4. DYNAMIKA: Tarcie. Praca, moc, energia - odpowiedzi

4.1. a)

ܨ

ு

=

௠௏

భ

௧

భ

;

b)

ܨ

ு

=

௠௏

భ

௧

మ

4.2.

ܨ = ݃ሺܯ + ݉ሻሺߤ

஽ௐ

+ ߤ

஽ௌ

ሻ

4.3. a)

ߙ = arctg ቀ

௩

మ

ோ௚

ቁ; b) ߤ =

௩

మ

ோ௚

4.4.

ߤ

ௌ

=

ி

ೞ

௠௚

= 0,5; ߤ

௄

=

ி

಼

௠௚

= 0,15

4.5.

ܵ =

௩

బ

మ

ଶఓ௚

4.6.

ܽ =

ி

௠

cosߙ − ߤ ቀ݃ −

ி

௠

sinߙቁ = 3,96

௠

௦

మ

4.7.

ܽ = ݃

௠

మ

ିఓ௠

భ

௠

భ

ାఓ௠

మ

4.8.

ݒ = ඥ2ߤ݈݃

4.9. droga hamowania nie zależy od masy:

ܵ =

௩

మ

ଶఓ௚

(por. zadanie 4.5)

4.10.

݉ =

ଶௐ

௩

మ

4.11.

ܽ =

ଶ௟

∆௧

మ

; ܨ =

ଶ௠௟

∆௧

మ

; ܲ =

ଶ௠௟

మ

∆௧

య

4.12.

ܹ = ܨܵ; ܲ = ܨݒ

4.13.

ܹ = 5݉݃ℎ

4.14.

݉ =

ఎ௉୼௧

௚௛

4.15.

ܹ = ܦሺݏ

ଶ

− ݏ

ଵ

ሻ +

஻

ଶ

ሺݏ

ଶ

ଶ

− ݏ

ଵ

ଶ

ሻ +

஼
ଷ

ሺݏ

ଶ

ଷ

− ݏ

ଵ

ଷ

ሻ

4.16.

ܹ =

ி௟

బ

ଶ

4.17.

ܵ =

௩

మ

ା௚ఓ௅

ଶ௚ఓ

4.18.

ܹ =

ଵ
ଶ

݈݉݃

4.19. Moc jest maksymalna gdy

ݒ =

௩

బ

ଷ

. ܹ = ݒݐ

௔ௌఘሺ௩

బ

ି௩ሻ

మ

ଶ

= 3,38 ∙ 10

ହ

J