1. Goals: Lecture 7 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
1st Exam Thursday, Oct. 6 from
7:15-8:45 PM Chapters 1-7(light) 1

2. Chaps. 5, 6 & 7 What causes motion
Chaps. 5, 6 & 7 What causes motion? (actually changes in motion) What kinds of forces are there ? How are forces & changes in motion related? 1

3. Newton’s First Law and IRFs
An object subject to no external forces moves with constant velocity if viewed from an inertial reference frame (IRF).
If no net force acting on an object, there is no acceleration.
The above statement can be used to define inertial reference frames.

4. IRFs
An IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”.
If one IRF exists, infinitely many exist since they are related by any arbitrary constant velocity vector!
In many cases (i.e., Chapters 5, 6 & 7) the surface of the Earth may be viewed as an IRF

5. No net force  No acceleration
If zero velocity then “static equilibrium”
If non-zero velocity then “dynamic equilibrium”
Forces are vectors

6. Newton’s Second Law
The acceleration of an object is directly proportional to the net force acting upon it.
The constant of proportionality is the mass.
This is a vector expression: Fx, Fy, Fz
Units
The metric unit of force is kg m/s2 = Newtons (N)
The English unit of force is Pounds (lb)

7. 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

8. Contact (e.g., “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).
Here: A contact force from the table opposes gravity,
Normal force is perpendicular to the surface.
FB,T

9. No net force  No acceleration
(Force vectors are not always drawn at contact points)
FB,G y
FB,T Normal force is always  to a surface

10. 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 the
crane’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 know
Height
Time

11. Important notes
Many contact forces are conditional and, more importantly, they are not necessarily constant
We have general idea of forces from everyday life.
In physics the definition must be precise.
A force is an action which causes a body to accelerate.
(Newton’s Second Law)
On a microscopic level, all forces are non-contact

12. Analyzing Forces: Free Body Diagram
A heavy sign is hung between two poles by a rope at each corner extending to the poles.
Eat at Bucky’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 ?

13. Step one: Define the system
Free Body Diagram
Step one: Define the system T2 T1 q1 q2
Eat at Bucky’s T2 T1 q1 q2 mg
Step two: Sketch in force vectors
Step three: Apply Newton’s 2nd Law
(Resolve vectors into appropriate components) mg

14. Free Body Diagram T1 T2 q1 q2 Eat at Bucky’s mg Vertical :
y-direction = -mg + T1 sinq1 + T2 sinq2
Horizontal :
x-direction = -T1 cosq1 + T2 cosq2

15. Scale Problem
You are given a 5.0 kg mass and you hang it directly on a fish scale and it reads 50 N (g is 10 m/s2).
Now you use this mass in a second experiment in which the 5.0 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?
50 N
5.0 kg ?
5.0 kg

16. 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

17. Examples of Contact Forces: A spring can push

18. A spring can pull

19. Ropes provide tension (a pull)
In physics we often use a “massless” rope with opposing tensions of equal magnitude

20. Moving forces around string T1 -T1 T2 T1 -T1 -T2
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 T2 T1
-T1
-T2
| T1 | = | -T1 | = | T2 | = | T2 |

21. Scale Problem
You are given a 5.0 kg mass and you hang it directly on a fish scale and it reads 50 N (g is 10 m/s2).
Now you use this mass in a second experiment in which the 5.0 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?
50 N
5.0 kg ?
5.0 kg

22. What will the scale read?
A 25 N
B 50 N
C 75 N
D 100 N
E something else

23. 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.) ?
5.0 kg

24. Scale Problem T ’ 3: 2: 1: T” T -T -T W -T ’ -mg ? ?
1.0 kg T ? -T -T W ?
-T ’
-mg
S 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 = 100 N
(We start with 50 N but end with 100 N)
5.0 kg

25. Home Exercise, Newton’s 2nd Law
A woman is straining to lift a large crate, without success. It is too heavy. We denote the forces on the crate as follows:
P is the upward force being exerted on the crate by the person
C is the contact or normal force on the crate by the floor, and
W is the weight (force of the earth on the crate).
Which of following relationships between these forces is true, while the person is trying unsuccessfully to lift the crate? (Note: force up is positive & down is negative)
P + C < W
P + C > W
P = C
P + C = W

26. 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”)! j N
FAPPLIED i ma
fFRICTION mg

27. If no acceleration No net force
So frictional force just equals applied force
Key point: It is conditional! j N
FAPPLIED i
fFRICTION mg

28. Friction...
Friction is caused by the “microscopic” interactions between the two surfaces:

29. Friction: Static friction
Static equilibrium: A block with a horizontal force F applied,
As F increases so does fs
S Fx = 0 = -F + fs  fs = F
S Fy = 0 = - N + mg  N = mg F m1
FBD fs N mg

30. Recap Assignment: Soon….HW4 (Chapters 6 & 7, due 10/4)
Read through first half of Chapter 7