2.A solid iron cylinder with a diameter of 150mm a height of 1m and a density of
7860 kg/m^3 is suspended in fresh water (density of fresh water is 1000 kg/m^3)
calculate the tension in the supporting cable when two thirds of the volume of the cylinder is submerged
r = (0.5*150)/1000 = 0.075 m
Vc=pi*r^2*h=3.14*0.075^2*1=0.01767 m^3 =
Vol. of the cylinder.
Vs = 2/3 * 0.01767 = 0.01178 m^3 = Vol.
submerged = Vol. of water displaced.
0.01178m^3 * 1000kg/m^3 = 11.78 kg = mass of water displaced.
m*g = 11.78kg * 9.8N/kg = 115.4 N = Wt.
of water displaced = Tension in cable.
NOTE: Density of water = 1000 kg/m^3.
thanks for doing my work for me <3
To calculate the tension in the supporting cable, we first need to find the weight of the submerged portion of the cylinder.
1. Find the volume of the cylinder:
- The radius of the cylinder is half of the diameter, so r = 150mm / 2 = 75mm = 0.075m
- The volume of a cylinder is given by:
V = πr^2h, where π is pi, r is the radius, and h is the height.
V = π(0.075m)^2(1m) = 0.0176715 m^3
2. Find the volume of the submerged portion:
- Two-thirds of the volume of the cylinder is submerged, so the volume of the submerged portion is:
V_submerged = (2/3) * V = (2/3) * 0.0176715 m^3 = 0.011781 m^3
3. Find the weight of the submerged portion:
- The weight can be calculated by multiplying the volume by the density and the acceleration due to gravity (g).
Weight_submerged = Volume_submerged * Density_water * g
Where Density_water is the density of fresh water (1000 kg/m^3) and g is the acceleration due to gravity (9.8 m/s^2).
Weight_submerged = 0.011781 m^3 * 1000 kg/m^3 * 9.8 m/s^2 = 115.14522 N
4. Find the tension in the supporting cable:
- The tension in the cable is equal to the weight of the submerged portion.
Tension = Weight_submerged = 115.14522 N
Therefore, the tension in the supporting cable when two-thirds of the volume of the cylinder is submerged is approximately 115.14522 N.
To calculate the tension in the supporting cable when two-thirds of the volume of the cylinder is submerged, we need to consider the buoyant force and the weight of the cylinder.
Here's how to calculate it:
1. First, calculate the volume of the cylinder:
Volume = π * (r^2) * h
Given that the diameter is 150mm, the radius (r) is half of that, which is 75mm. Converting it to meters, we get r = 0.075m.
The height (h) is given as 1m.
So, Volume = π * (0.075^2) * 1
2. Next, calculate the volume of the submerged portion:
The volume of the submerged portion is two-thirds of the total volume of the cylinder.
Submerged Volume = (2/3) * Volume
3. Then, calculate the weight of the cylinder:
Weight = density * volume * g
The density of the iron cylinder is given as 7860 kg/m^3.
The volume is the total volume of the cylinder, which we calculated in step 1.
The acceleration due to gravity (g) is approximately 9.8 m/s^2.
4. Now, calculate the buoyant force:
Buoyant Force = density of fluid * volume of submerged portion * g
The density of fresh water is given as 1000 kg/m^3.
The volume of the submerged portion is calculated in step 2.
The acceleration due to gravity (g) is approximately 9.8 m/s^2.
5. Finally, calculate the tension in the supporting cable:
The tension in the supporting cable is equal to the weight of the cylinder minus the buoyant force.
Tension = Weight - Buoyant Force
By following these steps, you can calculate the tension in the supporting cable when two-thirds of the volume of the cylinder is submerged.