Name
LESSON
8-1
Date
Class
Challenge
Scientific Variations
Many physical situations can be modeled with variation functions that
involve both direct and inverse relationships. These relationships may also
include exponents. Consider the following relationships.
Newton’s Law of Gravity states that any two objects have a gravitational
force between them that is directly proportional to the product of their
masses and inversely proportional to the square of the distance between
them.
1. Write Newton’s Law of Gravitation using F for the
gravitational force, m 1 and m 2 for the masses, G
for the constant of proportionality, and r for the
distance between the objects.
2. If two objects of mass 1.0 kg and 2.0 kg located
1.0 m apart exert a gravitational force of
1.3333 ⫻ 10 ⫺10 N on each other, what is the value
of the gravitational constant?
Gm 1 m 2
F ⫽ ________
r2
About 6.67 10
3. What is the gravitational force between two football
players with masses of 115 kg and 130 kg who
are lined up 1.5 m from one another?
11
5. If the voltage remains constant, how can the
amount of heat produced by the element be tripled?
6. If the resistance remains constant, how can the amount
of heat produced by the element be quadrupled?
2
About 4.43 10 7 N
The heat generated by an electric stove element varies directly
as the square of the voltage and inversely as the resistance.
4. Write an equation to model the relationship for the
heat generated by the stove element.
2
Nm per kg
2
kv
H ____
r
Reduce the resistance by a
1.
factor of __
3
Double the voltage.
The frequency, F, of a vibrating guitar string is directly proportional
to the square root of the tension, T, on the string and inversely
proportional to the length, L, of the string.
7. Write an equation to model the frequency of a
guitar string.
8. If both the tension on the string and the length are
doubled, what happens to the frequency?
T
k
兹
______
F
L
It would increase by a factor
of 兹 2 .
9. You want to modify your guitar so that you can play bass guitar. What are two
ways to cut the frequency of a string in half?
The length could be doubled or the tension cut by a factor of 4.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Holt Algebra 2
12/26/05 6:31:40 AM