For a new TV series "Stupidity Factor contestants are dropped into the ocean (p 1030 kg/ms) along with a Styrofoam soo kg/ms block that is mm x 3 mm X 20 cm thick. If too many contestants climb aboard the block and it sinks below the water surface, they are declared "stupid" and abandoned at sea. Find the maximum number of 7o kg contestants that the block can hold. (No fractional contestants, please.
Please Help me very hard need help
Your typos make this impossible.
However in general:
Archimedes says:
the force up on the people and block
is equal to the weight , rho *g * volume of water displaced
so
1030 * g * L* w * h = rho of block * g * L * w * h + 70 * g * n
so
n = (1030-rho block)* L * w * H/ (70)
To find the maximum number of 70 kg contestants that the block can hold, we need to determine the buoyant force acting on the block and compare it with the weight of the contestants and the block itself.
The buoyant force (Fb) is equal to the weight of the water displaced by the block. According to Archimedes' principle, the buoyant force is given by the formula:
Fb = ρwater * g * Vblock
Where:
ρwater is the density of water (1030 kg/m^3),
g is the acceleration due to gravity (9.8 m/s^2),
and Vblock is the volume of the block.
First, we need to calculate the volume of the block. The dimensions provided are:
Width (W) = mm = 0.001 m
Height (H) = 3 mm = 0.003 m
Thickness (T) = 20 cm = 0.2 m
Volume (Vblock) = W * H * T = 0.001 m * 0.003 m * 0.2 m
Next, we can calculate the buoyant force:
Fb = 1030 kg/m^3 * 9.8 m/s^2 * Vblock
Now, let's calculate the weight of the contestants and the block. We have:
Weight of contestants and block (Wtotal) = (Number of contestants + 1) * Mass of each contestant + Mass of block
We can then equate the buoyant force (Fb) with the weight of the contestants and the block (Wtotal) and solve for the maximum number of contestants:
Fb = Wtotal
By rearranging the equation, we have:
(1030 kg/m^3 * 9.8 m/s^2 * Vblock) = ((Number of contestants + 1) * 70 kg + soo kg)
Let's plug in the values and solve for the maximum number of contestants:
(1030 kg/m^3 * 9.8 m/s^2 * 0.001 m * 0.003 m * 0.2 m) = ((Number of contestants + 1) * 70 kg + soo kg)
Now, we can simplify and solve the equation for the maximum number of contestants. However, it seems there might be a typo in the values provided for the Styrofoam block's mass (soo kg). If you could provide the correct value, I can help you solve the equation and find the maximum number of contestants the block can hold.