A ship has a total displacement of 6000 tonnes. The following masses are located relative to amidships: 800…

Question

A ship has a total displacement of 6000 tonnes. The following masses are located relative to amidships: 800 tonnes at 60 m aft, 1200 tonnes at 35 m aft, 2000 tonnes at 11 m aft, 1000 tonnes at 15 m fo

ScanSolve AI Tutor · Accepted Answer

To calculate the distance of the Centre of Gravity (CG) from amidships, we use the principle of moments. We'll consider amidships as the reference point (0 m). Distances aft of amidships will be negative, and distances forward of amidships will be positive.

Define the masses and their positions relative to amidships.
- Masses aft of amidships:
  
  $M_1 = 800 \text{ tonnes}$ at $x_1 = -60 \text{ m}$
  
  $M_2 = 1200 \text{ tonnes}$ at $x_2 = -35 \text{ m}$
  
  $M_3 = 2000 \text{ tonnes}$ at $x_3 = -11 \text{ m}$
- Masses forward of amidships:
  
  $M_4 = 1000 \text{ tonnes}$ at $x_4 = 15 \text{ m}$
  
  $M_5 = 1000 \text{ tonnes}$ at $x_5 = 30 \text{ m}$
  
  $M_6 = 500 \text{ tonnes}$ at $x_6 = 50 \text{ m}$
Calculate the total moment about amidships.
The total moment is the sum of (mass $\times$ distance) for all components.
$\text{Total Moment} = (M_1 x_1) + (M_2 x_2) + (M_3 x_3) + (M_4 x_4) + (M_5 x_5) + (M_6 x_6)$ $\text{Total Moment} = (800 \times -60) + (1200 \times -35) + (2000 \times -11) + (1000 \times 15) + (1000 \times 30) + (500 \times 50)$ $\text{Total Moment} = -48000 - 42000 - 22000 + 15000 + 30000 + 25000$ $\text{Total Moment} = -112000 + 70000$ $\text{Total Moment} = -42000 \text{ tonne-meters}$
Identify the total displacement of the ship.
The problem states the ship has a total displacement of $6000 \text{ tonnes}$ .
(Note: The sum of the listed component masses is $800+1200+2000+1000+1000+5

A ship has a total displacement of 6000 tonnes. The following masses are located relative to amidships: 800 tonnes at 60 m aft, 1200 tonnes at 35 m aft, 2000 tonnes at 11 m aft, 1000 tonnes at 15 m fo

Step-by-step solution

Define the masses and their positions relative to amidships.

Calculate the total moment about amidships.

Identify the total displacement of the ship.

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