15-7
Chapter 15: Homework Problems
5.3 Below is a wind turbine with a single blade. There advantages and disadvantages to
using a single blade, but initially, we just want to estimate some of the forces. On a
given 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 what
causes 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 force
on the blade due to the wind? Sketch the vector in the x - y plane and determine the
magnitude and the angle it makes with the x axis.
z
y
~=I
x
F,
d1
15-9
Chapter 15: Homework Problems
5.5 Revisiting the gusset plate problem. Assume that 01 = 50°, O2 = 40°, 03 = 55°, and
04 = 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 y
components, its magnitude, and the angle it makes with the x axis.
J(
I
3S""
FJ
{O
~
--
~
fi
~
15
--
~
!=
'1
--
::
--x
Chapter 15: Homework Problems
15-10
5.6 The construction of the Eiffel tower was completed in 1889 and it weighs approximately
10,100 tons.
Consider lifting steel girders from the ground up to the construction point as shown
below. If the girder weighs 10,000 N, generating the force, F in the figure below (applied
at the point B) and the position vector from A to B is,
/
-)
<:2
tf::.
~
=-
+ (10m)] + (50m)k,
(15.1)
z..~:::: ../- o. ;q2.S7"-- ~ o.96Z 3 t: ,c;
rAB = (-lOm)i
C; -- -0,
r-
5"~lbl.:>
/"1
what is the scalar c&'li'ponent of the force in the direction of AB?
z
y
15-11
Chapter 15: Homework Problems
The position vector from A to C is r AC = 80m). Calculate the position vector from B
to C.
(-
Chapter 15: Homework Problems
15-12
5.7 As mentioned previously, this tower crane is doing something dangerous. You may
assume that a = 16m, b = 52m, c = 7m, and d = 4m. If the tension in the cable is 7.5
kN, determine its x, y, and z components. What is the component of the force in the
direction CA?
ilo
~
---a---I
c
x
( D
..•...
,e.CA -
o. 0716
-OJ~
Co'::: - l'(r"-
----y
rl-
+
G- 1(;-0);-
s: z k:) ~
<9.
<J 1382.
7,
-z
k-
I...( I I '.':
lz) h-!1J
Chapter 15: Homework Problems
15-14
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
F
-
x
---
~c; ~ -+
O.V;S'-\;:
p.() _ _3so..l. <-j
P
(F.~)l{f~
lb
I
----JLL
'IZ--) -+
..j..
/a/
y
'f.z..~}\~
0.'1(1
+o.3/~~