In reference to Newton’s 3 rd Law
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Transcript of In reference to Newton’s 3 rd Law
Physics 207: Lecture 7, Pg 1
"Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools." New York Times editorial, 1921, about Robert Goddard's revolutionary rocket work.
"Correction: It is now definitely established that a rocket can function in a vacuum. The 'Times' regrets the error." New York Times editorial, July 1969.
In reference to Newton’s 3rd Law
Physics 207: Lecture 7, Pg 2
Lecture 7 Goals:Goals:
Identify the types of forces
Use a Free Body Diagram to solve 1D and 2D problems with forces in equilibrium and non-equilibrium (i.e., acceleration) using Newton’ 1st and 2nd laws.
Distinguish static and kinetic coefficients of friction
Differentiate between Newton’s 1st, 2nd and 3rd Laws
Assignment: HW4, (Chapters 6 & 7)
Read Chapter 7
1st Exam Thursday, Oct. 7 from 7:15-8:45 PM Chapters 1-7
Physics 207: Lecture 7, Pg 3
Example Non-contact Forces
All objects having mass exhibit a mutually attractive force (i.e., gravity) that is distance dependent
At the Earth’s surface this variation is small so little “g” (the associated acceleration) is typically set to 9.80 or 10. m/s2
FB,G
Physics 207: Lecture 7, Pg 4
Contact (i.e., normal) Forces
Certain forces act to keep an object in place. These have what ever force needed to balance
all others (until a breaking point).
FB,T
Physics 207: Lecture 7, Pg 5
No net force No acceleration
FB,T Normal force is always to a surface
0
0
0net
y
x
F
F
amFF
FB,G
(Force vectors are not always drawn at contact points)
mgN
NmgFy
0
y
Physics 207: Lecture 7, Pg 6
No net force No acceleration
0net amFF
If zero velocity then “static equilibrium” If non-zero velocity then “dynamic equilibrium”
Forces are vectors
321net FFFamFF
Physics 207: Lecture 7, Pg 7
High Tension
A crane is lowering a load of bricks on a pallet. A plot of the position vs. time is
There are no frictional forces Compare the tension in thecrane’s wire (T) at the point it contacts the pallet to the weight (W) of the load (bricks+ pallet)
A: T > W B: T = W C: T< W D: don’t knowH
eigh
t
Time
Physics 207: Lecture 7, Pg 8
Analyzing Forces: Free Body DiagramA heavy sign is hung between two poles by a rope at
each corner extending to the poles.
Eat at Mickey’s
A hanging sign is an example of static equilibrium (depends on observer)
What are the forces on the sign and how are they related if the sign is stationary (or moving with constant velocity) in an inertial reference frame ?
Physics 207: Lecture 7, Pg 9
Free Body Diagram
Step two: Sketch in force vectorsStep three: Apply Newton’s 2nd Law (Resolve vectors into appropriate components)
mg
T1T2Eat at Mickey’s
T1
T2
mg
Step one: Define the system
Physics 207: Lecture 7, Pg 10
Free Body Diagram
Eat at Bucky’s
T1 T2
mg
Vertical : y-direction 0 = -mg + T1 sin1 + T2
sin2
Horizontal : x-direction 0 = -T1 cos1 + T2 cos2
Physics 207: Lecture 7, Pg 11
Scale Problem You are given a 1.0 kg mass and you hang it
directly on a fish scale and it reads 10 N (g is 10 m/s2).
Now you use this mass in a second experiment in which the 1.0 kg mass hangs from a massless string passing over a massless, frictionless pulley and is anchored to the floor. The pulley is attached to the fish scale.
What does the string do? What does the pulley do? What does the scale now read?
1.0 kg
10 N
?
1.0 kg
Physics 207: Lecture 7, Pg 12
Pushing and Pulling Forces String or ropes are examples of
things that can pull You arm is an example of an object
that can push or push
Physics 207: Lecture 7, Pg 13
Examples of Contact Forces:A spring can push
Physics 207: Lecture 7, Pg 14
A spring can pull
Physics 207: Lecture 7, Pg 15
Ropes provide tension (a pull)
In physics we often use a “massless” rope with opposing tensions of equal magnitude
Physics 207: Lecture 7, Pg 16
Moving forces around
Massless strings: Translate forces and reverse their direction but do not change their magnitude
(we really need Newton’s 3rd of action/reaction to justify)
Massless, frictionless pulleys: Reorient force direction but do not change their magnitude
string
T1 -T1
T1 -T1
T2
-T2| T1 | = | -T1 | = | T2 | = | T2 |
Physics 207: Lecture 7, Pg 17
Scale Problem You are given a 1.0 kg mass and you hang it
directly on a fish scale and it reads 10 N (g is 10 m/s2).
Now you use this mass in a second experiment in which the 1.0 kg mass hangs from a massless string passing over a massless, frictionless pulley and is anchored to the floor. The pulley is attached to the fish scale.
What force does the fish scale now read?
1.0 kg
10 N
?
1.0 kg
Physics 207: Lecture 7, Pg 18
What will the scale read?
A 5 NB 10 NC 15 ND 20 NE something else
Physics 207: Lecture 7, Pg 19
Scale Problem Step 1: Identify the system(s).
In this case it is probably best to treat each object as a distinct element and draw three force body diagrams. One around the scale One around the massless pulley (even
though massless we can treat is as an “object”)
One around the hanging mass
Step 2: Draw the three FBGs. (Because this is a now a one-dimensional problem we need only consider forces in the y-direction.)
?
1.0 kg
Physics 207: Lecture 7, Pg 20
Scale Problem
Fy = 0 in all cases 1: 0 = -2T + T ’ 2: 0 = T – mg T = mg 3: 0 = T” – W – T ’ (not useful here)
Substituting 2 into 1 yields T ’ = 2mg = 20 N(We start with 10 N but end with 20 N)
?
1.0 kg
? 1.0 kg
-mg
T
-T -T
-T ’
T”
W
1:2:3:T ’
Physics 207: Lecture 7, Pg 21
A “special” contact force: Friction
What does it do? It opposes motion (velocity, actual or that which
would occur if friction were absent!) How do we characterize this in terms we have learned?
Friction results in a force in a direction opposite to the direction of motion (actual or, if static, then “inferred”)!
maFFAPPLIED
ffFRICTION mgg
NN
ii
j j
Physics 207: Lecture 7, Pg 22
Friction...
Friction is caused by the “microscopic” interactions between the two surfaces:
Physics 207: Lecture 7, Pg 23
Static and Kinetic Friction Friction exists between objects and its behavior has been
modeled.
At Static Equilibrium: A block, mass m, with a horizontal force F applied,
Direction: A force vector to the normal force vector N N and the
vector is opposite to the direction of acceleration if were 0. Magnitude: f is proportional to the applied forces such that
fs ≤ s N
s called the “coefficient of static friction”
Physics 207: Lecture 7, Pg 24
Friction...
Force of friction acts to oppose motion: Parallel to a surface Perpendicular to a NNormal force.
maFF
ffF mgg
NN
ii
j j
Physics 207: Lecture 7, Pg 25
Sliding Friction: Quantitatively
Direction: A force vector to the normal force vector N N and the vector is opposite to the velocity.
Magnitude: ffk is proportional to the magnitude of N N
ffk = k N N ( = Kmg g in the previous example)
The constant k is called the “coefficient of kinetic friction” Logic dictates that S > K for any system
Physics 207: Lecture 7, Pg 28
Static Friction with a bicycle wheel You are pedaling hard
and the bicycle is speeding up.
What is the direction of the frictional force?
You are breaking and the bicycle is slowing down
What is the direction of the frictional force?
Physics 207: Lecture 7, Pg 30
Recap
Assignment: Soon….HW4 (Chapters 6 & 7, due 10/5) Read through first half of Chapter 7