Question

Объем камня 100 дм3, на него действует сила тяжести 2,5 кН. Какую силу нужно приложить, чтобы удержать камень в воде?

Answer 1

Fa=Vт*ρж*g
Fa=0,1м³*1000кг/м³*9,8Н/кг=1000Н=1кН
F=Fт-Fa
F=2,5кН-1кН=1,5кН

Answer 2

Calculation of the Force Required to Hold the Stone in Water

To calculate the force required to hold the stone in water, we need to consider the buoyant force acting on the stone. The buoyant force is equal to the weight of the water displaced by the stone.

The weight of the stone can be calculated using the formula:

Weight = mass × acceleration due to gravity

The volume of the stone is given as 100 dm^3, which is equivalent to 100 liters or 100 kg (since 1 liter of water weighs 1 kg).

The weight of the stone can be calculated as follows:

Weight = volume × density × acceleration due to gravity

Since the stone is submerged in water, its density is equal to the density of water, which is approximately 1000 kg/m^3.

Now, let's calculate the weight of the stone:

Weight = 100 kg × 9.8 m/s^2

According to the given information, the force of gravity acting on the stone is 2.5 kN (kilonewtons).

To calculate the force required to hold the stone in water, we need to subtract the buoyant force from the force of gravity.

The buoyant force can be calculated using the formula:

Buoyant force = weight of the water displaced

The weight of the water displaced is equal to the weight of the stone, which is 100 kg × 9.8 m/s^2.

Now, let's calculate the buoyant force:

Buoyant force = 100 kg × 9.8 m/s^2

To find the force required to hold the stone in water, we subtract the buoyant force from the force of gravity:

Force required = Force of gravity - Buoyant force

Force required = 2.5 kN - (100 kg × 9.8 m/s^2)

To calculate the final answer, we need to convert the weight of the stone from newtons to kilonewtons:

Force required = 2.5 kN - (100 kg × 9.8 m/s^2) = 2.5 kN - 980 N = 2.5 kN - 0.98 kN = 1.52 kN

Therefore, the force required to hold the stone in water is approximately 1.52 kN.