A car of mass m, traveling at constant speed, rides over
the top of a circularly shaped hill as shown. The magnitude of the normal force N of the road on the car
is ….
A)  Greater than the weight of the car, N > mg.
B)  Equal to the weight, N = mg.
C)  Less than the weight, N < mg.
L16 W 10/1/14 a*er lecture 1 A car of mass m, traveling at constant speed, rides over
the top of a circularly shaped hill as shown. N

Fnet
+x
mg
Write NII:
2
mv
0 < Fnet = ma =
= mg − N ⇒ N < mg
r
L16 W 10/1/14 a*er lecture 2 Assignments
curved mean = 75
About the exam:
• 
• 
• 
• 
• 
Raw average = 72. Each score is curved upward by 3 points. Student scores (increased by 3 points) are posted on D2L.
I have exam booklets for the early exam – pick up after class today.
See the course web site for suggestions about improving in the future.
Any questions about your grade should be sent to Prof. Munsat.
L16 W 10/1/14 a*er lecture 3 Assignments
About the exam:
• 
• 
• 
• 
• 
Raw average = 72. Each score is curved upward by 3 points. Student scores (increased by 3 points) are posted on D2L.
I have exam booklets for the early exam – pick up after class today.
See the course web site for suggestions about improving in the future.
Any questions about your grade should be sent to Prof. Munsat.
For this week:
•  Read Ch. 5 of Wolfson and Prof. Dubson’s notes. Begin Ch. 6.
•  Written HW5, from Red Workbook. Scans of the Red and Blue Workbooks
are on D2L.
For next week:
•  CAPA 6.
•  Written homework 6: begin to analyze the Megawoosh video.
L16 W 10/1/14 a*er lecture 4 Wri5en HW’s 6 -­‐ 8: Megawoosh vs. Waterslide Wipeout Megawoosh Video:
http://www.youtube.com/watch?v=b_1G72VzqB8&feature=watch_response
Your Question for HW6: Is trajectory of this stunt theoretically consistent
with Newton’s Laws, if air resistance and sliding friction are neglected? (Ignore
the ability of the man to survive the landing in the kiddie pool.)
Mythbusters Response:
http://dsc.discovery.com/videos/mythbusters-waterslide-wipeout-angle-5.html
https://www.youtube.com/watch?v=iHu6LVg-0Hs
Myth Busted: Mythbusters consider accuracy and distance in the real
world, where sliding friction and air resistance exist. They find the accuracy
is possible but distance is not under realistic conditions.
L16 W 10/1/14 a*er lecture 5 Dynamics: Newton’s Laws of Motion
Applications:
(1)  Sliding Blocks.
(2) Contact Forces.
(3) Suspended Bodies.
(4) Circular Motion.
(5) Friction.
L16 W 10/1/14 a*er lecture 6 Mass suspended from another supported mass
Atwood machine
⎛ M − m⎞
a=⎜
g
⎟
⎝ M + m⎠
T
T
+x
a
M
m
a
+x
Fg=Mg
Fg=mg
+x
M1
+T
⎛ M2 ⎞
a=⎜
g
⎟
⎝ M1 + M 2 ⎠
T
M2
Fg = M2g
1)  Choose a coordinate system.
2)  Specify the forces (free-body diagram).
3)  Consider Fnet = ma for each object.
4)  Solve for what’s needed.
5)  Does the result make sense?
L16 W 10/1/14 a*er lecture +x
7 Dynamics: Newton’s Laws of Motion
Applications:
(1)  Sliding Blocks.
(2) Contact Forces.
(3) Suspended Bodies.
(4) Circular Motion.
(5) Friction.
L16 W 10/1/14 a*er lecture 8 Example 2. A merry-go-round has a radius r = 5 m. If it’s pushed to have
a period of τ = 3 sec.
m = 25 kg
v 2 4π 2 r
aR =
= 2
r
τ
r=5m
aR = 22 m/s2
τ = 3 sec
What’s the centripetal force needed to hold
a m = 25 kg girl on the merry-go-round?
F = m aR = 25 kg (22 m/s2) = 550 N (1 lb/4.45 N) = 123 lb
L16 W 10/1/14 a*er lecture 9 Example 3. The Earth circles the Sun at an average distance of 1 AU =
1.5 x 1011 m in 1 year. What is its orbital centripetal acceleration?
E
r = 1 AU
v 2 4π 2 r
aR =
= 2
r
τ
4π 2 (1.5x1011 m)
=
(π x10 7 s)2
⎛ 1g ⎞
= 6x10 m/s ⎜
⎝ 9.8m/s 2 ⎟⎠
−3
2
≈ 0.06% of g
L16 W 10/1/14 a*er lecture 10 Example 3. The Earth circles the Sun at an average distance of 1 AU =
1.5 x 1011 m in 1 year. What is its orbital centripetal acceleration?
E
r = 1 AU
τ = 365 days
L16 W 10/1/14 a*er lecture v 2 4π 2 r
aR =
= 2 ≈ 0.06% of g
r
τ
What’s causing the centripetal
acceleration?
A)  The electrostatic force between the
Earth and Sun.
B)  The tension in the string connecting
the Earth to the Sun.
C)  The force of gravity between the
Earth and the Sun.
D)  Depends on the time of day. 11 Example 3. The Earth circles the Sun at an average distance of 1 AU =
1.5 x 1011 m in 1 year. What is its orbital centripetal acceleration?
E
r = 1 AU 
v 2 4π 2 r
aR =
= 2 ≈ 0.06% of g
r
τ
aR
τ = 365 days
It points towards the Sun at
all times, which may be in
the sky or not depending
on the time of day.
L16 W 10/1/14 a*er lecture You’re on the Earth. Which direction
does the centripetal acceleration point?
A)  Down
B)  Up
C)  Depends on the time of year.
D)  Depends on the time of day. 12 Consider the following two situations:
Situation I: A car on Earth rides over the top
of a round hill, with radius of curvature = 100
m, at constant speed v = 35 mph. Situation II: A monorail car in intergalactic space (no gravity) moves along a
round monorail, with radius of curvature = 100 m, at constant speed v = 35 mph.
Which car experiences the larger acceleration?
A)  Earth car. B) Space car. C) Both have the same acceleration.
Both cars have the same acceleration. The presence of gravity
doesn’t change the fact that the acceleration has magnitude a = v2/r. L16 W 10/1/14 a*er lecture 13 A ball of mass m is twirled on a string in a vertical circle of radius
r in the presence of gravity with a constant speed v. At which
position is the magnitude of the net force on the ball greatest?
(Ignore air resistance but consider gravity.)

v
Top
A) Top
B) Bottom
T1
C) Somewhere
r
r
between Top and
Bottom.
T2

mv
Fnet =
r
L16 W 10/1/14 a*er lecture 2
Bottom

v
D) Same at all
positions.
14 A ball of mass m is twirled on a string in a vertical circle of radius
r in the presence of gravity with a constant speed v. What is the
relation between the magnitude of the tension in the string at the
top and bottom of the circle? (Ignore air resistance but consider
gravity.)

v
Top
A) T1 = T2
T1
r
B) T1 > T2
C) T2 > T1
r
D)  Impossible to tell
T2
Bottom
L16 W 10/1/14 a*er lecture from the information

v
given. 15 A ball of mass m is twirled on a string in a vertical circle of radius
r in the presence of gravity with a constant speed v. What is the
relation between the magnitude of the tension in the string at the
top and bottom of the circle? (Ignore air resistance but consider
gravity.)

v
Bottom
Top
Top
T2
T1
m
a
r
+x
T2
Bottom

v
T2 > T1
L16 W 10/1/14 a*er lecture T1
m
mg
+x
a
mg
v2
Fnet = ma = m
r
= T1 + mg
v2
Fnet = ma = m
r
= T2 − mg
mv 2
∴T1 =
− mg
r
mv 2
∴T2 =
+ mg
r
16