Chapter 15: Homework Problems 15-7

5.3 Below is a wind turbine with a single blade. There advantages and disadvantages tousing a single blade, but initially, we just want to estimate some of the forces. On agiven day, we will assume that the thrust force on the blade (Fd is approximately 40 N.For an airfoil, this would be similar to the drag force. The lift force (F2) is then whatcauses the blade to rotate. In this case, it is approximately 250N. If d[ = 20 m, d2 =60 m, and d3 = 4.5 m and the forces act in the x - y plane, what is the resultant forceon the blade due to the wind? Sketch the vector in the x - y plane and determine themagnitude and the angle it makes with the x axis.

z

F,d1

y

x

~=-I

Chapter 15: Homework Problems 15-9

5.5 Revisiting the gusset plate problem. Assume that 01 = 50°, O2 = 40°, 03 = 55°, and04 = 35°. The forces are F1 = lOkip, F2 = 20kip, F3 = 70kip, F4 = 35kip, Fs =35kip. Determine the resultant force acting on the gusset plate. Calculate its x and ycomponents, its magnitude, and the angle it makes with the x axis.

J(I

3S""

FJ--x

{O

~

~--

fi~

15 --~!= -'1 -

::

15-10 Chapter 15: Homework Problems

5.6 The construction of the Eiffel tower was completed in 1889 and it weighs approximately10,100 tons.

Consider lifting steel girders from the ground up to the construction point as shownbelow. If the girder weighs 10,000 N, generating the force, F in the figure below (appliedat the point B) and the position vector from A to B is, / -) <:2 r-tf::. =- 5"~lbl.:>

~

rAB = (-lOm)i + (10m)] + (50m)k, (15.1)

C; -- -0, /"1 z..~:::: ../- o. ;q2.S7"-- ~ o.96Z 3t: ,c;what is the scalar c&'li'ponent of the force in the direction of AB?

z

y

Chapter 15: Homework Problems 15-11

The position vector from A to C is r AC = 80m). Calculate the position vector from Bto C.

(-

15-12 Chapter 15: Homework Problems

5.7 As mentioned previously, this tower crane is doing something dangerous. You mayassume that a = 16m, b = 52m, c = 7m, and d = 4m. If the tension in the cable is 7.5kN, determine its x, y, and z components. What is the component of the force in thedirection CA?

ilo ~

---a---I

x c ----y

..•...,e.CA -

( D -OJ~ rl- G- 1(;-0);-

Co'::: - l'(r"- + s:z k:) ~

o. 0716

-z<9. <J 1382. k-

7 , I...( I I '.':lz) h-!1J

15-14 Chapter 15: Homework Problems

5.9 The force, F. is directed from the origin to the point (a, b, c) where a = 3.5ft., b = 12ft.,and c = 4.2ft .. If the magnitude of the force is 708 Ibs., write the vector in the form,FIt. Then find the scalar component of that force in the direction of the position vector,(-2ft., -2ft., 2ft.). Finally, find the vector component of the force in the same direction.

z

~c; ~ -+ 'IZ--) -+ 'f.z..~}\~

O.V;S'-\;: ..j.. 0.'1(1 +o.3/~~

x

F

- I /--- /a----JLL

y

-p.() _ _3so..l.<-j lb

P

(F.~)l{f~