A spherical ball filled with air has a radius 4 inches weighs 0.27 kg. It is placed in a pool. what percentage (in volume) of the ball is under the water?
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Since the ball is floating, we see that:
F(buoyant) - F(weight of ball) = 0 ==> F(weight of ball) = F(buoyant).
Since F(buoyant) = pVg, we see that the volume of the ball under the water is:
F(weight of ball) = pVg
==> V = F(weight of ball)/(pg)
= m/p, since F(weight of ball) = mg, where m is the mass of the ball
= (0.27 kg)/(1000 kg/m^3)
≈ 2.7 x 10^-4 m^3.
Since 1 inch is about 2.54 cm = 0.0254 m, we see that:
1 in^3 = (0.0254 m)^3.
The volume of the ball in cubic inches is:
V = (4/3)πr^3, by the volume of a sphere
= (4/3)π(4 in)^3
= 256π/3 in^3.
In cubic meters, this is (256π/3)(0.0254)^3 ≈ 4.4 x 10^-3 m^3.
Therefore, the percentage of the ball under the water is:
(2.7 x 10^-4 m^3)/(4.4 x 10^-3 m^3) * 100 ≈ 6.1%.
I hope this helps!
F(buoyant) - F(weight of ball) = 0 ==> F(weight of ball) = F(buoyant).
Since F(buoyant) = pVg, we see that the volume of the ball under the water is:
F(weight of ball) = pVg
==> V = F(weight of ball)/(pg)
= m/p, since F(weight of ball) = mg, where m is the mass of the ball
= (0.27 kg)/(1000 kg/m^3)
≈ 2.7 x 10^-4 m^3.
Since 1 inch is about 2.54 cm = 0.0254 m, we see that:
1 in^3 = (0.0254 m)^3.
The volume of the ball in cubic inches is:
V = (4/3)πr^3, by the volume of a sphere
= (4/3)π(4 in)^3
= 256π/3 in^3.
In cubic meters, this is (256π/3)(0.0254)^3 ≈ 4.4 x 10^-3 m^3.
Therefore, the percentage of the ball under the water is:
(2.7 x 10^-4 m^3)/(4.4 x 10^-3 m^3) * 100 ≈ 6.1%.
I hope this helps!
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What percentage of the ball is under water?
Fraction under water = Volume of displaced water ÷ Volume of ball
A spherical ball filled with air has a radius 4 inches weighs 0.27 kg. It is placed in a pool. what percentage (in volume) of the ball is under the water?
Volume of Sphere = 4/3 * π * r^3
r = 4 in * 2.54 cm/in = 10.16 cm = 0.1016 m
Volume of ball = 4/3 * π * 0.1016^3 = 4.393 * 10^-3 m^3
The weight of the ball is causing the ball to accelerate downward.
The buoyant force is causing the ball to accelerate upward.
Weight of ball = 0.27 * 9.8 = 2.646 N
The buoyant force is the weight of a volume of water which is displaced by the ball.
If the ball is floating, the buoyant force= weight of ball
BF = 2.646 N
Weight = mass * g
Density = mass / volume
mass = Density * Volume
Weight = Density * Volume * g
Density of water = 1000 kg/m^3
Weight of displaced water = 1000 * V * 9.8 = 9800 * V
9800 * V = 2.646
V = 2.646 ÷ 9800
Volume of displaced water = 2.7 * 10^-4 Liters
Volume of ball = 4.393 * 10^-3 m^3
Fraction under = 2.7 * 10^-4 ÷ 4.393 * 10^-3 = 0.0615
% under = 0.0615 * 100 = 6.15%
OR
Fraction under = Density object/Density water
Density object = mass/ volume = 0.27 ÷ 4.393 * 10^-3 = 61.5 kg/m^3
Fraction under = 61.5/1000
% under = 61.5/1000 * 100 = 6.15%
Fraction under water = Volume of displaced water ÷ Volume of ball
A spherical ball filled with air has a radius 4 inches weighs 0.27 kg. It is placed in a pool. what percentage (in volume) of the ball is under the water?
Volume of Sphere = 4/3 * π * r^3
r = 4 in * 2.54 cm/in = 10.16 cm = 0.1016 m
Volume of ball = 4/3 * π * 0.1016^3 = 4.393 * 10^-3 m^3
The weight of the ball is causing the ball to accelerate downward.
The buoyant force is causing the ball to accelerate upward.
Weight of ball = 0.27 * 9.8 = 2.646 N
The buoyant force is the weight of a volume of water which is displaced by the ball.
If the ball is floating, the buoyant force= weight of ball
BF = 2.646 N
Weight = mass * g
Density = mass / volume
mass = Density * Volume
Weight = Density * Volume * g
Density of water = 1000 kg/m^3
Weight of displaced water = 1000 * V * 9.8 = 9800 * V
9800 * V = 2.646
V = 2.646 ÷ 9800
Volume of displaced water = 2.7 * 10^-4 Liters
Volume of ball = 4.393 * 10^-3 m^3
Fraction under = 2.7 * 10^-4 ÷ 4.393 * 10^-3 = 0.0615
% under = 0.0615 * 100 = 6.15%
OR
Fraction under = Density object/Density water
Density object = mass/ volume = 0.27 ÷ 4.393 * 10^-3 = 61.5 kg/m^3
Fraction under = 61.5/1000
% under = 61.5/1000 * 100 = 6.15%