1. Forces (Part the First)
Chapter 5
Forces (Part the First)

2. Forces “A push or a pull” Can cause acceleration
Aristotelian (wrong) vs Newtonian (mostly right) mechanics
Limitations of Newtonian mechanics
Objects moving very fast (special relativity)
Very small objects (quantum mechanics)
Very small objects moving very fast (quantum field theory)
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3. Forces Unit: kg m/s2 [Newtons] Force is a vector quantity
Direction and magnitude
The sum of the forces on an object is Fnet
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4. The Four Fundamental Interactions
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5. The Practical Forces of Nature
Gravity
Restoring forces
Springs, etc.
Constraining forces
Tension, normal force
Dissipative forces
Friction, air resistance
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6. Newton’s 1st Law
If there are no forces acting on an object, the velocity of the object will not change
The “law of inertia”
An object in motion will remain in motion, and object at rest will remain at rest, until acted upon by an outside force
Then why do things seem to slow down when we stop pushing them?
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7. Newton’s First Law vs Hollywood
Is this possible?
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8. Inertial Reference Frame
A reference frame in which Newton’s laws hold
Non-accelerating
The earth is approximately an inertial reference frame
Rotation, motion around the sun/galaxy/universe
Coriolis effect
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9. Newton’s 2nd Law
The net force on a body is equal to the product of the body’s mass and the acceleration of the body
Can break force into components
Treat each direction independently
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10. What is Mass? Intrinsic property
NOT dependent on an objects size, weight or density
Proportionality constant between force and acceleration
Difference between pushing a tennis ball and a bowling ball
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11. Newton’s 3rd Law
When object A exerts a force on object B, object B exerts a force on object A of equal magnitude and opposite direction
“Action and reaction” A B
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12. Forces: Gravity
An object of mass m in freefall will experience a force:
Weight is equal to magnitude of Fg
A peculiarity in Halliday, Resnick, and Walker
Note: Mass is intrinsic, while weight depends on where you are. They are NOT the same thing.
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13. Demo: Newton’s Carts Two people push off each other
The force is the same in magnitude, opposite in direction
FB on A
FA on B A B
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14. Demo: Newton’s Carts Double the mass on one cart. What happens? A B
FB on A
FA on B A B
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15. Forces: Normal
“Normal” in the mathematical sense meaning perpendicular
When an object pushes against a surface, the surface pushes back perpendicular to its surface with a force N N Fg
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16. Forces: Friction
Force that resists motion when an object slides over a surface
Always opposite to the direction of motion
We’ll discuss more next chapter v
Ffr
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17. Forces: Tension Force exerted by a rope
Always points in the same direction as the rope
Ropes are assumed to be massless unless otherwise specified v T
Ffr
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18. Tension (Continued) T T 1. A rope can only pull (cannot push)
Frope
1. A rope can only pull (cannot push)
2. Objects at the ends of a taut rope have the same
magnitude velocity and acceleration T
3. Frictionless and massless
pulleys only change direction
of rope, not the tension.
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19. Free Body Diagrams The first step in solving any force problem:
Sketch the object in question
Draw an arrow for each force acting on the object
Label each force
Indicate the direction of acceleration off to the side (acceleration is NOT a force) F2 F1 a F3
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20. Net Force
A free body diagram is used to calculate the net force on one object.
Fnet= m a
Note: The two equal forces in Newton’s Third Law are on different objects. They don’t appear on the same free body diagram.
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21. How to Solve a Force Problem
Draw a free body diagram
Guess at forces of unknown magnitude or direction
Break forces into components
Sum of all the forces in one direction = mass * acceleration in that direction
i.e. Fnet,x=m ax
Repeat step 3 for each direction
Solve for unknown quantities
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22. Example: A Standing Person
Say a man has a mass of 60 kg. Find the normal force exerted on him by the ground.
Draw a diagram N
Fg=mg
a = 0
2) Sum the forces in the y direction
Note: We know the direction of the normal force from the diagram
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23. Example: A Standing Person
Now say our 60 kg man is jumping with a = 2 m/s2
Draw a diagram
a=2 m/s2 N
Fg=mg
2) Sum the forces in the y direction
Notice: The normal force is variable
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24. Example: Ring on a Table
Ring centered on round table and strings with weights are attached
0.5 kg
How much force is needed to balance forces so the ring stays centered (zero acceleration)?
30°
1 kg
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25. Solution: Draw a Free-Body Diagram
A free body diagram shows all the forces operating on a single object
9.8 N
4.9 N F1 F2 F3
F3,x
F3,y
30° q
We had to make an educated guess for where to put F3. If we guessed wrong, that’s OK. We will just pick up a minus sign
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26. Solution: Break Forces Into Components
F3,x
F3,y
30°
F1 :
F2 :
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27. Solution: Summing Forces
In the x-direction:
In the y-direction:
4.9 N
F1=9.8 N F2 F3
F3,x
F3,y
30°
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28. Solution: Does it work? The magnitude of F3 is: The angle of F3 is: q
F1=9.8 N F2 F3
F3,x
F3,y
30° q
The angle of F3 is:
Does it work?
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29. Pig on Frictionless Inclined Planeq a Fg
Assume the pig has a mass of m and the angle of the ramp is q. Find N and a.
Need to consider forces || and  to plane…
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30. Pig Forces: Break Into Components
Acceleration: θ N Fg a y x
Fg,y
Fg,x
Normal Force:
Gravity:
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31. Pig Forces: Sum Forces y-direction: x-direction: y N x a θ Fg,y Fg
Fg,x
x-direction:
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32. Pig on a Plane: Sanity Checkq a Fg
N = mg cos θ and a = g sin θ
θ =  a = 0 and N = mg
θ = 90°  a = g and N = 0
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33. Cart on a Plane
Now let’s add friction. A cart of mass m is stationary on an inclined plane of angle q.
Find Ffr and N. q
Ffr Fg N
a = 0
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34. Cart on a Plane: Components
Normal Force: N
Ffr
Fg,y Fg
Gravity: q
Fg,x x y
Friction:
Once again, use a “tilted” coordinate system
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35. Cart: Summing the Forces
y-direction: q
Ffr Fg N
Fg,y
Fg,x
x-direction:
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36. Does it Work?
If we replace the normal force and friction with another force, the cart should stay stationary after the ramp is removed.
The mass of the cart is 1 kg and the angle of the ramp is 30°
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37. It is now attached to another bowling ball. What does it read?
Tension
A 16 lb. bowling ball is hung from a rope attached to a scale which is attached to a wall. The scale reads 16 lbs.
It is now attached to another bowling ball. What does it read?
A) 0 B) 16 lbs C) 32 lbs
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38. Tension in Two Dimensions
Consider the mass: m mg T1
Summing forces:
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39. Tension in 2-D (Continued)
Consider the knot:
60o
30o T1 T2 T3 m
60o
30o T1 T3 T2
y-direction:
x-direction:
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40. Tension in 2-D (Continued)
What we know:
Jumping through the algebraic hoops (left as an exercise for the ambitious student):
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41. What happens when we accelerate?
Example: Fuzzy Dice
With no acceleration
Frope Fg
Fnet,y = may = 0
Frope- Fg = 0
Frope= -Fg = mg
What happens when we accelerate?
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42. Fuzzy Dice… Find q: e.g. a=g  θ=45° x direction: q Frope y direction:Fg
Frope q
x direction:
y direction:
e.g. a=g
 θ=45°
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43. Another Example: m1 m2 m1 m2 Find the acceleration of this system:
Start with free body diagrams of both blocks m1 m2 m1 FG N T a1 x y m2 T FG a2 x y q
Recall: a1 = a2 = a
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44. Solution: m1 Summing forces in the x direction: a1 T NFG N T a1 x y
Summing forces in the y direction:
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45. Solution m2 T FG a2 x y
Summing forces in the y direction:
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46. Solution What we have: The tensions must be equal to each other m1 m2
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47. Fan Cart With a Sail: Will It Move?
A) Yes, in the same direction as without the sail
B) Yes, in the opposite direction
C) No
D) No Clue
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