A ball of circumference 71.5 cm and mass 640 g is forced to the bottom of a swimming pool and then released. After initially accelerating upward, it rises at a constant velocity. (The density of water is 103 kg/m3.)
(a) Calculate the buoyant force on the ball.
this gives me the answer for drag force
What would the equation for the drag force the ball experiences while it is moving upward at constant velocity be?
To calculate the buoyant force on the ball, we need to use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
The weight of the fluid displaced by the ball can be found by calculating the volume of the water displaced by the ball and then multiplying it by the density of water.
To find the volume of the water displaced, we need to know the radius of the ball. We can use the formula for the circumference of a circle, C = 2πr, where C is the circumference and r is the radius. Rearranging the formula, we get r = C / (2π).
In this case, the circumference of the ball is 71.5 cm. Converting this to meters, we get 0.715 m.
Using the formula for the radius, we can calculate the radius of the ball:
r = 0.715 m / (2π) = 0.1139 m.
The volume of the water displaced by the ball is equal to the volume of a sphere, V = (4/3)πr^3, where V is the volume and r is the radius.
Using the radius we calculated earlier, we can find the volume of the water displaced:
V = (4/3)π(0.1139 m)^3 = 0.00146 m^3.
Now that we have the volume of the water displaced, we can calculate the weight of the fluid using the formula:
Weight of fluid = Volume × Density × g,
where g is the acceleration due to gravity.
The density of water is given as 103 kg/m^3.
Weight of fluid = 0.00146 m^3 × 103 kg/m^3 × 9.8 m/s^2 = 0.0142 kg × m/s^2.
Therefore, the buoyant force on the ball is 0.0142 kg × m/s^2, which is equal to 0.0142 N.
densityball=mass/volume=.640kg/(4/3 PI r^3)
where radius r= .715/2PI
bouyant force: (mass displaced water-massball)g
= volume(densitywater-densityball)g
= volume (density water)g - massball*g
= you finish it. Keep units in SI: kg, m^3