Forces and the Laws of Motion
That which accelerates a mass
Non-zero forces always associated with a mass
Net force: vector sum
Balanced: vector sum is zero
Contact force: requires contact between objects to act
Noncontact force: acts through force fields
Inertia: a property of matter
Resist change in velocity (accelerations)
Equal to Mass of Object
Does not vary with location
Motion constant unless acted on by a net force
Net Force changes motion
Change in motion is proportional to the net force
Newton defined the change in motion as mass x velocity
We call this momentum
F = Dmv/Dt
F = ma
Unit: kg • m/s2 = Newton (N)
External: from environment
Internal: contained in object
temperature
Only external forces affect motion
Show all forces acting on body
Isolate body and align to geometry of problem
Draw forces as vectors. Show components if needed.
Indicate a coordinate system, the frame of reference
Show the positive direction
Draw diagrams
Whole problem
Freebody diagram for each object
Show forces as vectors
Concept: F = ma
Determine components of forces affecting motion
Combine forces as needed
Substitute values and solve
For each force on an object, the object exerts an equal but opposite force
Must be in contact
Effect of force determined by mass
Electromagnetic Force
Strong Force
Weak Force
Gravity
Dark (antigravity)
Strong: 1
EMF: 10-2
Weak: 10-13
Gravitational: 10-38
Dark: 10-?
Gravity
attractive force between masses
dependent on mass of body
follows inverse square rule
weakest force
mechanism unknown
Force on a planet is proportional to the square of its distance from the sun
derived from Kepler’s 1st law
F = constant • m/r2
(r is distance from center of Sun)
Observation of falling objects led to the conclusion that force was proportional to the mass of the object
F a m
Realized both objects attract
Combined observations
F a m1m2/r2
(r is distance between centers)
Added proportionality constant to calculate force
F = G(m1m2/r2)
Provided the 1st unification of theory
Kepler’s 3rd law can be derived from Newton's Law of Gravitation
Mass:
property of matter
amount of matter in object
does not vary with location
Weight:
force of gravity on mass
acts toward center of Earth
vary inversely with distance
vary directly with mass
W = GMem/r2
W also is ma. g used to represent acceleration from gravity \ mg = GMem/r2
g = GMe/r2
g = 9.80 m/s2
Gravitational: Balance mass against known weight
Inertial: move the mass and find ratio of unbalanced forces
Sixth Force:
Recent experiments find denser materials fall faster
Hypothesize a repellent force exists to account for difference
Interaction between charged particles
Like - repel; unlike - attract
1036 times as strong as gravity
positives and negatives balance
Responsible for:
strength
flexibility
support
combination of atoms
Force carrier: photon
Normally the number of protons is balanced by the number of electrons.
2 people next to each other with 1% more e- generate enough force to lift mass of earth.
Between Quarks and Baryons
Holds protons and neutrons together
Leftover strong force holds nucleus together
Decreases rapidly, mostly felt by adjacent particles
Force carrier: gluon
When number of protons too large:
repellent force of protons overcomes strong force
energy of strong force released as nuclear power
Interaction of particles in nuclear decay
Felt only by particles in decay
Force Carrier: W+, W-, Z
Related to electromagnetic force
Produced by dark energy (quintessence)
Has a negative pressure
Constant, equally distributed
Works against gravity
Described by some as negative from of gravity (symmetry w/other forces)
Universe starts expanding (Big Bang), Matter density is high
Gravity slows expansion
As universe expands matter density decreases
Dark Force accelerates expansion
Force surface exerts on an object placed on it
Act perpendicular to surface
Requires contact
Weight of object pushes on surface
Surface pushes back with FN
FN depends on fraction of W perpendicular to surface
FN still perpendicular to surface
W is directed toward center of Earth, only portion is perpendicular
Multiply W by sine or cosine to find FN
Weight is the effect of gravity
Apparent weight is FN
Acceleration inline with gravity changes FN
FN = mg + ma
A force on object by surface, parallel to surface
Surfaces must be in contact
Resists motion
Read Scientific American article on friction
Answer questions on the worksheet
Resists start of motion
Depends on:
Normal forces
Coefficient of Static Friction (ms)
Ff = msFN
Between moving surfaces
Resists motion, slows an object
Weaker than static friction
Depends on:
Normal force
Coefficient of kinetic friction
A pull on an object
Magnitude equal in both directions
T applied to a rope is passed to object
T is not affected by pulleys
System (object) has no acceleration
No net forces
SFx and Sfy are zero
Analyzing Equilibrium Situations
Object about which the most information is known.
If two or more objects are connected, it may be necessary to treat each object separately
Be sure to include only forces that act on the system.
Do each object separately
Do not include forces that the object exerts on its environment.
Resolve forces into components along axes
Apply equations 4.9a and 4.9b
Solve the equations for the unkowns
Net force is present
Follow same steps except