GravityGravity

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

13.1 Newton’s Universal Law of Gravity

Do 13-6

Caveats to Universal Law

• Does 1/r2 hold to very small scales (~1 mm)?

• Is G(t)?• 3 Body Problem• General Relativity

Concept Question 13.1

C.

A.

D.

B.

E.

13.2 Measuring the Gravitational Constant

G = 6.67 x 10-11 Nm2/kg2

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

13.4 Kepler’s Laws and the Motion of Planets

K1: Planet orbits about Sun are ellipses.

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

Show how to obtain the Universal Law from Kepler’s Third Law.

T2 = KSa3

Do P13.15 (p. 413)

Concept Question 13.2

C.

A.

D.

B.

E.

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

13.6 Gravitational Potential Energy

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

13.7 Energy Considerations in Planetary and Satellite Motion

Do 13.32, 13.34 and 13.51

Concept Question 13.3

total energy

C.

A.

D.

B.

E.

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?