Donald Duck and his nephews manage to sink Uncle Scrooge's yacht (m = 4843 kg), which is made of steel (ρ = 7850 kg/m3). In typical comic-book fashion, they decide to raise the yacht (which is now on the bottom of a lake) by filling it with ping-pong balls. A ping-pong ball has a mass of 2.70 g and a volume of 3.35·10-5 m3.
How many balls are required to float the ship?
The amount of mass that each ball will lift is (in grams)
Pwater*V - Mball
= 1.00 g/cm^3)*3.35*10^1 cm^3 - 2.70
= 30.8 g
The number of pingpong balls needed is 4843*10^3g/30.8 = 157,200
The density of steel does not matter. The answer depends upon the total mass that must be lifted.
To find out how many ping-pong balls are required to float the ship, we need to determine the volume of the ship and the total buoyancy force provided by the ping-pong balls.
First, let's calculate the volume of the ship. We know that the density of the ship is 7850 kg/m^3, and we can use the formula:
Density = Mass / Volume
Rearranging the formula, we get:
Volume = Mass / Density
Substituting the given values, we have:
Volume = 4843 kg / 7850 kg/m^3
Volume = 0.617 m^3
Now, let's calculate the buoyancy force provided by the ping-pong balls. The buoyant force is equal to the weight of the fluid displaced by the object, which in this case is the ship. This force needs to be equal to or greater than the weight of the ship for it to float. Since we want to fully float the ship, we need the buoyant force to be greater than the weight of the ship.
The weight of the ship can be calculated using the formula:
Weight = Mass x Gravity
Where the mass is given as 4843 kg and the gravity is 9.8 m/s^2 (assuming we are on Earth). Substituting these values, we have:
Weight = 4843 kg x 9.8 m/s^2
Weight = 47451.4 N (Newtons)
Now, let's calculate the buoyancy force using the formula:
Buoyancy Force = Weight of Fluid Displaced
Each ping-pong ball has a volume of 3.35 x 10^-5 m^3. To find out how many balls are required, we divide the volume of the ship by the volume of one ping-pong ball:
Number of Balls = Volume of Ship / Volume of One Ball
Substituting the values, we have:
Number of Balls = 0.617 m^3 / (3.35 x 10^-5 m^3)
Number of Balls ≈ 18432 balls
Therefore, approximately 18,432 ping-pong balls are required to float the ship.