Homework Chapter 3- Moments 9. a. In the abstraction of a wing system (below), t

Question

Homework Chapter 3- Moments 9. a. In the abstraction of a wing system (below), the two engines have the same weight, and the wing's center of mass (4.5 Mg) is 1/3 of the distance out from the wing root at point A. Find the total moment exerted at point A Value 8 kN Tip Tank Weight (empty) Ws)3kN Variable Engine weight (Wi and W) b. Using your data from part a, if the wing root (at Pt A) can safely handle a moment of 800 kN-m, how many kilograms of fuel can the wing tank safely hold? Or is the wing already unsafe as drawn? 10 m 10 m Tip Tank Engines 3

Explanation / Answer

(A) Here, as we know the moment of force(M) at any point is Force(F) * perpendicular distance (d) from that point.

M=F*d

Now as per question there are two engines and one empty tank attached to the wing plus the center of mass of wing is also given

We have to find the moment at point A because of all forces. We have all perpendicular distances from forces to point A

The total moment at Point "A" (M(t) = Moment by Weight o engine (W1)+Moment by weight engine (W2)+ Moment by Weight of Tip tank(W3) + Moment by the center of mass of wing(Let say W4)

M(t)= (8kN*10m)+(8kN*(10+7)m)+(3kN*(10+7+10)m)+0.0045kN*(1/3*27)m

M(t)= 80+136+81+0.0405

M(t)= 297kN.m

(B)

Now in this part, it is given that safe moment at point A ranges to 800kN.m so how many kgs of oil we can put in tip tank so that it falls in the safe zone. Our result is in the safe zone when the tank is empty.

Here it is given that tank weights 3kN i.e 3000N=m*g

So, m=3000/9.8= 306 kg (empty tank weight)

Now let's assume we put X kg oil in the tank

Now the total mass of the tank is (X+306)kg

And weight of tank is (X+306)*9.8 = (9.8X+2998)N

writing the equation of total moment in N.m

M(t)= W1*10+W2*17+(9.8X+2998)*27+W4*9

M(t) must be equal to 800,000N.m for the safer zone

800,000N.m= 80,000+136,000+80,968+265X+40.5

800,000= 297008+265X

X= 1895Kg

Hence, total 1895kg oil we can put in the empty tank to be on the safe side

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