I submitted the below question and received the answer i copied into this question as well. Im unsure if it is correct, so looking for a checkover. i am stuck on the part tan-1 (0.05) = 0.04996 radians. Just unsure where the value for the radians came from. Just need to know how they got that answer and how it is correct before moving on to the next part. If any of the below information is wrong, please feel free to give me a new answer or an entire new explanation. An Inclining experiment done on a ship thats 6500 t, a mass of 30t was moved 6.0 m transvesly causing a 30 cm deflection in a 6m pendulum, calculate the transverse meta centre height. Here is the step-by-step explanation: Given: Displacement of the ship (W) = 6500 tonnes = 6500×1000=6,500,000kg Mass moved transversely (w) = 30 tonnes=30×1000=30,000kg The transverse shift of mass (d) = 6.0 meters Pendulum length (L) = 6.0 meters Pendulum deflection (x) = 30 cm = 0.30 meters Step 1: Formula for Metacentric Height (GM): The metacentric height (GM) can be calculated using the following formula derived from the inclining experiment: GM=W⋅θw⋅d Here: (w)= mass moved transversely (d) = transverse distance moved (W) = total displacement of the ship (θ)= heel angle, which we can approximate using the pendulum deflection. Step 2: Calculate the Heel Angle (θ): The pendulum deflection (x) gives us the heel angle (θ) using the formula: tanθ=Lx Here: x = pendulum deflection (in meters) L = length of the pendulum (in meters) Substitute the values: tanθ=6.00.30=0.05 θ=tan−1(0.5) θ≈0.04996radians Step 3: Calculate the Metacentric Height (GM): We have: GM=W⋅θw⋅d Substitute the values: GM=6500000Kg×0.04996radians30000Kg×6.0m GM≈0.5543m So, the transverse metacentric height (GM) is approximately0.5543 meters Explanation: The metacentric height (GM) is a measure of the ship's initial stability. A larger GM indicates better stability, as it means the ship will return to an upright position more quickly if tilted. In this case, GM = 0.5543 meters means the ship has a moderate transverse metacentric height, which is indicative of stability under transverse tilting forces. This result is important for understanding how the ship will behave when subjected to tilting forces, like waves or shifts in cargo. arrow_forward Solution Final answer: The transverse metacentric height (GM) is approximately0.5543 m

I submitted the below question and received the answer i copied into this question as well. Im unsure if it is correct, so looking for a checkover. i am stuck on the part tan-1 (0.05) = 0.04996 radians. Just unsure where the value for the radians came from. Just need to know how they got that answer and how it is correct before moving on to the next part. If any of the below information is wrong, please feel free to give me a new answer or an entire new explanation. An Inclining experiment done on a ship thats 6500 t, a mass of 30t was moved 6.0 m transvesly causing a 30 cm deflection in a 6m pendulum, calculate the transverse meta centre height. Here is the step-by-step explanation: Given: Displacement of the ship (W) = 6500 tonnes = 6500×1000=6,500,000kg Mass moved transversely (w) = 30 tonnes=30×1000=30,000kg The transverse shift of mass (d) = 6.0 meters Pendulum length (L) = 6.0 meters Pendulum deflection (x) = 30 cm = 0.30 meters Step 1: Formula for Metacentric Height (GM): The metacentric height (GM) can be calculated using the following formula derived from the inclining experiment: GM=W⋅θw⋅d Here: (w)= mass moved transversely (d) = transverse distance moved (W) = total displacement of the ship (θ)= heel angle, which we can approximate using the pendulum deflection. Step 2: Calculate the Heel Angle (θ): The pendulum deflection (x) gives us the heel angle (θ) using the formula: tanθ=Lx Here: x = pendulum deflection (in meters) L = length of the pendulum (in meters) Substitute the values: tanθ=6.00.30=0.05 θ=tan−1(0.5) θ≈0.04996radians Step 3: Calculate the Metacentric Height (GM): We have: GM=W⋅θw⋅d Substitute the values: GM=6500000Kg×0.04996radians30000Kg×6.0m GM≈0.5543m So, the transverse metacentric height (GM) is approximately0.5543 meters Explanation: The metacentric height (GM) is a measure of the ship's initial stability. A larger GM indicates better stability, as it means the ship will return to an upright position more quickly if tilted. In this case, GM = 0.5543 meters means the ship has a moderate transverse metacentric height, which is indicative of stability under transverse tilting forces. This result is important for understanding how the ship will behave when subjected to tilting forces, like waves or shifts in cargo. arrow_forward Solution Final answer: The transverse metacentric height (GM) is approximately0.5543 m

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

An Inclining experiment done on a ship thats 6500 t, a mass of 30t was moved 6.0 m transvesly causing a 30 cm deflection in a 6m pendulum, calculate the transverse meta centre height.

Here is the step-by-step explanation:

Given:

Displacement of the ship (W) = 6500 tonnes = 6500×1000=6,500,000kg
Mass moved transversely (w) = 30 tonnes=30×1000=30,000kg
The transverse shift of mass (d) = 6.0 meters
Pendulum length (L) = 6.0 meters
Pendulum deflection (x) = 30 cm = 0.30 meters

Step 1: Formula for Metacentric Height (GM):

The metacentric height (GM) can be calculated using the following formula derived from the inclining experiment:

GM=W⋅θw⋅d

Here:

(w)= mass moved transversely
(d) = transverse distance moved
(W) = total displacement of the ship
(θ)= heel angle, which we can approximate using the pendulum deflection.

Step 2: Calculate the Heel Angle (θ):

The pendulum deflection (x) gives us the heel angle (θ) using the formula:

tanθ=Lx

Here:

x = pendulum deflection (in meters)
L = length of the pendulum (in meters)

Substitute the values:

tanθ=6.00.30=0.05

θ=tan−1(0.5)

θ≈0.04996radians

Step 3: Calculate the Metacentric Height (GM):

We have:

GM=W⋅θw⋅d

Substitute the values:

GM=6500000Kg×0.04996radians30000Kg×6.0m

GM≈0.5543m

So, the transverse metacentric height (GM) is approximately0.5543 meters

Explanation:

The metacentric height (GM) is a measure of the ship's initial stability. A larger GM indicates better stability, as it means the ship will return to an upright position more quickly if tilted.
In this case, GM = 0.5543 meters means the ship has a moderate transverse metacentric height, which is indicative of stability under transverse tilting forces.

This result is important for understanding how the ship will behave when subjected to tilting forces, like waves or shifts in cargo.

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Solution

Final answer: