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Aiticle l/9
PROBLEMS
I l/l Determinethe anglesmadeby the vectorV = -36i +
-15j
!with the positive r- andy-axes. Write the unit vector n in the directionofv
= 67'4"
Ans' 0'= 157'4o,0t
n: -0.923i + 0.385j
I
L-
Problems 2l
l/8
Supposethat two nondimensidnal quantities are exactly A = 8.67 and .8 = 1.429.Using the rules for significant figures as stated in this chapter, expressthe
four quantities (A + B), (A - B), (Ats), arad(AlB).
l/9
Compute the magnitude F ofthe force which the sun
exerts on the earth. Perform the calculaiion first in
pounds and then convert your rezult to neEtons.
Refer to Table D/2 for necessaryphysical quantities.
AtLs.F : 7.97(702t)lb, -F= 3.55(1022)
N
t/2 Determine the magnitude of the vector sum V :
Vr + V2 and the angle 0, which V makes with the
positive ,-axis. Complete both graphical and algebraic solutions.
Vz = 21 units
V1 = 27 units
Probleml/9
Prcblel'I t/2
l/l
l/lo
For the given vectors Vl and V2 of Prob. 1/2, determine the magnitude of the vector difference V' =
V2 - V1 and the angle d, *'hich V' makes with the
positive r-aris. Complete both graphical and algebraic solutions.
Azs. 7 = 36.1units,0.= L74.8"
The element of volume AVof ihe right circular cone
of altitude ll and base radius r is formed by slicing
the cone at a distaace r from the vert€x. If the slice
is of finite thickness Ar, shlw that its volume Ay is
lfl2lh2l lxz Lx " r,4"12 - | r^.rtrl. {Recall the formula for the volume of a cone.) Explain what hap
pens to the seconda::d third terms when Ar becomes
the infinitesimal dr.
l/4 A force is specifled by the vector I' : 160i + 80j 120k N. Calculate the anglesmade by F with the positive l-, y-, and z-axes.
(
\-
l/5 )What is the mass in both slugs and kilograms of a
_/' 1000-lbbeam?
Ans. rz = 31.1slugs,m = 453W
l/6 From the gravitational law calculate the weight W
(gravitational force vrith respect to the earth) of an
80-kg man in a spacecrafttraveling in a circular orbit
250 km sbove the earth's surface. Express W irr both
nen'tons and pounds.
,
l/7 trleterminethe weight in newtons ofa woman whose
- ,ikeight in poundsis 125.Also, find her massin slugs
and in kilograns. Determine your own weight in
newtons.
Azs. W: 556N, rz = 3.88slugs,m = 56.7kg
PloblemI /10
l/ll
What is the percent error z in replachg the sine of
20' by the value of the angle in radians? Repeat for
the tangent of 20', arrd erplain the qualitative differencein the two error percentages.
Ans.n:2.06Vo,n=4.09%