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Physics Exam 2 (Spring 2006) - Wheels and Star Problems, Exams of Physics
The second exam for the physics 2050h course in spring 2006. The exam covers topics related to wheels and star problems, including calculating maximum forces, finding the maximum angle of a hill, and determining the distance to stop a car. It also includes problems on conservative forces and potential energy.
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Physics 2050H / Exam 2 [Form-A]
Spring 2006
Page 2
Wheels
(50,000 points)
1.) (a) Jenny hops into her economy car (
m = 1110 kg
) and takes off as fast as she
can,
a = 3.28 m/s²
. Find this maximum force
F
1
that is moving the car.
F
ma
kg
m
s
N
1
2
b
gc
h
.
/
(b) If Jenny is driving up a hill at a constant speed of 25.0 m/s, find the maximum angle
of the hill given the maximum force
F
1
.
If you didn’t get an answer to (a), use F
1
=
5550 N.
F
F
w
F
w
mg
F
mg
N
kg
m
s
x
x
x
1
1
1
2
1
0
sin
sin
.
/
.
sin
.
.
b
gc
h
of friction are 0.950 and 0.680, find the distanceahead and all the cars have stopped. If she slams on the brakes, she will skid to a stop. If the coefficients (c) Jenny is driving on a flat, level road at a speed of 25.0 m/s when she sees that there’s construction
d
that it would take for Jenny to come to a stop.
F
F
mg
F
mg
F
F
mg
F
F
ma
y
n
n f
k
k
n
k
x
f
k
x
0
,
,
by kinematic equations
by Work-Energy Theorem
a
mg
m
g
m
s
m
s
v
v
a x
x
v
ad
ad
v
d
v
a
m
s
m
s
m
x
k
k
0
2
2
2
02
0
02
0 2
02
2
2
.
.
/
.
/
.
/
.
/
. b
gc
h
b
g
b
g
c
h
OR
W
Fd
F
d
mgd
W
K
K
K
K
mgd
K
mgd
mv
gd
v
d
v
g
m
s
m
s
m
f
k
k
f
i
i
k
i
k k
k
,
.
/
.
.
/
.
21
0 2
21
0 2
02
2
2
b
g
b
gc
h
Physics 2050H / Exam 2 [Form-A]
Spring 2006
(d) Unfortunately, before Jenny comes to a stop there’s a big sedan (
m = 2270 kg
) which has slowed down
in front of her. If she hits it totally inelastically, when her car was traveling at
v
1
= 12.0 m/s
and the sedan
was moving at
v
2
= 8.00 m/s
, find the speed
V
of the wreck.
p
p
m v
m v
m
m V
V
m v
m v
m
m
kg
m
s
kg
m
s
kg
kg
m
s
before
after
1 1 2 2 1 2
1
1
2
2
1
2
b
g
b
g
b
gb
g b
gb
g
b
g
.
/
.
/
.
/
(e) Instead, Jenny swerves at
v
i
= 12.0 m/s
only to find herself sailing off of a cliff and
final speedcrashing into the valley 166 meters below. Use Conservation of Energy to find her
v
f
just as she hits the ground.
mgh
mv
mgh
mv
h
mgh
mv
mv
gh
v
v
v
gh
v
v
gh
v
m
s
m
m
s
m
s
1
21
1 2
2
21
22
2
1
21
1 2
21
22
1
21
1 2
21
22
2 2
1
1 2
2
1
1 2
2
2
0
;
.
/
.
/
.
/
c
hb
g b
g
Physics 2050H / Exam 2 [Form-A]
Spring 2006
Page 4
2.) The What’s the Point of Star Problems? ANSWER: (50,000 points)
sprangle
force is given as
F = - C x
5
. If the
sprangle
force is a conservative force, then calculate
the equation of the potential energy term
U
sprangle
.
U
W
W
F ds
Cx i
dx i
C
x dx
C
x
const
declare const
U W C x C x
HG F
KJI
z
z
z
(
)
.
;
.
5
5
6
6
6
0
As with
U
g
and
U
s
, we can set
U = 0
wherever
we
like.
(b) An object of mass
m = 9.00 kg
begins its motion at
x
0
= 9.00 m
,
v
0
= 9.00 m/s
,
a
0
= 9.00 m/s²
and an initial jerk of
j
0
= 9.00 m/s³.
Find the equation for the force,
F
, acting on this object, where the
motion of the object is determined by the following equation:
a
d x dt
d x dt
m s
d x dt
d x dt
dt
m s dt
m s
t
C
C
j
m s
m s
t
m s
d x dt
d x dt
dt
m s
t
m s
dt
m s
t
m s
t
C
C
a
m s
a
m s
x x
z
z
z
z
2
2
4
4
4
3
3
4
4
4
4
0
3
4
3
2
2
3
3
4
3
4
2
3
0
2
;
.
/
.
/
(.
/
)
; (
.
/
)
(.
/
)
.
/
(.
/
)
.
/
(.
/
)
(.
/
)
; (
.
/
)
(.
/
c
h
4
2
3
2
4
2
3
2
2
2
00
)
(.
/
)
.
/
(.
) (.
/
)
(.
/
)
.
/
(
.
/
)
(81.
/ )
.
t
m s
t
m s
F
ma
kg
m s
t
m s
t
m s
N s
t
N s t
N
d x dt
m s
4
4
4
9 00
.
/
Physics 2050H / Exam 2 [Form-A]
Spring 2006
(c) Find the work done when
F
x i
y
j
N
m
N
m
3 00
4 00
2
2
.
.
and the displacement is
s
= 5.00 m @ 30°.
s
m
x
m
m
y
m
m
F
x i
y
j
W
F ds
F dx
F dy
x dx
y dy
x dx
y dy
x
y
N
m
N
m
x
x
y
y
N
m
x
N
m
y
N
m
x
N
m
y
N
m
m
N
m
m
z
z
z
z
z
z
z
2
2
2
2
2
0
0
0
2
0
0
2
0
2
0 4 330
3
0 2 500
.
@
.
cos
.
.
sin
.
.
.
.
.
.
.
.
.
.
.
b
gb
g
b
gb
g
b
g
c
h
b
g
c
h
.
.
.
.
.
.
.
00
2
3
2
N
m
N
m
m
m
J
J
J
b
gb
g
c
hb
g
Physics 2050H / Exam 2 [Form-A]
Spring 2006
(d) A block of mass
m
is attached to several pulleys, plus a rope being pulled by Fred, but the block is not
moving. Sketch the Free Body Diagram for the block
m
and then write the accompanying sum of forces
equations in the
x
- and
y
-directions.
But do not solve the equations!
F T T T T T
mg
T
T
mg
T
mg
T
mg
F
T
F
T
F
T
F
y
y
x
x
1
1
1
1
1
1
1
1 1 1
1
1
1
1
1
0
0
0
0
0
0
0
sin
sin
.
cos