Physics 1501: Lecture 15, Pg 1

Physics 1501: Lecture 15Physics 1501: Lecture 15TodayToday’’s Agendas Agenda

Midterm graded by next Monday (maybe …)

Homework #6: Due Friday Oct. 14 @ 11:00 AM

TopicsGravity (Chap.8)Review of Midterm I

Physics 1501: Lecture 15, Pg 2

Generalized Work Energy Theorem:Generalized Work Energy Theorem:

Suppose FNET = FC + FNC (sum of conservative and non-conservative forces).

The total work done is: WTOT = WC + WNC

The Work Kinetic-Energy theorem says that: WTOT = K. WTOT = WC + WNC = K WNC = K - WC

But WC = -U

So WNC = K + U = E

Physics 1501: Lecture 15, Pg 3

Conservative Forces Conservative Forces and Potential Energyand Potential Energy

We have defined potential energy for conservative forcesU = -W

But we also now that

W = Fxx

Combining these two,

U = - Fxx

Letting small quantities go to infinitessimals,

dU = - Fxdx

Or,

Fx = -dU/dx

Physics 1501: Lecture 15, Pg 4

New Topic - GravityNew Topic - Gravity Sir Isaac developed his laws of motion largely to explain observations

that had already been made of planetary motion.

Sun

Earth

Moon

Note : Not to scale

Physics 1501: Lecture 15, Pg 5

GravitationGravitation(Courtesy of Newton)(Courtesy of Newton)

Things Newton Knew,1. The moon rotated about the earth with a

period of ~28 days.2. Uniform circular motion says, a = 2R4. Acceleration due to gravity at the surface of

the earth is

g ~ 10 m/s2

5. RE = 6.37 x 106 m

6. REM = 3.8 x 108 m

Physics 1501: Lecture 15, Pg 6

GravitationGravitation(Courtesy of Newton)(Courtesy of Newton)

Things Newton Figured out,1. The same thing that causes an apple to fall from a tree to the ground is what causes the moon to circle around the earth rather than fly off into space. (i.e. the force accelerating the apple provides centripetal force for the moon)

2. Second Law, F = ma

So, acceleration of the apple (g) should have some relation to the centripetal acceleration of the moon (v2/REM).

Physics 1501: Lecture 15, Pg 7

Moon rotating about the Earth : Moon rotating about the Earth :

So = 2.66 x 10-6 s-1.

Now calculate the acceleration. a = 2R = 0.00272 m/s2 = .000278 g

Calculate angular velocity :

= v / REM = 2 REM / T REM = 2 / T

=

Physics 1501: Lecture 15, Pg 8

GravitationGravitation(Courtesy of Newton)(Courtesy of Newton)

Newton found that amoon / g = .000278 and noticed that RE

2 / R2 = .000273

This inspired him to propose the Universal Law of Gravitation:Universal Law of Gravitation:

|FMm |= GMm / R2

R RE

amoong

G = 6.67 x 10 -11 m3 kg-1 s-2

Physics 1501: Lecture 15, Pg 9

Gravity...Gravity...

The magnitude of the gravitational force FF12 exerted on an object having mass m1 by another object having mass m2 a distance R12 away is:

The direction of FF12 is attractive, and lies along the line connecting the centers of the masses.

R12

m1 m2FF12 FF21

Physics 1501: Lecture 15, Pg 10

Gravity...Gravity...

Compact objects:R12 measures distance between objects

Extended objects:R12 measures distance between centers

R12

R12

Physics 1501: Lecture 15, Pg 11

GravityGravity...... Near the earth’s surface:

R12 = RE

» Won’t change much if we stay near the earth's surface.

» i.e. since RE >> h, RE + h ~ RE.

RE

m

M

h FFg

Physics 1501: Lecture 15, Pg 12

Gravity...Gravity... Near the earth’s surface...

So |Fg| = mg = ma

a = g

All objects accelerate with acceleration g, regardless of their mass!

Where:

=g

Physics 1501: Lecture 15, Pg 13

Example gravity problem:Example gravity problem: What is the force of gravity exerted by the earth

on a typical physics student?

Typical student mass m = 55kgg = 9.8 m/s2.Fg = mg = (55 kg)x(9.8 m/s2 )

Fg = 539 NFFg The force that gravity exerts on any object is

called its Weight

W = 539 N