lecture 03: relative and circular motion - astronomybelz/phys2210/lecture03.pdf · lecture 03:...
TRANSCRIPT
Lecture 03: Relative and Circular Motion
Physics 2210Fall Semester 2014
Announcements
● Homeworks due 11:59 PM Tues/Thurs ● Schedule next few weeks:
● 9/08 – Unit 3● 9/10 – Unit 4● 9/15 – Unit 5● 9/17 – Unit 6● 9/22 – Unit 7, Exam Review● 9/24 – Exam 1, Units 1-6
Mechanics Lecture 2, Slide 3
Monkey Troubles
You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?
A) Right at the monkeyB) Below the monkeyC) Above the monkey
Mechanics Lecture 2, Slide 4
Monkey
x = xo
Dart
x = vo t
2
2
1gty −=
Shooting the Monkey…
2
2
1gty −=
Mechanics Lecture 2, Slide 5
Shooting the Monkey…
y = voy t − 1/2 g t 2
Still works even if you shoot upwards!
y = yo − 1/2 g t 2
Dart hits themonkey
Mechanics Lecture 2, Slide 6
Monkey Troubles
You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?
A) Right at the monkeyB) Below the monkeyC) Above the monkey
Mechanics Lecture 3, Slide 7
Classical Mechanics Lecture 3
Today’s Concepts:a) Relative motionb) Centripetal acceleration
“Lecture Thoughts” Responses● Numerical Examples!● Reference frames
● Sign conventions● Graphing
● Centripetal acceleration● Derivations● Angular velocity
Relative Motion
On your equation sheet...
Mechanics Lecture 3, Slide 9
Relative Motion
What is vMike,Ground
?
Follow-up: How would the previous problem change if Mike were running at 3 m/s with
respect to the train, to the left?
Mechanics Lecture 3, Slide 11
Prelecture 3, Question 1
Mechanics Lecture 3, Slide 12
Prelecture 3, Question 1
Mechanics Lecture 3, Slide 13
vbelt,ground = 2 m/s
vdog,belt = 8 m/s
A) 6 m/s B) 8 m/s C) 10 m/s
CheckPoint:What is the speed of the dog relative to the ground?
Mechanics Lecture 3, Slide 14
vdog, ground = vdog, belt + vbelt, ground
= (−8 m/s) + (2 m/s) = −6 m/s
+x
vbelt,ground = 2 m/s
vdog,belt = 8 m/s
What is the speed of the dog relative to the ground?
A) 6 m/s B) 8 m/s C) 10 m/s
Mechanics Lecture 3, Slide 15
CheckPoint
What is the speed of the dog relative to the woman?
vbelt,ground = 2 m/s
vdog,belt = 8 m/s
A) 6 m/s B) 8 m/s C) 10 m/s
Mechanics Lecture 3, Slide 16
A) Because she is actually moving and the two vectors are opposite, so together they make 6 m/s
B) Because she is not moving relative to the belt, and the dog is going 8 m/s relative to the belt, the dog is also moving 8 m/s
relative to her C) The dog and woman are running towards each other so when
you add the two velocities together it would be 8+2.
What is the speed of the dog relative to the woman?
vbelt,ground = 2 m/s
vdog,belt = 8 m/s
A) 6 m/s B) 8 m/s C) 10 m/s
Mechanics Lecture 3, Slide 17
Flashcard Question
Moving sidew
alk
2 m/s
1 m/s
4 m
A man starts to walk along the dotted line painted on a moving sidewalk toward a fire hydrant that is directly across from him. The width of the walkway is 4 m, and it is moving at 2 m/s relative to the fire-hydrant. If his walking speed is 1 m/s, how far away will he be from the hydrant when he reaches the other side?
A) 2 m
B) 4 m
C) 6 m
D) 8 m
Mechanics Lecture 3, Slide 18
Flashcard Question
Moving sidew
alk
2 m/s
1 m/s
4 m
A man starts to walk along the dotted line painted on a moving sidewalk toward a fire hydrant that is directly across from him. The width of the walkway is 4 m, and it is moving at 2 m/s relative to the fire-hydrant. If his walking speed is 1 m/s, how far away will he be from the hydrant when he reaches the other side?
A) 2 m
B) 4 m
C) 6 m
D) 8 m
Mechanics Lecture 3, Slide 19
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 swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees.
Who gets across the river first?
A) Ann B) Beth C) Carly
x
y
AnnBeth
Carly
Flashcard Question
Mechanics Lecture 3, Slide 20
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 swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees.
Who gets across the river first?
A) Ann B) Beth C) Carly
x
y
AnnBeth
Carly
Flashcard Question
Mechanics Lecture 3, Slide 21
x
y
Flashcard Question
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 swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees.
Who gets across the river second?
A) Ann B) Carly C) Both same
Ann Carly
Mechanics Lecture 3, Slide 22
x
y
Flashcard Question
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 swims perpendicular to the flow, Ann swims upstream at 30 degrees, and Carly swims downstream at 30 degrees.
Who gets across the river second?
A) Ann B) Carly C) Both same
Ann Carly
Centripetal Acceleration
Mechanics Lecture 3, Slide 24
A girl twirls a rock on the end of a string around in a horizontal circle
above her head as shown from above in the diagram.
If the string breaks at the instant shown, which of the arrows best represents the resulting path of
the rock?
A
B
C
D
Top view looking down
CheckPoint (& Demo)
Mechanics Lecture 3, Slide 25
A girl twirls a rock on the end of a string around in a horizontal circle
above her head as shown from above in the diagram.
If the string breaks at the instant shown, which of the arrows best represents the resulting path of
the rock?
A
B
C
D
Top view looking down
CheckPoint (& Demo)
Mechanics Lecture 3, Slide 26
Centripetal Acceleration
Example: What is the angular speed of the Earth as it rotates about its axis? What is the linear speed of a person on the equator, due to the Earth's motion? What about in Salt Lake City?
Radius of earth is 6,371 kmSLC is at 40.75 degrees North latitude
What is magnitude of centripetal acceleration?
Mechanics Lecture 3, Slide 28
v(t1) = v
1
v(t2) = v
2
Note that angle between v2 and
v1 is just !
So, a = dv/dt = vd/dt = v = v2/R
Mechanics Lecture 3, Slide 29
We can ignore acceleration due to Earth's rotation since it's small
Example: What would be radius of a sphere, with the same linear speed on its equator as the Earth, for which an object on its surface would experience a centripetal acceleration of g = 9.81 m/s2?
Mechanics Lecture 3, Slide 31
Prelecture Slide: Discuss