Bowling balls are roughly the same size but come in a variety of weights. Given that the official radius a bowling ball should have is roughly 0.111 m, calculate the weight of the heaviest bowling ball that will float in a fluid of density 1.100×103 kg/m3.
I used m = ρV = (1000 kg/m³) x [4/3 π (0.111)³m³] = 5.7287 Kg
I then multiplied by g to get the weight in N, which gave me 56.199 N
This was incorrect. Can anyone tell me why?
V = 5.7287 * 10*-3 meters^3
mass of fluid of that volume = 1.1 *10^3 * 5.7287*10^-3
= 6.3016 kg
the mass of the ball must be the mass of the fluid displaced by its volume to
be neutrally buoyant. You used pure water. This stuff is 10% heavier.
Oh, I got this one! The reason your calculation is incorrect is because you forgot to take into account the buoyant force acting on the bowling ball. When an object is submerged in a fluid, it experiences an upward force called buoyant force, which depends on the density of the fluid and the volume of the object.
To calculate the weight of the heaviest bowling ball that will float, you need to find the weight of the ball equal to the buoyant force. The buoyant force is given by the equation:
Buoyant force = Fluid density * Volume of the ball * Acceleration due to gravity
So, in this case, the weight of the heaviest bowling ball that will float is equal to the buoyant force, not just the weight of the ball itself.
The incorrect calculation you made was multiplying the mass (5.7287 kg) by the acceleration due to gravity (9.8 m/s^2) to find the weight in Newtons.
To correctly calculate the weight of an object, you simply multiply the mass by the acceleration due to gravity. In this case, the mass of the heaviest bowling ball is correct as 5.7287 kg. However, the acceleration due to gravity is approximately 9.8 N/kg, not 9.8 m/s^2.
So, the correct calculation for the weight of the heaviest bowling ball would be:
Weight = mass x acceleration due to gravity
Weight = 5.7287 kg x 9.8 N/kg
Weight = 56.17 N (rounded to two decimal places)
Therefore, the weight of the heaviest bowling ball that will float in a fluid of density 1.100x10^3 kg/m^3 is approximately 56.17 N.
The mistake in your calculation lies in the assumption that the density of the bowling ball is equal to the density of water (1000 kg/m³). However, in this problem, we are dealing with a fluid of density 1.100 x 10³ kg/m³, which is different from the density of water.
To find the weight of the heaviest bowling ball that will float in the given fluid, we can use Archimedes' principle, which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
We know the density of the fluid (1.100 x 10³ kg/m³) and the radius of the bowling ball (0.111 m). We also need to find the volume of the bowling ball.
The volume of a sphere can be calculated using the formula:
V = (4/3)πr³
Substituting the given values:
V = (4/3)π(0.111)³ = 0.007481 m³
Now, we can calculate the weight of the heaviest bowling ball that will float:
Weight = Buoyant force = Weight of the fluid displaced by the bowling ball
Buoyant force = Density of the fluid x Volume of the fluid displaced x gravitational acceleration
= (1.100 x 10³ kg/m³) x (0.007481 m³) x 9.8 m/s²
Calculating this, we get:
Weight = 81.181 N
Therefore, the weight of the heaviest bowling ball that will float in the given fluid is approximately 81.181 N, not 56.199 N.