Question

practice weight and balance quiz: question 28 of 55
an aircraft as loaded weighs 4,954 pounds at a cg of +30.5 inches. the cg range is +32.0 inches to +42.1 inches. find the minimum weight of the ballast necessary to bring the cg within the cg range. the ballast arm is +162 inches.
a 61.98 pounds.
b 30.58 pounds.
c 57.16 pounds.

Explanation:

Step1: Set up the formula

The formula for the new center of gravity (CG) is \(\text{New CG}=\frac{\text{Original Weight}\times\text{Original CG}+\text{Ballast Weight}\times\text{Ballast Arm}}{\text{Original Weight}+\text{Ballast Weight}}\). We want the new CG to be at the lower limit of the range (\(CG = 32.0\) inches). Let \(W\) be the ballast weight.

$$32=\frac{4954\times30.5 + W\times162}{4954 + W}$$

Step2: Cross - multiply

$$32\times(4954 + W)=4954\times30.5+162W$$

$$32\times4954+32W = 4954\times30.5+162W$$

Step3: Expand and simplify

$$158528+32W=151097+162W$$

$$158528 - 151097=162W - 32W$$

$$7431 = 130W$$

Step4: Solve for \(W\)

$$W=\frac{7431}{130}\approx57.16$$

Answer:

C. 57.16 pounds.