma = (d)(V)(g) - (1000)(V)(g)

(d)(V)(5) = (d)(V)(g) - (1000)(V)(g)

=> 5d = 10000 [ g = 10m/sec2 ]

=> d = 2000

5)

fource of buoyancy (F) = (1000)(V)(g) = actual weight (W) - apparent weight (A)

for block 1: F = 10 - 6 =4N

for block 2: F = 10 - 5 =5N

As force of buayoncy for block two is more => volume of block two is more => density of block 2 is less

So density of block 1 is more

6)

A1v1 = A2v2

=> As Area is more at point A => speed at point A is less => speed at point B is more

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