Physics 101: Lecture 27, Pg 1

More Constant Acceleration and More Constant Acceleration and Relative Velocity Relative Velocity

Physics 101: Lecture 07

Exam I

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 2

Some ChartsSome Charts

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Interactive Neutral Traditional

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Essential Useful Useless

Prelectures

Physics 101: Lecture 27, Pg 3

Extra ProblemsExtra Problems•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 4

Last TimeLast Time

X and Y directions are Independent!Position, velocity and acceleration are vectors

F = m a applies in both x and y direction

Projectile Motionax = 0 in horizontal directionay = g in vertical direction

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Physics 101: Lecture 27, Pg 5

TodayToday

More 2-D Examples

Newton’s 3rd Law Review

Relative Motion

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Physics 101: Lecture 27, Pg 6

Pulley, Incline and 2 blocksPulley, Incline and 2 blocks

T

m2gm1g

TN

y

x

A block of mass m1 = 2.6 kg rests upon a frictionless incline as shown and is connected to mass m1 via a flexible cord over an ideal pulley. What is the acceleration of block m1 if m2 = 2.0 kg?

X – direction Fx = m ax:

Block 1:T – m1g sin(30) = m1 a1x

T = m1g sin(30) + m1 a1x

y x

Y – direction Fy = m ay:

Block 2:T – m2 g = m2 a2y

Note: a1x = - a2y

Combine T – m2 g = m2 a2y

m1g sin(30) + m1 a1x – m2 g = m2 a2y

m1g sin(30) + m1 a1x – m2 g = -m2 a1x

m1 a1x +m2 a1x= m2 g - m1g sin(30)

(m1+m2) a1x= g (m2 - m1 sin(30)) 2 11

1 2

sin 30m ma g

m m

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1.49 m/s2

Physics 101: Lecture 27, Pg 9

Newton’s 3Newton’s 3rdrd Example ExampleA rope attached to box 1 is accelerating it to the right at a rate

of 3 m/s2. Friction keeps block 2 on top of block 1 w/o slipping. What is the tension in the rope?

M1

M2

T

x

y

W1N2

NT

f12 T

X-direction: F = ma

Block 2: f21 = m2 a2

Block 1: T – f12 = m1 a1

N3L says |f12| = |f21|

Combine: T - m2 a2 = m1 a1

T = m1 a1+ m2 a2

= (m1+m2) a•Same as if had one block M = m1+m2 !!!! 23

f21

N1

W2

Physics 101: Lecture 27, Pg 10

Relative VelocityRelative VelocityYou 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

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40 5

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Physics 101: Lecture 27, Pg 11

Relative VelocityRelative Velocity

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

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405

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Physics 101: Lecture 27, Pg 12

Relative VelocityRelative VelocityYou 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 mphB) 40 mph C) >40 mph

40 mph N + 5 mph W = 41 mph N

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405 22 540|| v

Physics 101: Lecture 27, Pg 13

Relative VelocityRelative Velocity 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 vector addition:

bcabac vvv

» vac is the velocity of the object relative to

the ground

» vab is the velocity of the object relative to a moving reference frame

» vbc is the velocity of the moving reference frame relative to the ground

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Physics 101: Lecture 27, Pg 14

Tractor Demo 1Tractor Demo 1

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

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1 2 3

Physics 101: Lecture 27, Pg 15

Tractor Demo (moving table)Tractor Demo (moving table)

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

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Physics 101: Lecture 27, Pg 16

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?

A) Ann

B) Beth

C) Carly

Preflight 7.1 Preflight 7.1

correct

A B C

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t = d / vy

Ann vy = v cos()Beth vy = v Carly vy = v cos()

49%

33%

18%

0% 10% 20% 30% 40% 50%

x

y

Physics 101: Lecture 27, Pg 17

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?

A) Ann B) Same C) Carly

ACT ACT

A B C

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t = d / vy

Ann vy = v cos()Beth vy = v Carly vy = v cos()

x

y

Physics 101: Lecture 27, Pg 18

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?

Swimmer Example Swimmer Example

A B C

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VAnn,ground = Vann,water+Vwater,ground

x

y

x-direction

0 = Vx,Ann,Water + 3

0 = -VAnn,Water sin() + 3

5 sin() = 3

sin() = 3/5

Physics 101: Lecture 27, Pg 20

Summary of ConceptsSummary of Concepts

X and Y directions are Independent!Position, velocity and acceleration are vectors

F = m a applies in both x and y direction

Newton’s 3rd Law

Relative Motion (Add vector components)

wgswsg vvv