Name:_______KEY__________________
Phys.115 Exam I
27 September 2006
Please do not turn the page until you are told to do so. Make sure that you have all three problems on your
copy of the test. In order to get credit on a problem, you must show your work. If you only write down an answer
without the work leading up to it, you will get no credit for it, even if it is the right answer.
1) You have just crossed Adelbert Rd. in front of the South Side dorms, when your roommate calls you from
across the street to tell you that he locked himself out of the room. You throw him the key across the street. The
keys leave your hand with a speed of 7.5 m/s directed at 60 above the horizontal and at a height of 1 m off the
ground.
a) If the width of the street is 7 m, will the keys make it all the way across the street?
x  dir : x  v 0 x t
y  dir : v0 y  v0 y  gt ; t 
 2v sin 
x  v 0 cos   0
g

1
y  y 0  v 0 y t  gt 2
2
2v0 y
g

2v0 sin 
g
2
 v 0 sin 2 7.5 m / s 2 sin 120
 

 5m
g
9.8 m / s 2

1 2
gt 2
2
4.9t 22  7.5 sin 60t 2  1  0
0  y0  v0 sin t 2 
 b  b 2  4ac  7.5 sin 60  7.5 sin 60  44.9 1  6.5  7.86
t2 


 1.5s or 0.14 s
2a
9.8
9.8
x  v0 cos t 2  7.5m/s cos 600.14s   0.5m
The total horizontal distance the keys will fly until they reach the ground is 5.5 m.
2
b) What you don’t notice is that your physics lecturer is driving by in her Honda Odyssey. The height of the car is
1.75 m. If the Odyssey is 2 m from the sidewalk (and from you), will the keys clear the car (fly over and miss the
car)?
x
x
2m
v0 x  ; t 

 0.53 s
t
v0 cos 7.5 m / s cos 60


1
2
y  y0  v0 yt  at 2  1m  7.5 m/s sin 600.53 s   4.9 m/s 2 0.53 s   3.1m
2
The keys will miss the car.
Problem1
Problem2
Problem3
Total/60
2) You are pushing a 10-kg wagon with a 5kg pumpkin on a horizontal frictionless
surface as shown. The surface between the
pumpkin and the wagon is roughened so that
there is no slipping between the two. You
are applying a 30-N push to the wagon as
suggested in the figure.
30N
a. (7 points) What is the acceleration of the wagon-pumpkin system?
 F  m
a
p
 mw a
30 N
 2 m/s 2
15 kg
b. (7 points) What is the force of static friction between the pumpkin and wagon?
F
p
 mpa


f  m p a  5 kg  2 m/s 2  10 N
c. (6 points) What is the minimum coefficient of static friction necessary to keep the pumpkin from slipping
on the wagon?
f  s FN  s m p g
s 
f
10 N

 0.2
m p g 5 kg  9.8 m/s 2


3) A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m at a constant speed. At the lowest
point of its motion the tension in the rope supporting the bucket is 50.0 N.
a) (3 points) Please draw a free body diagram of the bucket at the lowest point of its motion.
+x
FT
W
b) (5 points) Find the speed of the bucket.
 Fvertical  mac
v2
r
r ( FT  mg )
(1.10 m) 50.0 N   2.00 kg  9.80 m/s 2
v

 4.09 m/s
m
2.00 kg
c) (4 points) ) How long does it take for the bucket to go around the circular path once?
2r 2 1.10 m 
T

 1.69 s
v
4.09 m/s
FT  W  m



d) (3 points) Please draw a free body diagram of the bucket at the highest point of its motion.
W
FT
+x
e) (5 points) How fast must the bucket move at the top of the circle so that the rope does not go slack?
The condition for the rope to not go slack is the limiting condition for which FT=0.
F
vertical
 mac
v2
r
r(mg )
(1.10 m) 2.00 kg9.80 m/s 2 
v

 3.28 m/s
m
2.00 kg
W m



A  Ax2  Ay2  Az2
  tan 1

 r
v
t

 v
a
t
Ay
Ax
1
x  x0  v0 t  at 2
2
v  v0  at
v 2  v02  2ax


F  ma
mm
F G 122
R
f k  k FN
v2
r
2r
T
v
mv 2
Fc 
r
….. constants …..
g  9.8 m / s 2
ac 
G  6.67  1011 Nm2 / kg 2