Download Gravitational Fields Gravity: is the fundamental attractive force that

Gravitational Fields
Gravity: is the fundamental attractive force that exists between
objects that have a mass.
Weight: is the force of gravity (mass times acceleration) where
acceleration is due to gravity and called g. So Fg = mḡ (where ḡ is the
acceleration due to gravity in m/s2.)
Remember, gravity changes from point to point and is NOT exactly
9.8 in all areas of the earth’s surface. So we call it a gravitational field.
A gravitational field is a region in space in which a mass experiences a
force of gravity. Gravitational fields cause gravitational forces on
masses in them.dd More specifically, objects experience forces when
in a gravitational field.
The intensity of the field is determined by the rate of the Force
exerted over mass.
ḡ = Fg
m
where
Fg is the force of gravity in Newtons
m is the mass in kg
ḡ is the gravitational field intensity in N/kg
The gravitational field intensity is different from point to point along
the earth’s surface, but can be generalised as 9.8 N/kg or 9.8 m/s2.
This is the gravitational field constant!
The gravitational field varies over the surface of the earth in relatively
predictable ways. The greater the distance a point is from the Earth’s
center of mass, the less force is exerted at that point.
Altitude: as the altitude increases, the gravitational field intensity
decreases.
For example, in a city such as Toronto, the gravitational field intensity
is about 9.8049 N/ kg where the altitude is 162 m above sea level
whereas on Mt. Everest the gravitational field intensity is 9.7647
N/kg.
Latitude: as the latitude increases, the gravitational field intensity
increases. Remember, the shape of the earth is elliptical – so it’s flat
on the top and bottom.
For example, at the North Pole the gravitational field intensity is
9.8322 N/kg whereas the gravitational field intensity at the equator is
9.7805 N/kg.
Mass and Weight:
Mass – is the amount of matter in an object (kg). It is scalar.
Weight – is the force of gravity exerts on an object (N). It is a vector
quantity – both magnitude and direction.
Example 1) Calculating Weights on the earth and on the moon.
Isaac has a mass of 50 kg and lives on Earth. Albert has a mass of 100
kg and magically lives on the moon. The gravitational field intensity
constant on earth is 9.8 m/s2 and the gravitational field intensity
constant on the moon is 1.6 m/s2. Who weighs more?
True Weightlessness
According to the relationship we have established for weight, Fg = mḡ,
if there is no gravitational field, then the Force of gravity (weight) is
zero. An object is weightless at a given location if the force of gravity
on the object is 0 N, so if the mass is zero or the gravitational field
intensity is zero.
Apparent Weight
The normal force is referred to as the apparent weight.
Draw a free-body diagram of a person in an elevator that is stopped.
Draw a free-body diagram of a person in an elevator as it is
accelerating upward.
Draw a free-body diagram of a person in an elevator that has reached
its maximum velocity upward (constant velocity)
Draw a free-body diagram of a person in an elevator as it slows down
to a stop on the top floor.
Example 2) Apparent Weight in an elevator as it accelerates upward.
A person has a mass of 65 kg and is ascending in an elevator that is
accelerating at 3.00 m/s2. What is the apparent weight of this
person?
Notice Fn and Fg are not going to be equal!
Example 3) Apparent Weight in an elevator as it accelerates
downward.
A person has a mass of 65 kg and is descending in an elevator that is
accelerating at -3.00 m/s2. What is the apparent weight of this
person?
Apparent weightlessness
An astronaut experiences APPARENT weightlessness. They are still
within the influence of the earth’s gravitational field. The spacecraft
is accelerating and freely falling towards the earth so it appears as
though the astronauts are experiencing we
Gravitational Fields
Gravity: is the fundamental attractive force that exists between objects that have a mass.
Weight: is the force of gravity (mass times acceleration) where acceleration is due to gravity and called
g. So Fg = mḡ (where ḡ is the acceleration due to gravity in m/s2.)
Remember, gravity changes from point to point and is NOT exactly 9.8 in all areas of the earth’s surface.
So we call it a gravitational field.
A gravitational field is a region in space in which a mass experiences a force of gravity. Gravitational
fields cause gravitational forces on masses in them More specifically, objects experience forces when in
a gravitational field.
The intensity of the field is determined by the rate of the Force exerted over mass.
ḡ = Fg
m
where
Fg is the force of gravity in Newtons
m is the mass in kg
ḡ is the gravitational field intensity in N/kg
The gravitational field intensity is different from point to point along the earth’s surface, but can be
generalised as 9.8 N/kg or 9.8 m/s2. This is the gravitational field constant!
The gravitational field varies over the surface of the earth in relatively predictable ways. The greater the
distance a point is from the Earth’s center of mass, the less force is exerted at that point.
Altitude: as the altitude increases, the gravitational field intensity decreases.
For example, in a city such as Toronto, the gravitational field intensity is about 9.8049 N/ kg where the
altitude is 162 m above sea level whereas on Mt. Everest the gravitational field intensity is 9.7647 N/kg.
Latitude: as the latitude increases, the gravitational field intensity increases. Remember, the shape of
the earth is elliptical – so it’s flat on the top and bottom.
For example, at the North Pole the gravitational field intensity is 9.8322 N/kg whereas the gravitational
field intensity at the equator is 9.7805 N/kg.
Mass and Weight:
Mass – is the amount of matter in an object (kg). It is scalar.
Weight – is the force of gravity exerts on an object (N). It is a vector quantity – both magnitude and
direction.
Example 1) Calculating Weights on the earth and on the moon.
Isaac has a mass of 50 kg and lives on Earth. Albert has a mass of 100 kg and magically lives on the
moon. The gravitational field intensity constant on earth is 9.8 m/s2 and the gravitational field intensity
constant on the moon is 1.6 m/s2. Who weighs more?
True Weightlessness
According to the relationship we have established for weight, Fg = mḡ, if there is no gravitational field,
then the Force of gravity (weight) is zero. An object is weightless at a given location if the force of gravity
on the object is 0 N, so if the mass is zero or the gravitational field intensity is zero.
Example 2) Apparent Weight in an elevator as it accelerates upward.
A person has a mass of 65 kg and is ascending in an elevator that is accelerating at 3.00 m/s 2. What is
the apparent weight of this person?
Notice Fn and Fg are not going to be equal!
Example 3) Apparent Weight in an elevator as it accelerates downward.
A person has a mass of 65 kg and is descending in an elevator that is accelerating at -3.00 m/s2. What is
the apparent weight of this person?
Apparent weightlessness
An astronaut experiences APPARENT weightlessness. They are still within the influence of the earth’s
gravitational field. The spacecraft is accelerating and freely falling towards the earth so it appears as
though the astronauts are experiencing weightlessness.
Learning Activity 4.2
1. A vehicle is being designed to explore the moon’s surface and is being tested on earth, where it
weighs roughly six times more than it will on the moon. In one test, the acceleration of the
vehicle is measured. To achieve the same acceleration on the moon, will the net force acting on
the vehicle be greater, less than, or the same as that required on earth?
2. If a person has a mass of 60 kg on earth, what is his/her mass on the moon? Explain.
3. The gravitational field constant on the surface of Pluto is 0.31 N/kg. What would the gravitational
force be on a person of mass 50 kg on Pluto?
4. A space traveller whose mass is 115 kg leaves earth.
a. What are is mass and weight on earth?
b. What are his mass and weight in interplanetary space where there are nearby planetary
objects?
5. What are two factors that affect the gravitational field intensity at the surface of the earth? How
does each factor affect the value of the gravitational field intensity?
6. If you are floating in the Dead Sea (in Israel) that is below sea level, how would your weight be
different from your weight at the top of a mountain in the Andes? (South America)
7. If you are sunning yourself in Mexico, how is your weight different than if your freezing your
hiney in Winnipeg this Christmas?
8. Under what conditions can true weightlessness be experienced? Under what conditions can
apparent weightlessness be experienced?
9. What is apparent weight?
a. When is the apparent weight equal to the true weight of an object?
b. When is the apparent weight less than the true weight of an object?
c. When is the apparent weight greater than the true weight of an object?
10. A 75 kg person stands in an elevator. What will be the force the apparent weight of the person in
each of the following situations?
a. The elevator is at rest
b. The elevator is moving downward with a uniform acceleration of -2 m/s2.
c. The elevator moving upward with a uniform acceleration of 2 m/s2.
d. The elevator is moving upward with a uniform velocity of 1.5 m/s.