A cube of balsa wood (side length = 0.25 m) is tied with a string to the bottom of a waterfilled

container. The wood is completely immersed. What is the tension in the string?

T=F(buoyancy) –mg =

= ρ(water)Vg - ρ(balsa)Vg=
=Vg[ρ(water) - ρ(balsa)] =
=0.25³•9.8(1000 – 160)=129 N

To find the tension in the string, we can use the concept of buoyancy and consider the forces acting on the cube.

1. The weight of the cube: The weight of the cube is given by the formula W = mg, where m is the mass of the cube and g is the acceleration due to gravity (approximately 9.8 m/s^2). The mass can be calculated using the formula m = ρV, where ρ is the density of wood and V is the volume of the cube. The density of balsa wood is typically around 160 kg/m^3, and the volume of the cube is (side length)^3.

m = ρV
m = 160 kg/m^3 * (0.25 m)^3

2. The buoyant force: The buoyant force is equal to the weight of the water displaced by the cube. Since the cube is completely immersed, the buoyant force is equal to the weight of the water with a volume equal to the volume of the cube. The weight of this water can be calculated using the formula W = mg, where m is the mass of the water and g is the acceleration due to gravity. The density of water is approximately 1000 kg/m^3.

m = ρV
m = 1000 kg/m^3 * (0.25 m)^3

3. Tension in the string: The tension in the string is equal to the sum of the weight of the cube and the buoyant force acting upward.

Tension = Weight of the cube + Buoyant force
Tension = mg + mg
Tension = 2mg

Now, substitute the values of m and g to find the tension in the string.

m = 160 kg/m^3 * (0.25 m)^3
m ≈ 2 kg

g ≈ 9.8 m/s^2

Tension = 2 * 2 kg * 9.8 m/s^2
Tension ≈ 39.2 N

Therefore, the tension in the string is approximately 39.2 Newtons.

To find the tension in the string, we first need to understand the forces acting on the cube.

When an object is immersed in a fluid (in this case, water), it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object.

1. Find the weight of the water displaced:
The volume of the cube can be calculated using the formula V = s^3 (where s is the side length of the cube). In this case, the volume V = (0.25 m)^3 = 0.015625 m^3.
The density of water is approximately 1000 kg/m^3.
The weight of the water displaced can be calculated using the formula W = V x ρ x g (where ρ is the density of water and g is the acceleration due to gravity which is approximately 9.8 m/s^2). So, W = 0.015625 m^3 x 1000 kg/m^3 x 9.8 m/s^2 = 153.125 N.

2. Determine the tension in the string:
The tension in the string will be equal to the weight of the cube plus the weight of the water displaced. Since the cube is completely immersed, its weight is irrelevant, and we only need to consider the weight of the water displaced.
Therefore, the tension in the string will be 153.125 N.

In conclusion, the tension in the string tied to the bottom of the water-filled container is 153.125 N.