Question

5-ро рыбаков оказались на оторвавшейся льдине размером 50 м2 (квадратных). Толщина людины 20 см. Требуется определить промочат ли ноги рыбаки. Масса каждого 80 кг. Протность льда 800 кг/м2(квадратные).

Answer 1

5-ро рыбаков оказались на оторвавшейся льдине размером 50 м2 (квадратных). Толщина людины 20 см. Требуется определить промочат ли ноги рыбаки. Масса каждого 80 кг. Протность льда 800 кг/м2(квадратные).
Дано V=50 м2  h=0,2 м   m1=80 кг   p1=800 кг/м3

1) найдем вес льдины и рыбаков  F =5*m1*g + p1*g*S*h=5*80*10 + 800*10*50*0,2=
=4000  +  80000=84000 Н
2) Найдем силу Архимеда на полностью погруженную льдину
Fa=p2*g*S*h=1000*10*50*0,2=100 000 Н
Fa > F  значит льдина выдержит рыбаков

Answer 2

Analysis and Solution

To determine if the fishermen's feet will get wet, we need to compare the weight of the fishermen with the buoyant force exerted by the ice. If the buoyant force is greater than or equal to the weight of the fishermen, their feet will not get wet. Otherwise, their feet will get wet.

Buoyant Force Calculation

The buoyant force exerted by the ice can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is the water, and the object is the ice.

To calculate the buoyant force, we need to determine the volume of the ice that is submerged in the water. The volume of the ice can be calculated by multiplying the area of the ice by its thickness.

Given: - Area of the ice (A) = 50 m^2 - Thickness of the ice (h) = 20 cm = 0.2 m - Density of the ice (ρ_ice) = 800 kg/m^3

The volume of the ice (V_ice) can be calculated as follows: V_ice = A * h

Now, we can calculate the mass of the ice (m_ice) using the density and volume: m_ice = ρ_ice * V_ice

Weight of the Fishermen

Given: - Number of fishermen = 5 - Mass of each fisherman (m_fisherman) = 80 kg

The total weight of the fishermen (W_fishermen) can be calculated by multiplying the mass of each fisherman by the number of fishermen: W_fishermen = 5 * m_fisherman

Comparison

Now, we can compare the weight of the fishermen with the buoyant force exerted by the ice.

If the buoyant force (F_buoyant) is greater than or equal to the weight of the fishermen (W_fishermen), their feet will not get wet. Otherwise, their feet will get wet.

To calculate the buoyant force, we can use the formula: F_buoyant = ρ_water * g * V_ice

Given: - Density of water (ρ_water) = 1000 kg/m^3 (assumed value) - Acceleration due to gravity (g) = 9.8 m/s^2

Now, we can calculate the buoyant force and compare it with the weight of the fishermen.

Calculation

Let's calculate the values and determine if the fishermen's feet will get wet.

1. Calculate the volume of the ice: V_ice = A * h = 50 m^2 * 0.2 m = 10 m^3

2. Calculate the mass of the ice: m_ice = ρ_ice * V_ice = 800 kg/m^3 * 10 m^3 = 8000 kg

3. Calculate the weight of the fishermen: W_fishermen = 5 * m_fisherman = 5 * 80 kg = 400 kg

4. Calculate the buoyant force: F_buoyant = ρ_water * g * V_ice = 1000 kg/m^3 * 9.8 m/s^2 * 10 m^3 = 98000 N

Conclusion

The buoyant force exerted by the ice is 98000 N, which is greater than the weight of the fishermen (400 kg or 3920 N). Therefore, the fishermen's feet will not get wet because the buoyant force is greater than their weight.

Note: The assumptions made in this calculation include the density of water and the acceleration due to gravity. These values are commonly used in calculations involving buoyancy, but they may vary slightly depending on the specific conditions.