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.

a) What is the buoyant force on one ping-pong ball in water?
b)b) How many balls are required to float the ship?

bouyant force one ball= density water*volumeball

YOu decide if the duck's are in fresh water , or sea water.

i found it 0.0335 N with (bouyant force one ball= density water*volumeball) but it 's not truee :(

0.0335*9.8 (g) with this its true! thank you bobpursleyy !!!!

b) How many balls are required to float the ship? How can i find this. can you help me please bobpursley ??

To solve this problem, we will apply the principles of buoyancy. Buoyancy is the upward force exerted on an object submerged in a fluid, which opposes the gravitational force pulling the object downwards. The buoyant force is equal to the weight of the fluid displaced by the object.

a) To calculate the buoyant force on one ping-pong ball in water, we need to find the weight of the water displaced by the ball. This weight can be found using the equation:

Weight = density * volume * gravitational acceleration

The density of water is approximately 1000 kg/m^3, and the volume of one ping-pong ball is given as 3.35 x 10^-5 m^3. The gravitational acceleration (g) is approximately 9.8 m/s^2.

Weight = (1000 kg/m^3) * (3.35 x 10^-5 m^3) * (9.8 m/s^2)
Weight = 0.3283 N

Therefore, the buoyant force on one ping-pong ball in water is approximately 0.3283 N.

b) To determine the number of ping-pong balls required to float the yacht, we need to calculate the total buoyant force needed to counteract the weight of the yacht.

The buoyant force is given by the equation:

Buoyant Force = Weight of the yacht

The weight of the yacht can be calculated using the equation:

Weight of the yacht = mass of the yacht * gravitational acceleration

Given that the mass of the yacht is 4843 kg, and gravitational acceleration is 9.8 m/s^2, we can calculate the weight of the yacht:

Weight of the yacht = (4843 kg) * (9.8 m/s^2)
Weight of the yacht = 47451.4 N

Therefore, the total buoyant force needed to counteract the weight of the yacht is 47451.4 N.

To determine the number of ping-pong balls required, we need to divide the total buoyant force needed by the buoyant force exerted by one ping-pong ball:

Number of balls = Total buoyant force / Buoyant force per ball

Number of balls = 47451.4 N / 0.3283 N
Number of balls ≈ 144,605

Therefore, approximately 144,605 ping-pong balls are required to float the ship.