GRAVITATIONAL FORCE

NEAR EARTH

Recap: Gravitational Force Field

Recall that gravity is an action-at-a-distance force that pulls on objects (regardless of their size or mass) without making any contact with them

This occurs because the Earth is surrounded by a gravitational force

A force field is a region of space surrounding an object that can exert a force on other objects

To represent the force field around Earth, we draw lines of force that point toward Earth’s centre

All of the vectors point toward Earth’s centre, and their magnitude indicate that the field becomes weaker as the distance from Earth’s centre increases

As discussed earlier, it is the “direction toward the centre” that defines what we mean by “downward” on Earth’s surface

Gravitational Field Strength

To determine the magnitude of Earth’s gravitational force field at a particular location near its surface, physicists use a quantity called gravitational field strength

The gravitational field strength is the force per kilogram (N/kg) acting on an object with a gravitational field

**at Earth’s surface, the gravitational field strength, on average, is 9.8 N/kg[down]

**recall that 1 N = kg-m/s2…….N/kg and m/s2 are the same

Gravitational Field Strength

Since Earth is not a perfect sphere, the magnitude

of the gravitational field strength at Earth’s surface

varies according to geographic location

For example, at the North Pole the gravitational

field strength is 9.8322 N/kg, whereas at the

equator it is 9.7805 N/kg

Gravitational Field Strength (copy)

Since the gravitational field strength and the acceleration due to gravity are numerically equal, the same symbol, , is used for both

Gravitational Field Strength ( )

Force per unit mass acting on an object in a gravitational field (N/kg)

Decreases as altitude increases

Varies according to location since Earth is not a perfect sphere

On Earth g = 9.8 N/kg or 9/8 m/s2

Gravitational Field Strength & Force of

Gravity

The gravitational field strength can be applied

using the equation for Newton’s second law of

motion, Fg = mg, to determine the force of gravity

acting on an object at Earth’s surface

(remember?)

Practice

1. The force of gravity on a 250 kg spacecraft on the moon’s surface is 408 N[down]

A) what is the gravitational field strength on the moon?

B) what is the acceleration due to gravity of a free-falling object on the surface of the moon?

2. A 50 kg person is standing on a bathroom scale inside an elevator. The scale is calibrated in newton’s. Use a FBD to help find the reading on the scale when the elevator is

A) at rest

B) moving up at a constant speed

C) accelerating up at 2.2 m/s/s

D) accelerating down at 3.0 m/s/s

Gravitational Field Strength – polar

ice caps

The huge masses of major polar ice caps, such as the one covering much of Greenland, have a large gravitational attraction on nearby ocean waters

As polar ice caps melt due to global warming, their gravitational attraction decreases, so they are unable to keep as much water near them

Thus, sea levels farther from the melting ice caps will rise more than the seal levels near the ice caps

The Difference Between Mass &

Weight

The terms “mass” and “weight” are used

interchangeably in everyday language, but these

two word have different meanings

*copy Mass (m) Weight (Fg)

-Quantity of matter in an

object (kg)

-Constant – only changes if the

quantity of matter changes

-Measured using a balance

-Measure of the force of

gravity acting on an object (N)

-Varies – depends on the

magnitude of g in that location

-Measured using a spring scale

Practice

1. An astronaut on the surface of Mars finds that a

rock accelerates at a magnitude of 3.6 m/s2 when

it is dropped. The astronaut also finds that a force

scale reads 180 N when the astronaut steps on it.

A) what is the astronauts mass as determined on the

surface of Mars?

B) What should the force scale read if the astronaut

stepped on it on Earth?

Free fall, Weightlessness &

Microgravity

Astronauts aboard the International

Space Station experience a sensation

often referred to as weightlessness

or microgravity while on the station

orbiting Earth

However, the term weightless and

microgravity are misleading because

they do not explain what is really

happening

Free fall, Weightlessness &

Microgravity

At the altitude where the space station

orbits Earth, the force of gravity acting

on the astronauts and the station is

about 90% of what it is on Earth’s

surface

With such a large force, microgravity

or weightlessness are not good

descriptions

Free fall, Weightlessness &

Microgravity

It was Newton who first saw the connection between falling objects, projectiles, and satellites in orbit

Imagine a large cannon on the top of a high mountain firing cannon balls horizontally at greater and greater speeds

At first the cannon ball falls quickly to the ground

As their initial speeds increase, the cannon balls travel farther and farther

At very high speeds, a new factor affects the distance

Since the Earth is round, the surface of landing curves downwards

Free fall, Weightlessness &

Microgravity

The cannonball must travel down and around before landing

When a certain critical speed is reached, the cannon ball’s path curves downward at the same rate as Earth’s curvature

The cannon ball is then said to be in orbit – a constant free fall, always falling toward Earth, but never landing

The space station and everything inside also undergo the same type of accelerated motion as the imaginary cannon ball does

Free Fall, Weightlessness &

Microgravity

When you jump from a height to the ground, you

momentarily experience free fall

Virtually no force is acting upward on you as the

force of gravity pulls you down toward Earth

However, the time interval is so short that the

sensation does not really have time to take effect

The interval of free fall or ‘weightlessness” is

extended for astronauts during

training

http://www.youtube.com/watch?v=v1VrkWb0l2M

Copy: Weightlessness or Micro Gravity

Terms often used to describe falling objects (and the

sensation)

Are misleading because gravity is still in effect

(needed by objects to keep them in orbit around

Earth)

A better explanation is “the object is experiencing

constant free-fall effect” (i.e. the object is falling

towards the Earth’s surface but never reaches it)

Practice

1. A 74 kg astronaut goes up to the ISS on a mission. During his stay, the gravitational field strength on the station is 8.6 N/Kg

A) what is the mass of the astronaut on the station?

B) what is the difference between the astronaut’s weight on Earth’s surface and his weight on the station?

C) why does the weight of the astronaut change but not his mass when moving from the surface of Earth to the station?

Wd

D) why does the astronaut appear weitghtless on the staton?

Text

Pg. 167, #5,6,7,10