I have a length of string and I want to know the maximum tension the string can support. I tie one end of the string to the ceiling and the other end to a glass of mass 100 g. The glass is cylindrical, with a cross-sectional radius of 4 cm and a height of 15 cm. I fill the glass with water (density of 1 g/cm3) and discover that the string breaks when the glass is 2/3 full. What is the maximum tension in N the string can support?

Question

I have a length of string and I want to know the maximum tension the string can support. I tie one end of the string to the ceiling and the other end to a glass of mass 100 g. The glass is cylindrical, with a cross-sectional radius of 4 cm and a height of 15 cm. I fill the glass with water (density of 1 g/cm3) and discover that the string breaks when the glass is 2/3 full. What is the maximum tension in N the string can support?

Details and assumptions
The acceleration of gravity is −9.8 m/s2.

Answer 1

the answer is 5.91

Answer 2

Well, apparently I have a different answer. Supposedly the live period is long over so I guess it is safe to discuss. Meanwhile, in the future, refrain from posting brilliant problems.

Step 1: F_g = (m_w + m_g)* g

Step 2: m_w = 𝜌 * V_m

Step 3: For step 2, V_m = π r^2 h

Step 4: Sub everything in

Answer 3

To find the maximum tension the string can support, we need to consider the forces acting on the glass when it is 2/3 full.

First, let's find the mass of the water in the glass:
The glass is cylindrical with a cross-sectional radius of 4 cm and a height of 15 cm. The volume of the glass can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

The radius of the glass is 4 cm, which is 0.04 m.
The height of the glass is 15 cm, which is 0.15 m.

So the volume of the glass is: V = π(0.04)^2(0.15) = 0.03π m^3.

The density of water is given as 1 g/cm^3, which is equivalent to 1000 kg/m^3. So the mass of the water in the glass is:
m = density * volume = 1000 kg/m^3 * 0.03π m^3 = 30π kg.

Next, let's find the mass of the glass itself. The mass is given as 100 g, which is equivalent to 0.1 kg.

The total mass of the glass and water is the sum of the mass of the glass and the mass of the water:
Total mass = mass of glass + mass of water = 0.1 kg + 30π kg.

Now, let's calculate the weight of the glass and water when it is 2/3 full.
The weight can be calculated using the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity.

The acceleration due to gravity is given as −9.8 m/s^2 (negative because it acts downwards).

So the weight of the glass and water is W = (0.1 kg + 30π kg) * (-9.8 m/s^2), in Newtons.

Finally, the maximum tension the string can support is equal to the weight of the glass and water. Thus, the maximum tension is (0.1 kg + 30π kg) * (-9.8 m/s^2) Newtons.