both boxes slide together top box slides and bottom box...
TRANSCRIPT
1) Par t A) Force P is applied at a location very close to the bottom
of the top box and it ’s magnitude star ts from zero and is slowly
increased. Descr ibe all possible cases of impending motion of
the boxes if the man does not slip. The coefficient of fr ict ion at
all contact ing sur faces is known. (9 pts)
Case 1 : __both boxes slide together________________________________________________
Case 2 : __top box slides and bottom box stays in place______________________
Case 3 : __both boxes t ip together about point B________________________________
Case 4 : __top box t ips away from man and bottom box stays in place___
(Case 4 will not happen unless m is very very large and weight is very very small because P is
applied close to bottom of box.)
Case 5 : ____________________________________________________________________________________
Case 6 : _____________________________________________________________________________________
Case 7 : ______________________________________________________________________________________
Case 8 : ______________________________________________________________________________________
Case 9 : ______________________________________________________________________________________
Case 10 : _____________________________________________________________________________________
Par t B) The carpenter pushes the board
hor izontally over the top of the sawhorse.
The board weighs 54 lb and the sawhorse
weighs 15 lb with a center of gravity at G.
Determine if the sawhorse will stay in
posit ion, slip, or t ip if the board is pushed
forward. Ver ify your answer by checking
ALL condit ions of impending motion and
compar ing the hor izontal force exer ted by
the carpenter , Cx. (16 pts)
Note: The carpenter applies both a ver tical and hor izontal force to keep the board in equilibr ium in
the posit ion shown.
i) if the sawhorse stays in posit ion and the board slips: Cx =__24 .3_ lb
ii) if the sawhorse slips: Cx =__19 .08 _ lb
iii) if the sawhorse t ips: Cx =__21 .2 _ lb
∴ the sawhorse will _____SLIP_____________./ 25
10 ft
C
2) A counterclockwise moment M = 1500 lb-in. is applied to the
flywheel. If the coefficient of fr ict ion between the band and the
wheel is 0 .20 , compute the minimum force P necessary to prevent
the wheel from rotat ing. (20 pts)
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3) Par t A) For the angle shape shown to the r ight,
determine the vert ical distance from point A to the
hor izontal centroidal axis. Select the best answer
from the choices below. (8 points)
(a)35 .8 mm
(b)44 .8 mm
(c)47 .2 mm Correct – Full credit
(d)53 .5 mm
(e)77 .2 mm Half credit
(f) 85 .0 mm
(g)115 .0 mm
(h)122 .8 mm Half credit
(i)125 .3 mm
(j)134 .2 mm
(k)152 .8 mm Half credit
Par t B) Determine for the shape to the
r ight. For maximum par t ial credit, show your
calculat ions in the tabular format below. (17
pts)
3
2
282,971.248 mm29.988 mm
9,436.283 mmy
/
Shape iA iy i iy A
Triangle 3,750 mm2 25.00 mm 93,750.000 mm
3
Middle Rectangle
6,000 mm2 37.50 mm 225,000.000 mm
3
Add-on Rectangle
1,100 mm2 47.50 mm 52,250.000 mm
3
Semicircle Cutout
–1,413.717 mm2 62.268 mm –88,028.752 mm
3
9,436.283 mm2 282,971.248 mm
3
Shape iA iy i iy A
Triangle 3,750 mm2 25.00 mm 93,750.000 mm
3
Rectangle 7,500 mm2 37.50 mm 281,250.000 mm
3
Semicircle Cutout
–1,413.717 mm2 62.268 mm –88,028.752 mm
3
Square Cutout
–400 mm2 10.00 mm –4,000.000 mm
3
9,436.283 mm2 282,971.248 mm
3
y
Par t B) (continued solut ion)...
Shape iA iy i iy A
Full Rec-tangle
15,000 mm2 37.50 mm 562,500.000 mm
3
Triangle Cutout
–3,750 mm2 50.00 mm –187,500.000 mm
3
Semicircle Cutout
–1,413.717 mm2 62.268 mm –88,028.752 mm
3
Square Cutout
–400 mm2 10.00 mm –4,000.000 mm
3
9,436.283 mm2 282,971.248 mm
3
Shape iA iy i iy A
Triangle 3,750 mm2 25.00 mm 93,750.000 mm
3
55-mm-tall Rectangle
5,500 mm2 47.50 mm 261,250.000 mm
3
Semicircle Cutout
–1,413.717 mm2 62.268 mm –88,028.752 mm
3
20-mm-tall Rectangle
1,600 mm2 10.00 mm 16,000.000 mm
3
9,436.283 mm2 282,971.248 mm
3
4) Par t A) Circle the most appropr iate answer. Pressure acts __________ to the sur face at a given
point. (4 pts)
(a)parallel
(b) normal
(c) vert ical
(d) hor izontal
Par t B) Draw the fluid pressure distr ibut ion curves on the left side of each of the two submerged
plates shown in bold below. (4 pts)
Par t C) The dam has its center of gravity located at
CG. Determine if the dam will be able to resist
over turning about point A. The mass density of
concrete is ρc = 2 .0 Mg/ m
3 and it ’s cross-sectional
area shown is 0 .75 m2. The width of the concrete
dam, measured into the page, is 3 m. The mass
density of water is ρw = 1 .0 M g/ m
3. The gravitat ional
constant is g = 9 .81 m/ s2. (14 pts)
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