An aircraft with an initial mass of 1950 kg has cargo of 450 kg added at a distance of 1.75 m from its…

Question

An aircraft with an initial mass of 1950 kg has cargo of 450 kg added at a distance of 1.75 m from its original center of gravity. Calculate the shift in the center of gravity in cm.

ScanSolve AI Tutor · Accepted Answer

To calculate the shift in the center of gravity (CG) when mass is added, we use the formula:

\Delta CG = \frac{M_{added} \times d}{M_{initial} + M_{added}}

where:
$M_{added}$ is the mass added.
$d$ is the distance of the added mass from the original CG.
$M_{initial}$ is the initial mass of the aircraft.

Identify the given values.
Initial mass of aircraft ( $M_{initial}$ ) = 1950 kg
Mass added ( $M_{added}$ ) = 450 kg
Distance of added mass from the original CG ( $d$ ) = 1.75 m
Calculate the total mass after adding the cargo.
$M_{total} = M_{initial} + M_{added}$ $M_{total} = 1950 \text{ kg} + 450 \text{ kg} = 2400 \text{ kg}$
Calculate the shift in the center of gravity.
$\Delta CG = \frac{M_{added} \times d}{M_{total}}$ $\Delta CG = \frac{450 \text{ kg} \times 1.75 \text{ m}}{2400 \text{ kg}}$ $\Delta CG = \frac{787.5}{2400} \text{ m}$ $\Delta CG = 0.328125 \text{ m}$
Convert the shift in CG from meters to centimeters.
$\Delta CG = 0.328125 \text{ m} \times 100 \frac{\text{cm}}{\text{m}}$ $\Delta CG = 32.8125 \text{ cm}$
Round the result to the nearest whole number and select the closest option.
The calculated shift is approximately 33 cm.

Comparing this to the given options:
A) 34 cm
B) 30 cm
C) 33 cm
D) 40 cm

The closest option is C.

The loaded CG will move by:
$\boxed{\text{C) 33 cm}}$

An aircraft with an initial mass of 1950 kg has cargo of 450 kg added at a distance of 1.75 m from its original center of gravity. Calculate the shift in the center of gravity in cm.

Step-by-step solution

Identify the given values.

Calculate the total mass after adding the cargo.

Calculate the shift in the center of gravity.

Convert the shift in CG from meters to centimeters.

Round the result to the nearest whole number and select the closest option.

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