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SWK 122 2020: Partial Memo Semester Test 1
Note that the partial solutions for all four questions are given for specific
sets of parameters that will not necessarily resemble your sets of parameters.
Question 1
(a)
F
A = (0, 1.7 tan 55◦ , 0) m
Q
b
(b) P = (0.85, 1.214, 0) m and OP = 1.482 m
(c)
Q = (0.85, 1.214, − OP tan 42◦ ) m
42◦
55◦
OQ = 1.994 m
x
B = (1.7, 0, 0) m
b
α = arccos(0.85/1.994)
β = arccos(1.214/1.994)
b
A
P
b
y
z
γ = arccos(−1.334/1.994)
Question 2
(a)
Fmin = (1.4 − 1.1) kN, α = 180◦ + 128◦
Fmax = (1.4 + 1.1) kN, α = 180◦ + 128◦
(b) If α = 334◦, F is orientated as follows.
T = 1.4 kN
ℓ
F
α
F
ℓ
b
P
128◦
334◦
S
Minimum magnitude of F + T is obtained
if F and F + T ≡ S are perpendicular.
90◦
F
26◦
T
Solve to find S = 1.4 sin 26◦ kN
and F = 1.4 cos 26◦ kN.
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Question 3
W = 0.5 kN and point A lies 2.8 m above the xy−plane. If your part (a) is incorrect,
you do not get marks for part (b).
(a)
z
T O = TO (0.2704i − 0.5948j − 0.7570k)
A
T B = TB (0.2704i + 0.5948j − 0.7570k)
b
0.4 m
C
TO = 0.3002 kN
1m
(b)
TB = 0.03002 kN
O
2.2 m
TC = 0.3103 kN
2.2 m
1m
T C = TC (−0.2877i + 0.5179j − 0.8056k)
y
B
x
Question 4
The direction cosine of OA with respect to the x−axis is 0.38 and the direction angle
of OA with respect to the y−axis is 33◦ .
z
O
y
b
ℓ=
2m
x
b
A
F
=
0
−3
0
i+
(a) dx = 0.38, dy = cos 33◦ , dz = −0.3902 and no unit.
(b) A = (0.7600, 1.677, −0.7803) m.
(c) P = −7.017i − 15.49j + 7.205k N.
(d) Opposite sense.
(e) 582.8 N.
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30
0
j+
40
N
k
0