0.2 Force, momentum and impulse (Page 21/35)

Maths test

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a_{o} = \frac{F}{m_{o}}

So we substitute equation [link] into Equation [link] , and we find that

a_{o} = \frac{G m_{e}}{r^{2}}

Since it doesn't matter what $m_{o}$ is, this tells us that the acceleration on a body (due to the Earth's gravity) does not depend on the mass of the body. Thus all objects experience the same gravitational acceleration. The force on different bodies will be different but the acceleration will be the same. Due to the fact that this acceleration caused by gravity is the same on all objects we label it differently, instead of using $a$ we use $g$ which we call the gravitational acceleration.

Comparative problems

Comparative problems involve calculation of something in terms of something else that we know. For example, if you weigh 490 N on Earth and the gravitational acceleration on Venus is 0,903 that of the gravitational acceleration on the Earth, then you would weigh 0,903 x 490 N = 442,5 N on Venus.

Principles for answering comparative problems

Write out equations and calculate all quantities for the given situation
Write out all relationships between variable from first and second case
Write out second case
Substitute all first case variables into second case
Write second case in terms of first case

A man has a mass of 70 kg. The planet Zirgon is the same size as the Earth but has twice the mass of the Earth. What would the man weigh on Zirgon, if the gravitational acceleration on Earth is 9,8 m $\cdot$ s $^{- 2}$ ?

Determine what information has been given
The following has been provided:
- the mass of the man, $m$
- the mass of the planet Zirgon ( $m_{Z}$ ) in terms of the mass of the Earth ( $m_{E}$ ), $m_{Z} = 2 m_{E}$
- the radius of the planet Zirgon ( $r_{Z}$ ) in terms of the radius of the Earth ( $r_{E}$ ), $r_{Z} = r_{E}$
Determine how to approach the problem
We are required to determine the man's weight on Zirgon ( $w_{Z}$ ). We can do this by using:

$w = m g = G \frac{m_{1} \cdot m_{2}}{r^{2}}$

to calculate the weight of the man on Earth and then use this value to determine the weight of the man on Zirgon.
Situation on Earth
$\begin{matrix} w_{E} & = & m g_{E} = G \frac{m_{E} \cdot m}{r_{E}^{2}} \\ = & (70 kg) (9, 8 m \cdot s^{- 2}) \\ = & 686 N \end{matrix}$
Situation on Zirgon in terms of situation on Earth
Write the equation for the gravitational force on Zirgon and then substitute the values for $m_{Z}$ and $r_{Z}$ , in terms of the values for the Earth.

$\begin{matrix} w_{Z} = m g_{Z} & = & G \frac{m_{Z} \cdot m}{r_{Z}^{2}} \\ = & G \frac{2 m_{E} \cdot m}{r_{E}^{2}} \\ = & 2 (G \frac{m_{E} \cdot m}{r_{E}^{2}}) \\ = & 2 w_{E} \\ = & 2 (686 N) \\ = & 1 372 N \end{matrix}$
Quote the final answer
The man weighs 1 372 N on Zirgon.

A man has a mass of 70 kg. On the planet Beeble how much will he weigh if Beeble has mass half of that of the Earth and a radius one quarter that of the Earth. Gravitational acceleration on Earth is 9,8 m $\cdot$ s $^{- 2}$ .

Determine what information has been given
The following has been provided:
- the mass of the man on Earth, $m$
- the mass of the planet Beeble ( $m_{B}$ ) in terms of the mass of the Earth ( $m_{E}$ ), $m_{B} = \frac{1}{2} m_{E}$
- the radius of the planet Beeble ( $r_{B}$ ) in terms of the radius of the Earth ( $r_{E}$ ), $r_{B} = \frac{1}{4} r_{E}$
Determine how to approach the problem
We are required to determine the man's weight on Beeble ( $w_{B}$ ). We can do this by using:

$w = m g = G \frac{m_{1} \cdot m_{2}}{r^{2}}$

to calculate the weight of the man on Earth and then use this value to determine the weight of the man on Beeble.
Situation on Earth
$\begin{matrix} w_{E} & = & m g_{E} = G \frac{m_{E} \cdot m}{r_{E}^{2}} \\ = & (70 kg) (9, 8 m \cdot s^{- 2}) \\ = & 686 N \end{matrix}$
Situation on Beeble in terms of situation on Earth
Write the equation for the gravitational force on Beeble and then substitute the values for $m_{B}$ and $r_{B}$ , in terms of the values for the Earth.

$\begin{matrix} w_{B} = m g_{B} & = & G \frac{m_{B} \cdot m}{r_{B}^{2}} \\ = & G \frac{\frac{1}{2} m_{E} \cdot m}{{(\frac{1}{4} r_{E})}^{2}} \\ = & 8 (G \frac{m_{E} \cdot m}{r_{E}^{2}}) \\ = & 8 w_{E} \\ = & 8 (686 N) \\ = & 5 488 N \end{matrix}$
Quote the final answer
The man weighs 5 488 N on Beeble.

Questions & Answers

differentiate between demand and supply giving examples

Lambiv Reply

differentiated between demand and supply using examples

Lambiv

what is labour ?

Lambiv

how will I do?

Venny Reply

how is the graph works?I don't fully understand

Rezat Reply

information

Eliyee

devaluation

Eliyee

WARKISA

hi guys good evening to all

Lambiv

multiple choice question

Aster Reply

appreciation

Eliyee

explain perfect market

Lindiwe Reply

In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,

Ezea

What is ceteris paribus?

Shukri Reply

other things being equal

AI-Robot

When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab

Kelo

Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)

Kelo

yes,thank you

Shukri

Can I ask you other question?

Shukri

what is monopoly mean?

Habtamu Reply

What is different between quantity demand and demand?

Shukri Reply

Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded

Ezea

Shukri

how do you save a country economic situation when it's falling apart

Lilia Reply

what is the difference between economic growth and development

Fiker Reply

Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.

Shukri

production function means

Jabir

What do you think is more important to focus on when considering inequality ?

Abdisa Reply

any question about economics?

Awais Reply

sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏

Asui

it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs

Awais

thank you so much 👍 sir

Asui

In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p

Cornelius

Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .

Feyisa Reply

Answer

Feyisa

Jabir

the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema

Gsbwnw Reply

suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product

Abdureman

types of unemployment

Yomi Reply

What is the difference between perfect competition and monopolistic competition?

Mohammed

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Source: OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2

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