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15 Cards in this Set
- Front
- Back
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F_b
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buoyant force
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F_b formula
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F_b = ρ g V
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Consider the following statement:
The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true? 1 for every object submerged partially or completely in a fluid 2 only for an object that floats 3 only for an object that sinks 4 for no object submerged in a fluid |
1 for every object submerged partially or completely in a fluid
F_b = ρ g V, and ρ = m / V, and W = mg subbing in for rho F_b = (m / V) g V, the V's cancel, leaving F_b = mg = W |
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Consider the following statement:
The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object. Under what circumstances is this statement true? 1 for an object that is partially submerged in a fluid 2 only for an object that floats 3 for an object completely submerged in a fluid 4 for no object partially or completely submerged in a fluid |
3 for an object completely submerged in a fluid
If F_b = weight of fluid that fills the same total volume as the object, then the object must be completely submerged to displace a like volume of fluid |
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Consider the following statement:
The magnitude of the buoyant force equals the weight of the object. Under what circumstances is this statement true? 1 for every object submerged partially or completely in a fluid 2 for an object that floats 3 only for an object that sinks 4 for no object submerged in a fluid |
2 for an object that floats
If F_b = W, the object is at equilibrium in the liquid, neither sinking nor rising, i.e. floating Floating = not sinking It could be partly or completely submerged, but a completely submerged object could be either sinking or floating |
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Consider the following statement:
The magnitude of the buoyant force is less than the weight of the object. Under what circumstances is this statement true? 1 for every object submerged partially or completely in a fluid 2 for an object that floats 3 for an object that sinks 4 for no object submerged in a fluid |
3 for an object that sinks
If F_b < object weight, then object must be sinking because the downward force of weight is more than the upward buoyant force |
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An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a denser liquid. What would you observe?
1 The object would sink all the way to the bottom. 2 The object would float submerged more deeply than in the first container. 3 The object would float submerged less deeply than in the first container. 4 More than one of these outcomes is possible. |
3 The object would float submerged less deeply than in the first container
F_b = ρ g V, or since g & V aren't changing F_b / ρ = g V If the second liquid is denser, its ρ is larger ∴ F_b / ρ is smaller g doesn't change, so for F_b / ρ to be smaller, V must also be smaller, meaning the object floats higher in the second liquid |
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An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a less dense liquid. What would you observe?
1 The object would sink all the way to the bottom. 2 The object would float submerged more deeply than in the first container. 3 The object would float submerged less deeply than in the first container. 4 More than one of these outcomes is possible. |
4 More than one of these outcomes is possible
Given F_b / ρ = g V If the second liquid is less dense, F_b / ρ is bigger, and so since g doesn't change V must be bigger, so either it could sink completely or just submerge more deeply It's impossible to know which of these is true because the relationship of the densities of the 2nd fluid & object aren't known. |
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Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true?
1 Object T has a greater density than object B. 2 Object B has a greater density than object T. 3 Both objects have the same density. |
2 Object B has a greater density than object T
Both B & T are floating in equilibrium in the same fluid B is fully submerged while T is only partially submerged B & T have the same volume, though T displaces less volume than B Given F_b = ρ g V since submerged V_b > submerged V_t buoyant force of b > buoyant force of t Also, F_b = W, where W is the weight of the liquid displaced by the object (the object's volume) Given that buoyant force b > buoyant force t W_b > W_t Given D = W / V (where V is the volume of the object), D_b > D_t because W_d > W_t |
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A Ping-Pong ball is held submerged in a bucket of water by a string attached to the bucket's bottom.
Salt is now added to the water in the bucket, increasing the density of the liquid. What happens to the tension in the string ? Increase, decrease, or stay the same? |
Increases
The ball is less dense than either water or salt water Given F_b = W, add'l downward force (the string) is required to hold the ball submerged Since F_b = ρ g V, and ρ_salt > ρ_water, then F_b_salt > F_b_water Since F_b got bigger, the force needed to counter act it to hold the ball submerged needs to increase |
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A Ping-Pong ball is held submerged in a bucket of water by a string attached to the bucket's bottom.
What happens to the tension in the string if the Ping-Pong ball is replaced by a smaller spherical object of equal weight? increase, decrease, or stay the same? |
Decreases
D = W / V ∴ D_2 > D_ball because it's the same weight packed into a smaller space Since F_b = ρ g V, and V_2 < V_1 F_b_2 < F_b_1 since there's less buoyant force, the tension on the string decreases because it doesn't need to generate as much force to counteract F_b |
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A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline.
What is the buoyant force acting on the block? a 2W b W c 12W d The buoyant force cannot be determined. |
b W
The block is floating at equilbrium ∴ F_net = 0 F_net = F_b - F_w (net force = buoyant force - force of weight) Since F_net = 0, F_b = W |
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A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline.
The density of water is 1.00 g/cm3. What is the density of the block? a 2.00 g/cm³ b between 1.00 and 2.00 g/cm³ c 1.00 g/cm³ d between 0.50 and 1.00 g/cm³ e 0.50 g/cm³ f The density cannot be determined. |
e 0.50 g/cm³
F_b = W of displaced fluid F_b = ρ g V, so ρ_water g V/2 = ρ_block g V (V of displaced water 1/2 of V of block, cancel the g's, cancel the V's) ρ_water /2 = ρ_block |
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A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline.
Masses are stacked on top of the block until the top of the block is level with the waterline. This requires 20 g of mass. What is the mass of the wooden block? a 40 g b 20 g c 10 g |
b 20 g
Originally F_ba = W Given that entire V of block is now submerged, V displaced is now 2V So if F_ba = ρ g V and V doubles, then F_bb doubles F_bb = ρ g 2V → F_ba / 2 = ρ g V Given that buoyant force doubled, weight also doubled F_bb = 2W = 2mg F_bb = 2mg & F_bb = (m+20g)g, set equivalencies equal to each other 2mg = (m+20g)g, divide by g 2m = m+20g, isolate for m 2m - m = 20g 1m = 20g |
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A rectangular wooden block of weight W floats with exactly one-half of its volume below the waterline.
The wooden block is removed from the water bath and placed in an unknown liquid. In this liquid, only one-third of the wooden block is submerged. Is the unknown liquid more or less dense than water? What is the density of the unknown liquid? |
More dense, 1.5 g/cm³
If V is the total volume of the block F_bwater = ρ_w g V/2 and F_bunknown = ρ_u g V/3 and F_b = W = mg = ρ g V, and mg hasn't changed, so ρ_w g V/2 = ρ_u g V/3, cancel the g's & V's ρ_w /2 = ρ_u /3, mult by LCD & reduce fractions 3ρ_w = 2ρ_u ρ_u = 3/2 ρ_w = 1.5 ρ_w → unknown liquid is 1.5 times as dense as water To solve for density of unknown, sub in known value of water ρ_u = 1.5 * 1.0 g/cm³ = 1.5 g/cm³ |
