Download Nature`s Forces, F due to Gravity, and Grav. Field

Name: _____________________ ____________________
Period: ____
Date: _____________________
Dynamics:
Forces of Nature and Gravity
-
There are only 4 different natural forces. “Natural forces” are those that can exist anywhere in the
universe.
o
o
o
o
-
Gravity is the weakest force but has shaped the universe due to it having the longest range.
The Force of Gravity
All masses are surrounded by a gravitational force field. The
Force of gravity per
1.0 kg mass on
surface
greater the mass, the ________________the gravitational
force. The table at the right compares the gravitational forces
Mass of Earth
5.98 x 1024 kg
9.8 Newtons
on the surfaces of the Earth and moon.
Mass and Weight: recall the important distinction between
the mass and weight of an object. Mass is a measure of the
Radius of Earth
6.38 x 106 m
Mass of Moon
7.35 x 1022 kg
amount of _____________________ there is in an object and is
measured in kilograms. Weight, however, is the measure of
Radius of Moon
1.74 x106 m
____________________ ____________________
on an object and is measured in ___________________. Thus,
when you go from Earth to the moon, your mass stays
constant, while your weight reduces to about 1/6th of your Earth
weight.
The relationship between mass and weight is given by the formula
Fg = mg
Fg is the force of gravity (i.e., weight) on an object measured in Newtons
m is its mass in kg
g is the gravitational field strength of 9.8 N/kg which results in an
acceleration of 9.8 m/s2 near the Earth’s surface (sea level)
1.6 Newtons
The changing values of “g” can be seen in the following table.
Location
Equator
Value of “g”
9.781 m/s2 or
N/kg
9.832 m/s2 or
N/kg
north or south pole
Location
6400 km above Earth’s surface
surface of the moon
Value of “g”
2.45 m/s2 or
N/kg
1.60 m/s2 or
N/kg
Sample Questions
Q1. On the surface of Earth, the mass of an object is
6.3 grams. What is its weight in Newtons?
Q2. Calculate the mass, in kg, of an object which has
a weight of 35 N on the moon. The value of “g”
on the moon is 1.6 m/s2.
The Law of Universal Gravitation
The force of gravity between two objects is as follows:
F is __________________________________________________________
m1 and m2 are __________________________________________________
d is __________________________________________________________
G is the ____________________ ____________________ of 6.67 x 10-11 Nm2/kg2
Sample Questions
Ex. 1. Calculate the weight (force of gravity) on a 75 kg person near sea level on Earth using the above formula
and the Earth’s data from the first page.
Ex. 2. An object on our moon is attracted towards the moon by a 320 N
force. What is the object’s mass?
Ex. 3. Calculate the gravitational field strength, “g,” on Mercury, which has a mass of 3.303 x1023 kg and a
radius of 2,440 km.
Some Confusing Things About Units
MKS units
There are, in fact, many different units of force. Three common units are newtons, dynes, and pounds.
In physics 11/12, we will focus on a system of units based on the fundamental units of the Meter,
Kilogram, and Second, or MKS for short. Therefore, when a force is measured in newtons, distances
should be measured in _______________, mass in ________________, and time in ________________.
A force in “pounds” is used in the English system where distance is measured in feet, mass in slugs and time in
seconds. A force measured in “dynes” uses the centimeter, gram, and second as its fundamental units (CGS
units).
Blaise Pascal
Equivalent Units
Units like “Newtons,” “Pascals (pressure), or “Joules” (energy) are not fundamental units
(e.g., kg, meters, and seconds), but rather, special unit names usually given to honour
famous scientists of the past (i.e., Isaac Newton, Blaise Pascal, and James Joule). All
special unit names have fundamental unit equivalents. The fundamental units of force can be obtained from
weight <==> mass conversion formula Fg = mg. A rule of any formula is that the units of the left hand side of
the equal sign MUST be the same as the units on the right hand side.
Therefore:
Incorrect Units
Unfortunately, the general public incorrectly uses kilograms to indicate weight. Weigh scales are incorrectly
calibrated in kilograms (instead of ____________________).
Summary
Please re-read the notes package on your own (or with a partner ) and come up with your own summary.
Exercises 4.1 (Forces and Gravity)
1. Define a "force".
_____________________________________________________________________________________
2a Scientists believe that there are only four "natural" forces in the universe. These are:
1)______________________________________ 2) _______________________________________
3) _________________________________________ 4) _______________________________________
2b Two of the above forces are probably not very familiar to you. Where do these two little known forces
act?
_____________________________________________________________________________________
3. Distinguish between the terms "mass" and "weight". Use an example which clearly shows the difference
between the two.
Mass: ________________________________________________________________________________
Weight: ______________________________________________________________________________
Example ______________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
4a The gravitational acceleration constant "g" is also called the "gravitational field strength" because it is
related to the strength of the force of gravity. How does the value of "g" change relative to the height
above the surface of the Earth?
_____________________________________________________________________________________
_____________________________________________________________________________________
4b Explain why the value of "g" is slightly larger at the poles compared to the equator?
_____________________________________________________________________________________
_____________________________________________________________________________________
5. What is the formula used to convert between mass and weight? _________________________________
6a What is meant by the “MKS” system of units?
_____________________________________________________________________________________
_____________________________________________________________________________________
6b The “Newton” is a special unit name of force. What are the equivalent fundamental units of force?
_____________________________________________________________________________________
6c As you know, the fundamental units of “g” are m/s2. But “g” also has a set of equivalent units. From the
equation Fg = mg, g can be isolated as g =
Fg
. Using this form of the equation what are alternate units
m
for “g”?
____________________________
6d In the MKS system, the unit of Energy is the “joule”. Energy is also defined by the formula
E = Fd (Energy = force x distance). Using this equation and your answer to question 6b, determine the
fundamental units of energy.
____________________________
7. Calculate the weight , in newtons, of...
a) a 50 kg bag of sugar
b) a 75 gram pen.
c) At the equator "g" has a value of 9.781; at the north pole its value is 9.832. What is the difference in weight
between an 85.0 kg person at the North pole and an 85.0 kg person at the equator?
8) Calculate the mass, in kilograms, of...
a) a 500 Newton bale of hay.
b) 6.5 N.
9) A 250 kg spacecraft weighs 2.04x103 N on the
surface of the Mars. What is the value of "g" on
the Mars?
10. A 20 kg object out in space is attracted to the
Earth by a force of gravity of 100 N. What is the
rate of acceleration of this object toward the
Earth in free fall?
11) A 1250 kg spacecraft is 6.38 x 107 m from the
center of the Earth. What is the force of gravity
between the craft and Earth ?
12. Calculate the force of gravity between two 2575
kg asteroids 50.0 cm apart? What is the force
when they are 5.00 cm apart? How much
stronger as a ratio is the force when the distance
is a tenth?
Answers: 6c) N/kg, 6d) kg.m2/s2 , 7a) 490 N, 7b) 0.74 N, 7c) 4.3 N, 8a) 51 kg
8b) 0.66 kg, 9) 8.16 m/s2, 10) 5.0 m/s2. 11) 122 N 12) 1.77 x 10-3, 1.77 x 10-1, 100