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Unformatted text preview: Print your LAST name here , 7 Problem 1. (20 points) On a wall clock, the distances
from the center of the dial to the tips of the minute and hour
hands are 30cm and 21cm, respectively. Use a coordinate sys—
tem in which the x—axis points toward three o’clock and the
y—axis points toward twelve o’clock. When the time is 10:00: (a) (4 points) Find the m— and y—components of the vector dis—
placement M between the dial center and the tip of the
minute hand. szo M7 3 BOLM (b) (4 points) Find the x— and y—components of the vector displacement I? between the
dial center and the tip of the hour hand. Mk:  {210%} also” 2 43.24%
Hy: (2%) $35: (0,9 m. (c) (5 points) In the space below, show graphical calculations of the vectors fl = I? + M andéz2M—H. .7
H
[‘7‘ k ‘7 \;I\ l
‘\)J *7 ‘7 M /‘ A l
\A; “*M (—a a ~—7 (E (T a
‘\ ( B‘lM‘H 0/; QM
i Kl « f ,
a \ I ~
I
<1
H C \
Print your LAST name here ‘9 l Problem 2. (25 points) A tractor pulls two blocks of ice, with masses m A : 370kg
and m3 = 180kgr across a frozen lake. A single horizontal rope connects the two blocks. A
second rope from the tractor is connected at an angle 27° above horizontal to block A and
applies a constant force of magnitude 1720N. Assume that all surfaces are frictionless, and
neglect the masses of the ropes. (a) (5 points) In the space below, draw two free—body diagrams, one for each block, showing
all forces acting on that block. ~> 4’ ﬁt; Orly (“~wa ' “A a
T < A: “"3 (OH. wall: i mi N 5 M463 wag—c: (Jim/CE Ck¢¢£
‘9 Comwont unﬁlled ’CUM an. (b) (5 points) In the table below, list each force in your diagram and indicate what object exerts the force. 144ch forces on block A forces on block B
force exerted by...
. to T W’F'<
“b e‘ 0e. F%Q,T: wwka SM O’C‘P‘OM ’ CL: 'T T. W15 a CM wv5£< (LL45 ‘ WA+M8
MM $6 51904: F one : Q4” we.) ’01 ‘ » ’ 
l9 «ft MW L F E\ It ~
(d) (8 points) What is the tension in the rope connecting the globclzs‘f? Q a “4/5 1  ~ 5 N WWW “Mk5 Syg~l3c~¢5 XLamﬁanl’wj’
“i ThtO’I/wf
W Law/H, AL Mfg Print your LAST name here SO Problem 3. (25 points) A hot air balloon 42.0111 above
the ground is travelling horizontally at a speed 8.6mW/s. At
this point7 a 36.0—kg sandbag comes loose and falls. Neglect
air resistance. (a) (5 points) What is the horizontal component of the sand—
bag’s velocity when it reaches the ground? Vx 1 \/ I; bx (b) (8 points) What is the vertical component of the sandbag’s
velocity when it reaches the ground? Vy ‘ ” g“ 3% vyz" ' 239%) (c) (8 points) How long does the sandbag take to reach the g ound? .0 L . ~
Wyatvﬁl‘izak M Vf'ﬂv‘ﬂJC 'V 1%.7‘47/8 J01; «17.) 4‘ Jo : e _,‘:I z = 2,6133
7 3 3 WWW
4::\/2(4M) 1 2,5333
‘lﬂ‘ﬁ/y’ (d) (4 points) By chance, the sandbag happens to land in an empty cart rolling on level
ground in the same direction as the balloon at 21.0m/s. What is the magnitude of the
sandbag’s velocity relative to the cart? géw/g. ‘L’ U4£
/ h—a
9,3,7ay:1\ V \ Vx ; 3.6m/s '2lm/5
6’ : ‘(2.4'%/9 1
V7 " ’18.7 «4/5 U 0 ._—————/~1
\l 1 \/\/a1 LVYZ : via/S Print your LAST name here ’i’wf IMPORTANT NOTE: In order to receive credit for Problems 4 and 5b, you must
provide justiﬁcations for your answer. » _’
Problem 4. (10 points) Vectors fl, B, C“, and 5 all have the C
same magnitude. The angle between adjacent vectors is 60°, as
shown in the diagram. Which one of the following vector equa—
tions is correct? In order to receive credit, you must sketch a diagram demonstrating that the equation holds.
’7 if (\L Problem 5. (20 points) The graph
shows the position of two objects, A and
B, as a function of time. (a) (10 points) 0n the time (ms of the
graph, mark any times when both ' position objects are at the same position
with a P and mark any times when both objects have the same velocity 9 p
with a v. P v P time (b) (10 points) Which one of the following situations is correctly represented by the
graph? In order to receive credit, you must justify your answer (on the back
of this sheet if you need more space) by comparing the position, velocity, and
acceleration of object A and object B throughout the time interval shown. i. A nickel (A) and a feather (B) are dropped from rest at t = 0. ML A— Originally, car A and car B both travel at constant speeds. After passing car
W B, car A runs over some broken glass, gets a flat tire, brakes, and comes to
(#97 a)“ rest, allowing car B to pass. iii. Ball A is thrown straight up into the air. One second later, ball B is thrown
up with a larger initial velocity. M4 Mg iv. Car A, travelling in excess of the speed limit, races past car B (a parked police
t“ 0/5 car). A few seconds later, car B accelerates to chase the Speeder. After car
M B catches up, both cars brake and come to rest at the side of the road. v. Car B is following too close behind car A. When car A brakes unexpectedly,
car B collides with it from behind. Both cars come to rest together. B MV)Q>O
A®c~dw
@Wa, vW’éyC’a
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This note was uploaded on 07/08/2009 for the course PHY 1221 taught by Professor Staff during the Winter '00 term at Northeastern.
 Winter '00
 STAFF

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