1. Chapter 4
Forces and Mass

2. Classical Mechanics Conditions when Classical Mechanics does not apply
very tiny objects (< atomic sizes)
objects moving near the speed of light

3. Newton’s First Law
If the net force SF exerted on an object is zerok the object continues in its original state of motion. That is, if SF = 0, an object at rest remains at rest and an object moving with some velocity continues with the same velocity.
Contrast with Aristotle!

4. Forces Usually think of a force as a push or pull Vector quantity
May be contact or field force

5. Contact and Field Forces

6. Fundamental Forces Types Characteristics Strong nuclear force
Electromagnetic force
Weak nuclear force
Gravity
Characteristics
All field forces
Listed in order of decreasing strength
Only gravity and electromagnetic in mechanics

7. Fundamental Forces Types Characteristics Strong nuclear force
Electromagnetic force
Weak nuclear force
Gravity
Characteristics
All field forces
Listed in order of decreasing strength
Only gravity and electromagnetic in mechanics

8. Strong Nuclear Force
QCD (Quantum chromodynamics) confines quarks to interior of protons and neutrons
Force between protons and neutrons responsible for formation of nuclei
QCD: Exchange of gluons
Nuclear Force: Exchange of pions

9. Electromagnetic Force
Opposites attract, like-signs repel
Electric force responsible for binding of electrons to atoms and atoms to each other
Magnetic forces arise from moving charges and currents
Electric motors exploit magnetic forces

10. Electromagnetic Force
Opposites attract, like-signs repel
Electric force responsible for binding of electrons to atoms and atoms to each other
Magnetic forces arise from moving charges and currents
Electric motors exploit magnetic forces

11. Weak Nuclear Force Involves exchange of heavy W or Z particle
Responsible for decay of neutrons

12. Gravity Attractive force between any two bodies
Proportional to both masses
Inversely proportional to square of distance

13. Inertia
Tendency of an object to continue in its original motion

14. Mass
A measure of the resistance of an object to changes in its motion due to a force
Scalar quantity
SI units are kg

15. Newton’s Second Law
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
F and a are both vectors

16. Units of Force SI unit of force is a Newton (N)
US Customary unit of force is a pound (lb)
1 N = lb
See table 4.1

17. Weight
The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object

18. Weight and Mass Mass is an inherent property
Weight is not an inherent property of an object
Weight depends on location

19. Newton’s Third Law
If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1.
Equivalent to saying a single isolated force cannot exist
For every action there is an equal and opposite reaction

20. Newton’s Third Law cont.
F12 may be called the action force and F21 the reaction force
Either force can be the action or the reaction force
The action and reaction forces act on different objects

21. Some Action-Reaction Pairs
n and n’
n is the normal force, the force the table exerts on the TV
n is always perpendicular to the surface
n’ is the reaction – the TV on the table
n = - n’

22. More Action-Reaction pairs
Fg and Fg’
Fg is the force the Earth exerts on the object
Fg’ is the force the object exerts on the earth
Fg = -Fg’

23. Forces Acting on an Object
Newton’s Law uses the forces acting on an object
n and Fg are acting on the object
n’ and Fg’ are acting on other objects

24. Applying Newton’s Laws
Assumptions
Objects behave as particles
ignore rotational motion (for now)
Masses of strings or ropes are negligible
Interested only in the forces acting on the object
neglect reaction forces

25. Problem Solving Strategy
Make a free-body diagram
Identify object (free body)
Label all forces acting on object
Resolve forces into x- and y-components, using convenient coordinate system
Apply equations, keep track of signs!

26. Examples of Mechanical Forces
Strings, ropes and Pulleys
Gravity
Normal forces
Friction
Springs (later in the book)

27. Some Rules for Ropes and Pulleys
When a rope is attached to an object, the force of the rope on that object is away from that object
The magnitude of the force is called the tension
The tension does not change when going over a pulley (if frictionless)

28. Equilibrium
An object either at rest or moving with a constant velocity is said to be in equilibrium
The net force acting on the object is zero

29. Do Cable Pull Demo

30. Example
Given that Mlight = 25 kg, find all three tensions
T3 = 245.3, T1 = kg, T2 = kg

31. Example a) Find acceleration b) Find T c) Find T3
d) Find force ceiling must exert on pulley
a) a=g/6, b) T = 57.2 N c) T3=24.5 N, d) Fpulley=2T = N

32. Inclined Planes
Choose x along the incline and y perpendicular to incline
Replace force of gravity with its components

33. Example
Find the acceleration and the tension
a = 4.43 m/s2, T= 53.7 N

34. Forces of Friction
Resistive force between object and neighbors or the medium
Examples:
Sliding a box
Air resistance
Rolling resistance

35. Sliding Friction Proportional to the normal force
Direction is parallel to surface and opposite other forces
Force of friction is nearly independent of the area of contact
The coefficient of friction (µ) depends on the surfaces in contact

36. Coefficients of Friction

37. Static Friction, ƒs f F ms is coefficient of static friction
n is the normal force f F

38. Kinetic Friction, ƒk f F mk is coefficient of kinetic friction
Friction force opposes F
n is the normal force F

39. Example
The man pushes/pulls with a force of 200 N. The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is For each case: What is the frictional force opposing his efforts?
What is the acceleration of the child?
f=59 N, a=4.7 m/s / f=29.1 N, a=5.7 m/s2

40. Example Given m1 = 10 kg and m2 = 5 kg:
a) What value of ms would stop the block from sliding?
b) If the box is sliding and mk = 0.2, what is the acceleration?
c) What is the tension of the rope?
ms = 0.5, a=1.96 m/s2

41. Example
What is the minimum ms required to prevent the sled from slipping down a hill of slope 30 degrees?
ms = 0.577

42. Example
You are calibrating an accelerometer so that you can measure the steady horizontal acceleration of a car by measuring the angle a ball swings backwards.
If M = 2.5 kg and the acceleration, a = 3.0 m/s2: a) At what angle does the ball swing backwards?
b) What is the tension in the string?
q = 17 deg T= 25.6 N q

43. Quiz, All Sections
1) What is your section number?

44. Quiz, Section 1 A only A and B only A, B and C only All statements
2) Which statements are correct? Assume the objects are static.
A) T1 must = T2
B) T2 must = T3
C) T1 must be < Mg
D) T1+T2 must be > Mg
A only
A and B only
A, B and C only
All statements
None of the statements
cos(10o)= sin(10o)=0.173

45. Quiz, Section 2 A only A and B only A, B and C only All statements
2) Which statements are correct? Assume the objects are static.
A) T1 must = T2
B) T2 must = T3
C) T1 must be < Mg
D) T1+T2 must be > Mg
A only
A and B only
A, B and C only
All statements
None of the statements
cos(10o)= sin(10o)=0.173

46. Quiz, Section 3 A only A and B only A, B and C only All statements
2) Which statements are correct? Assume the objects are static.
A) T1 must = T2
B) T2 must = T3
C) T1 must be < Mg
D) T1+T2 must be > Mg
A only
A and B only
A, B and C only
All statements
None of the statements
cos(10o)= sin(10o)=0.173