For Exercises 131-132, refer to the formula F = G m 1 m 2 d 2 . This gives the gravitational force F (in Newtons, N) between two masses m 1 and m 2 (each measured in kg) that are a distance of d meters apart. In the formula, G = 6.6726 × 10 − 11 N-m 2 /kg 2 . Determine the gravitational force between the Earth mass = 5.98 × 10 24 kg and an 80-kg human standing at sea level. The mean radius of the Earth is approximately 6.371 × 10 6 m .
For Exercises 131-132, refer to the formula F = G m 1 m 2 d 2 . This gives the gravitational force F (in Newtons, N) between two masses m 1 and m 2 (each measured in kg) that are a distance of d meters apart. In the formula, G = 6.6726 × 10 − 11 N-m 2 /kg 2 . Determine the gravitational force between the Earth mass = 5.98 × 10 24 kg and an 80-kg human standing at sea level. The mean radius of the Earth is approximately 6.371 × 10 6 m .
Solution Summary: The author explains the formula used to calculate the gravitational force between the Earth and a human weighing 80kg.
For Exercises 131-132, refer to the formula
F
=
G
m
1
m
2
d
2
.
This gives the gravitational force
F
(in Newtons, N) between two masses
m
1
and
m
2
(each measured in kg) that are a distance of
d
meters apart. In the formula,
G
=
6.6726
×
10
−
11
N-m
2
/kg
2
.
Determine the gravitational force between the Earth
mass
=
5.98
×
10
24
kg
and an 80-kg human standing at sea level. The mean radius of the Earth is approximately
6.371
×
10
6
m
.
Consider the current flow of electricity within an electrical circuit. The formula of Ohm's Law says that when electric current is flowing through a
resistor, the current i (measured in amps) can be calculated from the voltage v (measured in volts) and the resistance R of the resistor (measured in
ohms).
Complete Part (a) and Part (b) using the given formula:
R
Part (a). The resistor in a radio circuit was measured to be 5000 ohms.
I. What is the formula for the current i in the radio circuit?
Use lower-case letter v for voltage.
IL. Select the graph of your formula for i versus v.
2.5
1.5
1.5
0.5
05
3000 4000 5000 6000
1000 2000 3000 4000 s000 6000
OGraph 1
OGraph 2
25
2.5
1.5
1.5
0.5
0.5
1000 2000 3000 4000 5000 6000
1000 2000 3000 4000 5000 6000
OGraph 3
OGraph 4
II. What happens to the current when voltage increases?
O As the resistance increases, so does the current.
A
O As the voltage increases, so does the resistance.
As the voltage increases, so does the current.
Part (b). The…
Use the weight of the rocket to answer the question. (Use 4000 miles as the radius of Earth and do not consider the effect of air resistance.)
3-ton rocket
(a) How much work (in mile-tons) is required to propel the rocket an unlimited distance away from Earth's surface?
mile-tons
(b) How far (in mi) has the rocket traveled when half the total work has occurred?
mi
A stone is thrown straight up from the edge of a roof, 625 feet above the ground, at a
speed of 14 feet per second.
A. Remembering that the acceleration due to gravity is -32 feet per second squared,
how high is the stone 4 seconds later?
B. At what time does the stone hit the ground?
C. What is the velocity of the stone when it hits the ground?
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY