Download Newton s Second and Third Laws and Gravity

Newton s Second
and Third Laws
and Gravity
Announcements
This week:
n  Solutions for Quiz #1 are posted on the website:
www.astro.umass.edu/~calzetti/astro100
n  Homework # 1 is due on Thu, Sept. 29th;
n  Homework # 2 starts on SPARK/OWL on Thu,
Sept 29th. It is due on Friday, Oct. 7th!
Next week:
q Quiz #2 is going to be on Tue Oct 4th!
It is based on Units: 6,7,8,10,11,12,13,14,15,19
q EXAM 1: on Thu, Oct. 6th!
Announcements - 2
n  Tips
1. 
2. 
3. 
4. 
5. 
for a successful exam:
Study all assigned units; use the problems at
the end of each unit to test your learning.
Attend class; ask questions.
Try to do Homework # 2 before the exam.
Review Homework # 1.
Review Quiz # 1 (posted on the web) and come
to Quiz # 2.
Quiz 1, Q. 9
n 
If you measure the angle between zenith and
Polaris to be 50 degrees, you must be located
at:
¨  0
degrees latitude
¨  50 degrees latitude
¨  40 degrees latitude
¨  0 degrees longitude
¨  50 degrees longitude
Quiz 1, Q. 9
n 
If you measure the angle between zenith and
Polaris to be 50 degrees, you must be located
at:
¨  0
degrees latitude
¨  50 degrees latitude
¨  40 degrees latitude
¨  0 degrees longitude
¨  50 degrees longitude
Quiz 1, Q. 3
n  Each
day, from a point of Earth north of
the equator, most stars appear to
¨ Remain
stationary overhead
¨ Rise in the East and set in the West
¨ Rise in the West and set in the East
¨ Move to the North
¨ Move to the South
Quiz 1, Q. 3
n  Each
day, from a point of Earth north of
the equator, most stars appear to
¨ Remain
stationary overhead
¨ Rise in the East and set in the West
¨ Rise in the West and set in the East
¨ Move to the North
¨ Move to the South
Today s Goals
1) To discuss Newton s Second Law
2) To introduce and discuss Newton s Third
Law
3) To start introducing Newton s
formulation of gravity (what keeps the
Universe together!)
Assigned Reading
Second half of Unit 14
n  Unit 15
n  First half of Unit 16
n 
Force
•  To change the momentum (or motion, or
state) of a body, you need a apply a force.
•  The force needs to be a `net force :
–  two people pushing equally against a box, but
from opposite directions, will produce no change
in the motion of the box.
–  Rephrased: their net force is zero.
•  The force can change the velocity, or the
direction of motion (or both).
Vocabulary Words
•  Speed is the distance traveled in each
second – it s measured in meters per
second (m/s).
•  Velocity is the speed in a particular
direction – it s measured in meters per
second (m/s).
•  Acceleration is the change in velocity in
each second – it s measured in meters per
second per second (or m/s2)
Acceleration
•  An acceleration is a
change in velocity
a = (Δ v) / (Δ t) .
•  Acceleration occurs when
either the magnitude or
direction of the velocity
(or both) are altered.
•  Uniform Circular Motion
is Accelerated Motion
How many ways can your car be accelerated?
Which of the following does NOT
describe an acceleration:
•  a car traveling with constant speed
around a bend
•  a car decreasing speed on a straight
road
•  a car traveling with constant speed on
a straight road
•  a planet traveling around a Sun
Newton s First Law (Law of Inertia)
can also be stated as:
•  In the absence of a net force, the
acceleration of an object must be zero
•  If an object is being accelerated, there
must be a net force exerting on it
Newton s Second Law
•  Acceleration is caused by force but also
related to the mass of the object
Force = Mass x Acceleration
F = m·a
Or
a = F/m
In other words: the same force applied to a bigger (more
massive) object imparts it a smaller acceleration
Survey Question
Two identical spacecraft are to be accelerated by
rockets. The first rocket fires with a force 4 times
as great as that of the second rocket. The
acceleration of the first rocket is _____ times as
great as the acceleration of the second rocket.
1)
2)
3)
4)
5)
1/4
1/2
the same
2 times
4 times
There must be a force acting
on the apple. What force?
There must be a force acting
on the apple. What force?
The force of gravity:
Our own planet s `pull on all
objects
The gravitational force on an object near
the surface of Earth is:
Fgrav = m·g
(g = 9.8m/s2)
Question: How do objects accelerate due
to the force of gravity?
Question: Should a heavy object fall
faster than a light one?
Yes
No
Question: Should a heavy object fall
faster than a light one?
Yes
No
The heavier object
feels a larger
force, but has also
larger inertia!
Newton s Third Law
n  For
every ACTION (I.e. application of a
force) there is an equal and opposite
REACTION (re-action)
F1 = -F2
Newton s Third Law
For any force that does not result in an
acceleration, there always is an equal
and opposite reaction force.
Newton s third law saves us from accelerating away
Box pushes down
on table due to gravity.
Table
pushes
back on
box
The Third Law: F1 = - F2
a=F/m
The lighter skater
receives the largest
acceleration
The two skaters pushing on each other exert opposite forces
Survey Question
Is the momentum (P= m v) of the two
skaters conserved?
Yes
No
Why?
Survey Question
Is the momentum (P= m v) of the two
skaters conserved?
Yes
No
Why?
Pbefore = 0
Pafter = m1 v1 + m2 v2 = 0
P1=m1v1
P2=m2v2 =-m1v1
Survey Question
You are a shuttle astronaut returning after attempting to fix the ISS
with a hammer. As you are jetting back to your shuttle, your
lifeline breaks, your jets run out of fuel, your radio goes dead, and
you miss the shuttle. To get back safely, you should:
1) use a swimming motion with your arms and legs
2) throw the hammer at the shuttle to get someone s attention
3) throw the hammer away from the shuttle
4) make a hammering motion in the direction of the shuttle
5) make a hammering motion away from the shuttle
What propels jets?
n  A
jet-propelled airplane moves forward.
Why?
It flaps its wings, like birds
¨  The fuel gasses from the jet engines expand
behind the jet and propel it forward
¨  The fuel gasses accelerate towards the back,
giving a forward reaction force to the jet
¨ 
What propels jets?
n  A
jet-propelled airplane moves forward.
Why?
It flaps its wings, like birds
¨  The fuel gasses from the jet engines expand
behind the jet and propel it forward
¨  The fuel gasses accelerate towards the back,
giving a forward reaction force to the jet
¨ 
Gravity
n  What
force is responsible for motions in
the universe?
n  What force makes objects fall?
n  What keeps us on the rotating Earth?
n  Why don’t planets move in straight lines,
but orbit around the Sun instead?