Misalan karo marasa ƙarfi

Misalai 5 na karo mara sassauƙa

1. Harsashi mai nauyin gram 30 yana tafiya a gudun mita 30/s zai bugi wani katako mai nauyin kilogiram 1 wanda yake hutawa. Kayyade saurin toshe idan harsashin ya makale a cikin toshen!
Tattaunawa
An sani :
Nauyin harsashi (m)₁) = gram 30 = 0,03 kg
Nauyin tubalin (m₂) = 1 kg
Saurin farko na harsashi (v)₁) = 30 m/s
Saurin farko na toshe (v)₂) = 0 (toshe mai tsayawa)
An tambaya : saurin harsashi da toshewa bayan karo (v')
Jawab :
Tsarin dabara dokar kiyaye yanayin motsi idan abubuwa biyu suka manne tare bayan karo:
m₁ v₁ +m₂ v₂ = (m₁ +m₂) v'
(0,03) (30) + (1) (0) = (0,03 + 1) v'
0,9 + 0 = 1,03 v'
0,9 = 1,03 v'
v' = 0,9/1,03
v' = 0,87 m/s
Saurin harsashin da toshewar bayan karo shine 0,87 m/s.

2. Abubuwa A da B kowannensu yana da nauyin kilogiram 2 kuma suna tafiya zuwa ga juna a gudun v._A = 6 ms^-1 kuma v_B = 4 ms^-1Idan duka biyun sun yi abu ɗaya karo mara sassauƙa gaba ɗaya, to saurin abubuwa biyu bayan karo shine...
Tattaunawa
An sani :
Nauyin abu A (m)_A) = 2 kg
Nauyin abu B (m)_B) = 2 kg
Saurin farko na abu A (v)_A) = -6 m/s
Saurin farko na abu B (v)_B) = 4 m/s
An tambaya : saurin abubuwa biyu bayan karo (v')
Jawab :
m_A v_A +m_B v_B = (m_A'+ m_B) v'
(2) (-6) + (2) (4) = (2 + 2) v'
-12 + 8 = 4 v'
-4 = 4 v'
v' = -4 / 4
v' = -1 m/s
Saurin abubuwa biyu bayan karo shine 1 m/s.

3. Abubuwa biyu kowannensu yana da nauyin m₁ = 3 kg da m₂ = 4 kg suna tafiya a akasin alkibla zuwa ga juna a gudun v₁ = 10 m/s da v₂ = 12 m/s. Abubuwa biyu sun yi karo kuma bayan karo sun manne tare. Saurin abubuwa biyu bayan karo shine…
Tattaunawa
An sani :
Nauyin abu 1 (m₁) = 3 kg
Nauyin abu 2 (m₂) = 4 kg
Saurin abu na 1 (v)₁) = -10 m/s
Saurin abu na 2 (v)₂) = 12 m/s
An tambaya : gudu abubuwa biyu bayan karo (v')
Jawab :
m₁ v₁ +m₂ v₂ = (m₁'+ m₂) v'
(3) (-10) + (4) (12) = (3 + 4) v'
-30 + 48 = 7 v'
18 = 7 v'
v' = 18/7
v' = 2,6 m/s
Saurin abubuwa biyu bayan karo shine 2,6 m/s.

4. Wata motar bas da aka tsayar ta buge ta da wata bas da ke tafiya a gudun kilomita 36/awa. Bayan hatsarin, sai motar bas da motar suka yi karo da juna. Idan nauyin motar bas ya kai kilogiram 2000 kuma nauyin motar bas ya kai kilogiram 1000, menene saurin motocin biyu bayan hatsarin?

A. 3,45 m/s

B. 4,67 m/s

C. 5,45 m/s

D. 6,67 m/s

E. 7,67 m/s

Tattaunawa:

An sani :

v bas = 36 km/h = 36000 m/3600 s = 10 m/s

bas m = 2000 kg

v sedan = 0

mitar sedan = 1000 kg

An tambaya :

Saurin sedan da bas bayan karo (v')?

Jawab :

m₁ v₁ +m₂ v₂ = (m₁ +m₂) v'

(2000) (10) + (1000) (0) = (2000 + 1000) v'

20.000 = 3000 v'

v' = 20.000 / 3000 = 6,67 m/s

Amsar da ta dace ita ce D.

5. Harsashi mai nauyin gram 20 da ke tafiya a gudun mita 100/s zai bugi wani toshe na itace da ba ya tsayawa ya kuma makale a ciki. Idan nauyin toshe na itace ya kai gram 500, menene saurin toshe na itace da harsashin nan da nan bayan karo?

A. 1,50 m/s

B. 2,55 m/s

C. 3,85 m/s

D. 4,75 m/s

E. 5,65 m/s

Tattaunawa:

An sani :

harsashi m = gram 20 = 0,02 kg

harsashi v = 100 m/s

tubalin m = gram 500 = 0,5 kg

toshe v = 0

An tambaya :

Saurin harsashi da toshewar nan da nan bayan karo (v')?

Jawab :

m₁ v₁ +m₂ v₂ = (m₁ +m₂) v'

(0,02) (100) + (0,5) (0) = (0,02 + 0,5) v'

2 + 0 = 0,52 v'

2 = 0,52 v'

v' = 2 / 0,52 = 3,85 m/s

Amsar da ta dace ita ce C.