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Unbalanced forces

In this module, we begin a study of the influence of unbalanced forces acting on bodies along with a study of the motion produced in bodies as a result ofunbalanced forces.

Statics versus dynamics

The earlier modules dealt with statics . We now begin a study of dynamics . The study of dynamics hinges largely on three important laws of motion, which werestated by Sir Issac Newton in 1686.

Making bodies move

We know from experience that we can cause small bodies to move by pulling or pushing them with our hands. In other words, we can cause a body to move by exerting a force onthe body. We also know that larger bodies can be caused to move by pulling or pushing them with a machine or with a beast of burden.

We are also familiar with the idea of falling bodies that move independently of someone pushing orpulling. We have come to know this as the result of the gravitational attraction between masses.

Aristotle's contribution, or lack thereof

I have never forgotten my physics professor, Brother Rudolph, at St. Mary's University in San Antonio, Texas, telling the class that Aristotle was ahindrance to science.

Aristotle taught that heavier bodies fall faster than lighter bodies, but he was wrong. It has been proven that all bodies fall towards the earth at the sameacceleration when the effects of air resistance are eliminated.

This is not too difficult to prove for yourself. A small piece of paper will fall to the ground much moreslowly than a coin when the paper is in its normal state. However, if the paper is crumpled into a very tight ball, greatly reducing the effect of air resistance, itwill fall to the ground almost as fast as the coin.

Galileo's contribution

Galileo and Newton clarified the ideas of motion through a series of experiments. For example, Galileo discovered the important relationship between force andacceleration. He concluded that in the absence of air resistance, freely falling objects have the same acceleration regardless of their differing weights.

Acceleration of gravity is constant

By rolling balls down inclined planes, Galileo discovered that the distance covered under a steady force is proportional to the square of the time ofdescent. By this, he concluded that acceleration is constant, at least near the surface of the earth.

Two cannon balls

The story goes that Galileo dropped two cannon balls of different weights off the Leaning Tower of Pisa and observed that they struck the ground below atexactly the same time. From this, he concluded that falling bodies are subject to the same acceleration regardless of their weight.

Inertia

By rolling a ball down one inclined plane and up a facing incline plane, Galileo observed that the ball tended to rise to (almost) the original height on thesecond inclined plane. This was true even if the second incline plane was less steep than the first.

This suggested that if the second inclined plane were perfectly flat, the ball would roll forever trying to regain its original height. From this, Galileo issaid to have concluded that objects at rest tend to remain at rest, and objects in motion tend to remain in motion with the same velocity. (Recall that a changein direction is a change in velocity.)

Questions & Answers

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
what is the meaning
Dominic
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
×/×+9+6/1
Debbie
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
16
Makan
x=16
Makan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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