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Student
A.
Kf'{
APPHYSICS B
Date
------
Newton's Laws & Inclined Planes
1.
T
3.0m
1
A box is being pushed at constant speed up an inclined plane to a vertical height of 3.0 m above
the ground, as shown in the figure above. The person _exertsa force parallel to the plane. The
mass m of the box is 50.0 kg, and the coefficient ofk:inetic friction f.1Ic between the box and the
plane is 0.30.
- .
(a) On the dot below that represents the box, draw and label the forces (not components) acting
on the box.
)I~
'v
I'
_
F'N
<,
-_ "
'-
'-
b) Calculate the normal force of the plane on the box. If you need to draw anything other than
what you have shown in part (a) to assist in your solution, use the space below. Do NOT add
anything to the figure in part (a).
(100"- ~\:c:h.l(.e 0"\ -hlf)
(F='N"='
f", - ~.,
4(,1 ~
Fe,,-=: F~'1--=- r~cosw<>= 5olc.g(q.~I~)coS2Qo
=-0
(c) Calculate the component of the force of gravity acting on the box that is arallel to the plane.
(s;J -::F'~ Sl\l'\ 20
C
-=- ""'~
S l'", 20
a
Q.
(d) Calculate the friction force between the plane and the box.
l3]-=jAKFN -=
O.'3~(4btN)Z[\~8~
(e) Calculate the force applied by the perso.n on the box.
.....
FC,ff -
F.f ic.
-
F~)( - 0
~_r=
~-
Fc
'fk- + ~)(
t
(f) Calculate the work done by the person pushing the box, assuming the box is raised to the
vertical height of3.0 m.
0 ~)
-- rZ b 84
G
\1\1 -==-
Fc0..,,, •
X
-=
"30
b N.
(~.
S,~200
;)
~30bNJ
- ~
J'J
_
2.
A 4700 kg truck carrying a 900 kg crate is traveling at 25 mls to the right along a straight, level
highway, as shown above. The truck driver then applies the brakes, and as it slows down, the
truck travels 55 m in the next 3.0 s. The crate does not slide on the back of the truck.
(a) Calculate the magnitude of the acceleration of the truck, assuming it is constant.
d
= VLt
-t-
J.. ai ~
+
5S"",::: '2..~~(3.QS)
~
L
2'
a.
(3.0$
)'
(b) On the diagram below, draw and labe~lall the fo~es acting on the crate during braking.
r;.fJ
\
i. Calculate the minimum coefficient offriftfun between the crate and truck that prevents
the crate from sliding.
h:::
Fl'let
H. FN -=- \N\ (A
(c)
~+S.-=f'FN
fS
I~
)As
ii. Indicate whether this friction is static or kinetic.
V
Static
i l>::: vi ~
G:d;: 3.:: ~
Kinetic
lCJ ~
q.gl
~~.
t.,~)
Now assume the bed of the truck is frictionless, but there is a spring of spring constant 9200 N m
attaching the crate to the truck, as shown below. The truck is initially at rest.
(d) If the truck and crate have the same acceleration, calculate the extension of the spring as the
(
)
truck accelerates from rest to 25 mls in 10 s.
L
t f
v
~~ _ qOOI{! 2.~ ~
..
rY\~ 'T -.s:
,..-::. - ----dU-._---V f - vI.
2.S - 0 IIW\
"'"
\L
q
a.:::
t
=-
\0
s;.. =-
2. ~ S'i-
~
a_::::
k
X
2.QO N·M
(e) At some later time, the tru.ck is moving at a constant speed of 25 mls and the crate is in
~
equilibrium.
~
Indicate whether the extension of the spring is greater than, less than, or the same as in part (d)
when thetruck was accelerating.
Greater
V Less
The same
:
O. 24 ~
I
C~\I\s+a",-t Sp-eeJ
"",~a",> -z...eor-() ,Q.cc.e
+ "-ev--efa .. e f\l\e. t = 0 -:=- r5 = 1'-X' ) S' 0
Explain your reasoning.
vJ\..\G~
\S
\"4e
t e)) f-i'ttt ~
-e..,d-e~~I.·()'"
0 , 1..~
~
.
O}
+~<.
-h, a 11\
~rfA
)
-=- 0
)(
SfY-~'\
)
..
15°
---------------------
An empty sled of25 kg slides down a muddy hill with a speed of2.4 mls. The slope of the hill is
inclined at an angle of 15° with the horizontal as shown in the figure above.
(a) Calculate the time it takes the sled to go 21 m down the slope.
-= 21M
V
2,y ....,/~ _
(b) On the dot below that represents the sled, draw the free-body diagram for the sled as it slides
down the slope.
'
-= {rg.
t::..!i
7,
S]
-
__-_~--~~<--~~--_
f~
----
~
(c) Calculate the frictional force on the sled as it slides down the slope.
Ff\<.. - F~)c
-::=.0
Ffk=
F~x-=- "M.~~lhISo=
:-:\
F.f'(,~ 63.5" ~
.
,
SO
'2..5\~(q.~(~,J~(·~1
(d) Calculate the coefficient of friction between the sled and the muddy surface of the slope.
r-
fv..
h
~
t'1C.. ( ~~
0)
"1..S'"
'=-r"r,\'1
==
c.oS/5
/1C.":.2t;1'
(q.g/!:!)CO$I~
(e) The sled reaches the bottom of the slope and continues on the horizontal ground. Assu~ the S'"
same coefficient of friction.
(i) In te.rms of velocity and acceleration; ~escrib~ the motion of the sled as it travels on
the horizontal ground.
~CC€'~"'o.."h.Q'"
l~
Ccvdt4",f
("'f>~~+~\'€)
""\t\~\e
",-e.IOCl~)'
de,crefAreJ
(ii) On the axis below, sketch a graph of the velocity versus time for the sled. Include
both the sled's travel down the slope and across the horizontal ground. Clearly indicate
with the symbol 1/ the time at which the sled leaves the slope.
r.flt.-=
tJ
-
r;, '" 0 2-71
t..!'L - . ~
t-~e
v
.
4.
///////////
Student B
60 kg
Student A
70 kg
/
A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as
shown below. One end of the rope is held by student A of mass 70 kg, who is at rest on the floor.
The opposite end of the rope is held by student B of mass 60 kg, who is suspended at rest above
the floor.
(a) On the dots below that represent the students, draw the free-body diagrams showing the
1FT
forces on student A and student B.
y
B
1(\
"
yFN
F:
F. ::: cO\1( q.~1 ~ )
~
-:: ~]
F~~
r~He.
F~~-:::FT
+ FrJ - F~A::::0
~~T
bott(UI~)
;: 5 g9 N
FN
-
F~A
t:L
'
(b) Calculate the magnitude of the force that the floor exerts on stUdent A.
-=
f",-:
Student B now climbs up the rope at constant acceleration
of 0.25 m/s2 with respe
(d) As student B is accelerating,
f\!letA:=
F-
(e) With what minimum acceleration
off the floor?·
C () Q
b~7N -
.' .
F",-
~~~S
F'l~ ~
~ove>.
4fvJClYc(
(fN-:=CJ8tJJ
to the floor.
81> rJ
FT -:::: b '87 rJ
M~
c;t
~e""
B
b
O~
F"" /'
.roO r t'-'a. t
Q.,.~ F"T-
~-
F", -=
( sofT
Wle.
S0
-
(,971\1-
N
)5+3 Nk
a "ffe
r::::::-,
~
0J
~
- F~ ::: 0
F~$ _
N
;J~'
must student B climb up the rope to lift student A upward
stl.4.de\'\t A
F-r -
T
~
.
' 'FT:::
~8+
~A ~
is student A pulled upward off the flo . ustify your antwer.
~
V.J~~(,~
F-
-
c:
-M(A
r~G13.
~-
f"T-t-fN- FqA ~ bQ~.N ., 6f7N r f",-=
1\
F; 1\
Pille t 8 :::-Yv\p,t?
(c) Calculate the tension in the rope while student B is accelerating.
'
=0
F.e-tA
~
L::::'O
A
T
>.
®
®
)
SWQ::1I.b3"::
(JO~
-
0
5"2.
5.
Blocks 1 and 2 of masses m I and m2, respectively, are connected by light strings as shown above.
These blocks are further connected to a block of mass M by another light string that passes over
a pulley of negligible mass and friction. Blocks 1 and 2 move with a constant velocity v down
the inclined plane, which makes an angle
with the horizontal. The kinetic frictional force on
block 1 is f and on block 2 is 2f
J
e
1
(a) On the figure above, draw and label all the forces on block mi.
.
/
X ~//
,
-r
f~\
~'"
0
//
;,"
~",~"
~"'~
f
//"'~
~~~:
~\~
J
.
Express your answers to each of the following in terms of'm., m2, g,
(b) Determine the coefficient of kinetic friction between the inclined
":.r(w.I,!cose)
{:::rFI\I\
e andf
lane and block 1.
r= _t_-t
-)
M\
~S~
(c) Determine the value of suspended mass M that allows
oc sand
velocity down the inclined plane.
Fo
eV\1Lre
+'-'.e
,,"-'e\'.e.ko\{i?
VV\I ~
t ~.e.~
o..d. c! ~
Sl\-\e -
f + ""'"l
\""
r +0
(d) The string between blocks 1 and 2
is on the inclined plane.
f
I I
O~
S,"he -
~
IS
~l'"e
F~e+-
-z_ e ~ 0 ;
-=' \"(\ C\.
2.( - M <a :::. 0
now cut" Determine the accelerati4:0bIOCk
11\
"
Dl OCIL
UJ
0'"
''t ·
I
2 to move with constant
~'1s.+ellV\ TI>
~
l'lo\tfV'V\.C.
(
a :::
0
C-..
QJ
I
S llo1U II=(O.-st
'I,-,V'"(
1 while it
,
M :::(~I+~l.) Jth& -
"'1.£
2L