AE331 (INTRODUCTION TO AEROSPACE STRUCTURES )Home Work set 1

(Due August 28,2015)

Q.1 Find the direction cosines of the vectorVector u=(2,2,1)

Q.2 Find the angle between the vectorsu=(1,1,-1) and v=(2,2,1).

Q.3 Calculate the vector projection of the vectoru=(2,1,0) on the vector v=(-3,4,0)

Q.4 Find the volume of the parallelepipedformed by the vectors:

Q.5 Calculate the volume of the tetrahedronwhose vertices are the points A = (3, 2, 1), B =(1, 2, 4), C = (4, 0, 3) and D = (1, 1, 7).

Q.6 Consider the angle section shown in figure

(a)Verify that the centroid of the angle sectionhas the location shown

(b)Show that the moments of inertia are:

Izz= bh3/36

Iyy= hb3/36

Iyz= -b2h2/72

(c)Show that the principal moments of inertiaare:

I11=98.2 in4

I22=21.4 in4

Home Work Set 1 file:///home/kamle/courses_combined/ae331_revised/numerical_que...

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(d)Find the angle between the principalmoments of inertia axes and the y-axis. Show theprincipal moments of inertia axes through asketch.

Q.7 Assume the airplane of figure 4.25 is landingat 75 mph on a runway and brakes are appliedto the rear wheels equal to 0.4 of the verticalrear wheel reaction. What is the horizontaldeceleration and the stopping distance for theairplane?

Q.8 The flying patrol boat in Fig.4.27 makes awater landing with the resultant bottom waterpressure of 250,000 lbs. as shown in the figure.Assume lift and tail loads as shown. Th epitchingmoment of inertia of the airplane is 10 millionlb.sec2 in. Determine the airplane pitchingacceleration. What is the total load on the crewmember who weighs 200 lbs. and is located in aseat at the rear end of the hull?

Home Work Set 1 file:///home/kamle/courses_combined/ae331_revised/numerical_que...

2 of 2 Monday 17 August 2015 05:22 PM