TeXercises.com

Minimum energy to place Sputnik 1 into orbit

About points...

We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.

That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.

About difficulty...

We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

Physics Mechanics Gravitation

Physics Mechanics Work, Energy, Power

https://texercises.com/exercise/minimum-energy-to-place-sputnik-1-into-orbit/

Question

Solution

Short

Video

\(\LaTeX\)

Need help? Yes, please!

The following quantities appear in the problem: Masse \(m\) / Kraft \(F\) / Arbeit \(W\) / Geschwindigkeit \(v\) / Strecke \(s\) / Radius \(r\) / Winkelgeschwindigkeit / Kreisfrequenz \(\omega\) /

The following formulas must be used to solve the exercise: \(W = \int F(s)\,\text{d}s \quad \) \(F = G \dfrac{m_1m_2}{r^2} \quad \) \(F = m\dfrac{v^2}{r} \quad \) \(F = mr\omega^2 \quad \)

Hide help

No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!

Exercise:
The first artificial Earth satellite was the Soviet Sputnik . It had a mass of mO and reached a nearly circular orbit at an altitude of approximately hO above the Earth's surface in October . Calculate the minimum mechanical energy that the R- launch vehicle had to supply in order to place the satellite o this orbit.

Solution:
The satellite’s orbital period is determined by sscFZ &mustbe sscFG mromega^ fracGMmr^ omega sqrtfracGMr^ sqrtfracncG MR+h^ w T fracpiomega pi sqrtfracr^GM fracpiw T approx TmP ThP The energy that had to be supplied to the satellite has two components: kinetic energy and potential energy. The potential energy is: sscEpot _R^R+hfracGMmr^ mboxdr GMm leftfracR-fracR+hright Ep The kinetic energy of the satellite is: sscEkin frac mv^ frac mr^omega^ frac m R+h^ Ek So the satellite must have a total energy of: E sscEpot + sscEkin Ep + Ek E approx ES EP

Meta Information

\(\LaTeX\)-Code

Contained in these collections:

Arbeitsintegral und Gravitationsgesetz by TeXercises

5 | 5
Arbeitsintegrale 2 by uz

1 | 8

Asked Quantity: Energie \(E\) in Joule \(\rm J\)

Attributes & Decorations

Branches	Gravitation, Work, Energy, Power
Tags	arbeitsintegral, energie, gravitation, integralrechnung, kinetische energie, mechanik, physik, satellit, umlaufzeit, usa, zentripetalkraft
Content image
Difficulty	(3, default)
Points	4 (default)
Language	(English)
Type	Calculative / Quantity
Creator	uz
Decoration
File
Link