Exam 1 is one week from Monday
Today is the last lecture for Exam 1 material
No circular motion on exam 1 – different from past years!
I will hold a special office hour 10-11 Friday in 235 Loomis
Physics 101: Lecture 27, Pg 1

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Essential
Prelectures
Useful Useless
Tablet
Physics 101: Lecture 27, Pg 2

•Ch 2 Problems: 1,5,7,11,13,17,29,49,69
•Ch 3 Problems: 5,13,33,47,57,65,67
•Ch 4 MC all, Problems: 1, 3,5,9, 17,19,23,25,27,35,41,53,55
Physics 101: Lecture 27, Pg 3

 X and Y directions are Independent!
 Position, velocity and acceleration are vectors

S
F = m a applies in both x and y direction
 Projectile Motion
 a x
= 0 in horizontal direction
 a y
= g in vertical direction
Physics 101: Lecture 27, Pg 4 8

 More 2-D Examples

Newton’s 3 rd Law Review
 Relative Motion
Physics 101: Lecture 27, Pg 5 10

A block of mass m
1
= 2.6 kg rests upon a frictionless incline as shown and is connected to mass m
1 via a flexible cord over an ideal pulley. What is the acceleration of block m
1 if m
2
X – direction
S
F x
= m a x
:
Block 1:
T – m
Y – direction F
Block 2:
T – m
1
2 g sin(30) = m y
= m a g = m
2 a y
:
2y
1
T = m
1 g sin(30) + m
1
= 2.0 kg? a
1x a
1x
Combine
N m
1 g sin(30) + m
1 m
1 g sin(30) + m
1
T
T – m
2
1x
– m
2 a
1x
– m
2
T 2 g = m
2 y a a
2y
2y g = -m
2 a
1x m
1 a
1x
+m
2 a
1x
= m
2 g - m
1 g sin(30)
(m
1
+m
2
) a
1x a
1 m

1 g m
2
2

- m m
1
1 m
1
 m
2 m sin 30
2 g g
Note: a
1x
= - a
2y 1.49 m/s 2
Physics 101: Lecture 27, Pg 6 17 x

y
rd
A rope attached to box 1 is accelerating it to the right at a rate of 3 m/s 2 . Friction keeps block 2 on top of block 1 w/o slipping. What is the tension in the rope?
M
2
X-direction: F = ma
M
1
Block 2: f
21
= m
2 a
2 N
1
T x
Block 1: T – f
12
= m
1 a
1 N
T f
21
N3L says |f
12
| = |f
21
| f
12
T W
2
Combine: T - m
2
T = m
1 a a
2
1
= m
+ m
1
2
= (m
1
+m
2
) a a
1 a
2
W
1
N
2
•Same as if had one block M = m
1
+m !!!!
23

You are on a train traveling 40 mph North. If you walk 5 mph toward the front of the train, what is your speed relative to the ground?
A) 45 mph B) 40 mph C) 35 mph
40 mph N + 5 mph N = 45 mph N
40 5
45

You are on a train traveling 40 mph North. If you walk 5 mph toward the rear of the train, what is your speed relative to the ground?
A) 45 mph B) 40 mph C) 35 mph
40 mph N - 5 mph N = 35 mph N
40
5
35
Physics 101: Lecture 27, Pg 11 27

You are on a train traveling 40 mph North. If you walk 5 mph sideways across the car, what is your speed relative to the ground?
A) < 40 mph B) 40 mph C) >40 mph
40
40 mph N + 5 mph W = 41 mph N
5 | v |

40
2 
5
2

 Sometimes your velocity is known relative to a reference frame that is moving relative to the earth.
 Example 1: A person moving relative to a train, which is moving relative to the ground.
 Example 2: a plane moving relative to air, which is then moving relative to the ground.
 These velocities are related by
:
 v ac

 v ab

 v bc
» v ac is the velocity of the object relative to the ground
» v ab is the velocity of the object relative to a moving reference frame
» v bc is the velocity of the moving reference frame relative to the ground
Physics 101: Lecture 27, Pg 13 32

Which direction should I point the tractor to get it across the table fastest?
A) 30 degrees left
B) Straight across
C) 30 degrees right
1 2 3
Physics 101: Lecture 27, Pg 14 34

 Which direction should I point the tractor to get it across the table fastest?
A) 30 degrees left
B) Straight across
C) 30 degrees right 1 2 3
Physics 101: Lecture 27, Pg 15 37

y
Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time.
Relative to the water, Beth (B) swims perpendicular to the flow,
Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race?
x
A) Ann
B) Beth
C) Carly correct t = d / v y
Ann v y
= v cos( q
)
Beth v y
Carly v y
= v
= v cos( q
)
18%
33%
49%
0% 10% 20% 30% 40% 50%
A B C
Physics 101: Lecture 27, Pg 16 39

y
Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Who gets across second
Ann or Carly?
x
A B C
A) Ann B) Same C) Carly t = d / v y
Ann v y
= v cos( q
)
Beth v y
Carly v y
= v
= v cos( q
) q
Physics 101: Lecture 27, Pg 17 42

y
x
What angle should Ann take to get directly to the other side if she can swim 5 mph relative to the water, and the river is flowing at 3 mph?
V
Ann,ground
= V ann,water
+V water,ground x-direction
0 = V x,Ann,Water
0 = -V
Ann,Water
5 sin( q
) = 3
+ 3 sin( q
) + 3 sin( q
) = 3/5
A B C q
Physics 101: Lecture 27, Pg 18 48

 X and Y directions are Independent!
 Position, velocity and acceleration are vectors
 F = m a applies in both x and y direction

Newton’s 3 rd Law
 Relative Motion (Add vector components)
 v sg

 v sw

 v wg
Physics 101: Lecture 27, Pg 20