Board Work

1. A satellite revolves around its planet in a perfectly circular orbit at a constant speed.

a. At each of the four positions, draw a vector representing the net force on the satellite. Label all the force vectors F.

b. At each position, draw a vector to represent the satellite’s velocity. Label each vector v.

Board Work

c. Are all F vectors the same magnitude?

d. Are all v vectors the same magnitude?

e. What is the angle between F and v at any position of the satellite?

f. Is any component of F ever parallel to v?

g. Is the KE of the satellite varying or constant?

Gravity

The laws of physics are universal

What’s the point?

• Gravity is one of the fundamental forces.

Objectives

• Determine the gravitational attraction between objects.

• Interpret vector and field line depictions of gravitational fields.

Historical Background

• Earthly and celestial objects thought fundamentally different– Earthly objects seek a lowly position– Celestial objects move in perfect circles

Newton’s Insight

• The force pulling us to the ground is the same force curving the moon’s path: gravity!

Poll Question

Which is greater?

A. The pull of gravity from the earth on the moon.

B. The pull of gravity from the moon on the earth.

C. Both forces are equally strong.

D. Cannot tell without more information.

Newton’s Law of Universal Gravitation

Force between two objects:

F = Gm1m2

d2

m1, m2: masses of the objects

d: distance between objects’ centers of mass

G: universal gravitational constant, 6.672  10–11 Nm2/kg2

Properties of Gravity

F = Gm1m2

d2

• direction is toward the other object• magnitude decreases as (distance)2

increases• never becomes zero• infinite at zero separation (?!)

Poll Question

Two satellites orbit at the same distance from a planet. One has twice the mass of the other. How do their gravitational attractions to the planet compare?

A. They have the same attraction.

B. The massive satellite is attracted with twice the force of the light satellite.

C. The massive satellite is attracted with half the force of the light satellite.

Poll Question

Two satellites orbit at the same distance from a planet. One has twice the mass of the other. How do their gravitational accelerations toward the planet compare?

A. They have the same acceleration.

B. The massive satellite accelerates twice as much as the light satellite.

C. The massive satellite accelerates half as much as the light satellite.

Poll Question

When two objects are separated by a distance D, the gravitational force between them is F. If they move closer, to 1/2 the distance (D/2), the force becomes

A. F/2.

B. 2F.

C. 4F.

D. Cannot tell without more information.

D

F F

D/2

Gravitational Potential Energy

Work to bring two objects from separation to separation d:

• Negative because you must push against gravity to hold them

• The farther the d, the less negative the PE

PE = –Gm1m2

d

Escape Speed

• A fast enough object can “escape” a gravitational field.

• Can occur if KE + PEgrav > 0.

• Although gravity forever pulls it back, it never turns around!

Gravitational Field

F = m · field

• Gives the force acting on an object of mass m

• M = mass of object creating the field

• d = distance from the object

• field is a vector!

field = g =GM

d2

Group Work

2. Draw gravitational field vectors for all positions indicated. One is shown.

Poll Question

At which position is the satellite speeding up?

A. Position A.

B. Position B.

C. Position C.

D. Position D.

E. None of these.

Quick Question

At which position is the satellite slowing down?

A. Position A.

B. Position B.

C. Position C.

D. Position D.

E. None of these.

Poll Question

At which position is the satellite changing its direction but not its speed?

A. Position A.

B. Position B.

C. Position C.

D. Position D.

E. None of these.

Board Work

3. Rank the positions in descending order of:

a. Gravitational force.b. Acceleration.c. Speed.d. Kinetic energy.e. Gravitational potential

energy.f. Total energy.g. Angular momentum.

Gravity between Real Objects

The actual force acting on an object is the sum of all forces on all its particles from all the particles of the other object!

..

A Lucky Break

The gravitational field around a sphere is the same as would be around a point particle of the same mass at the center of the sphere.

Gravity on Earth

• G = 6.670  10–11 Nm2/kg2 • Earth’s mass = 5.976 1024 kg = M• Earth’s radius = 6378174 m = d• so the field g is

g = (6.670  10–11 Nm2/kg2 )(5.976 1024 kg )

(6378174 m )2

= 9.8 N/kg

look familiar?

Reading for Next Time

• Electric forces

• Big Ideas:– Electric charge– Coulomb’s force law– Electric fields

• representation by field vectors • representation by field lines

– Electric potential