gravity. 1600 to 1900 classical physics mechanics thermodynamics electromagnetism 1900 to 1940...
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1600to1900
ClassicalPhysics
Mechanics
Thermodynamics
Electromagnetism
1900to1940
ModernPhysics
RelativityLarge speeds (108 m/s).
Quantum MechanicsVery small scales (10-10 m).
1940topresent
CurrentPhysics
Particle Physics
Cosmology
Force / Motion Concept Map
Given some forces
1. F 2. m
1. Motion: r,v,a 2. F
Motion: r,v,a
Determine unknown forces
m
Vectors and component resolution
ENGINE
F = ma 1. Draw Picture. 2. Isolate Bodies. 3. Draw FBD. 4. Choose Axes. 5. Apply Fx = max Fy = may
6. Solve 7. Check
Special Cases 1. Constant v a = 0 v = r / t 2. Constant a a = v / t = F/m Example: ax=0, ay=-9.8m/s2 3. Motion in a circle ar = v2/r at = dv/dt
Models 1. Ropes massless and don't stretch. 2. Pulleys massless and frictionless. 3. Weight: Fg = mg 4. Equilibrium: F = 0 5. Friction: fs sn fk = kn f along common plane n common plane dimensionless materials parameter
v is slope of x vs t a is slope of v vs t
1. Motion: r,v,a 2. m
F and individual forces
INPUTS OUTPUTS
Constant Acceleration Kinematics
vxf = vxi + axt x = (vxi+vxf)t/2 x = vxit + axt
2/2 vxf
2 = vxi2 + 2axx
Work/Energy/Momentum Concept Map
E = ½mv2 + mgy + ½kx2
W = F•d W = Fdx = Area
I = Fdt = Area
d, v, F, m
d, v, x, y, F, m
pi, pf, vi, vf, t, Fav, m
Vectors and component resolution
ptot = mivi collisions
pi, pf, vi, vf, m,
Model Inputs Outputs
1. Draw Picture. 2. Label before and after with subscripts for different bodies and for before and after quantities. 3. Equate before and after quantities when quantity is conserved or use work theorems.
W = K always works Generally WNC = E, but E = 0 when only conservative forces ptot = 0 if Fext = 0 I = p always
Impulse approximation: ignore smaller external forces and conserve momentum. Friction model: fs sn and fk = kn
Theorems
Caveats to Universal Law
• Does 1/r2 hold to very small scales (~1 mm)?
• Is G(t)?• 3 Body Problem• General Relativity
Problem
Using Newton’s framework (Newton’s Laws) and the Universal Law of Gravity, find an expression for g (acceleration of gravity) at the surface of the Earth given ME, RE, and G.
13.3 Freefall Acceleration and the Gravitational Force
K2: Planets sweep out equal areas in equal times as the orbit the Sun.
K3: The square of the planet’s period is proportional to the cube of the planet’s semimajor axis (a). The semimajor axis is roughly the average distance of the planet from the Sun.
Squeak Demo
This question is asking about the dependence of the force of Earth’s gravity on mass. The force of the Earth on a mass m is directly proportional to m. F = mg = ma so a = g a constant. Common misconception - The student indicates that the gravitational force is the same magnitude for all objects near the earth. Correct answer
Common misconceptions - Objects in water have a smaller gravitational force by Earth because the water pushes up (e.g., the scale reading underwater is interpreted as a measure of the gravitational force) or Earth's pull on an object is a magnetic force or Earth's gravitational force of an object is proportional to the water pressure acting down on it. Correct answer
Common misconceptions - The student thinks the distance between objects does not affect the size of the gravitational force or the student does not understand the factors that affect the strength of the gravitational force. Correct answer
“Point” Mass Uniform Field near Earth’s Surface
Gravity Fields – Two Cases
mT
13.5 The Gravitational Field
k
r
^
^
M
13.7 Energy Considerations in Planetary and Satellite Motion
E = K + U is conserved because gravity is a conservative force (work is independent of the path).
For a circular orbit:
K = GMm/2r U = -GMm/r E = -GMm/2r
Note: K 0 K = |E| K = |U|/2
Thinking Map
Newton’s Laws: Calculate the acceleration of gravity at the Earth’s surface
Input Parameters: G, ME, RE
Output: g
Force Law(s): Universal Law
of Gravity
Reflect: How can this be used? Is it reasonable?
Simplifications: Earth uniform and perfect sphere, neglect air resistance
Mathematics: algebra
Generalizations: What is g(r)? Other planets?
What do I need to know?