F=mg+mv^2/R eching

$$F = m g + \frac { m v ^ { 2 } } { R }$$

R uchun yechish

$$\left\{\begin{matrix}R=-\frac{mv^{2}}{gm-F}\text{, }&v\neq 0\text{ and }m\neq 0\text{ and }F\neq gm\\R\neq 0\text{, }&\left(F=gm\text{ and }v=0\right)\text{ or }\left(v\neq 0\text{ and }F=0\text{ and }m=0\right)\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

R qiymati 0 teng bo‘lmaydi, chunki nolga bo‘lish mumkin emas. Tenglamaning ikkala tarafini R ga ko'paytirish.

$$FR=mgR+mv^{2}$$

Ikkala tarafdan mgR ni ayirish.

$$FR-mgR=mv^{2}$$

Shartlarni qayta saralash.

$$-Rgm+FR=mv^{2}$$

R'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-gm+F\right)R=mv^{2}$$

Tenglama standart shaklda.

$$\left(F-gm\right)R=mv^{2}$$

Ikki tarafini F-mg ga bo‘ling.

$$\frac{\left(F-gm\right)R}{F-gm}=\frac{mv^{2}}{F-gm}$$

F-mg ga bo'lish F-mg ga ko'paytirishni bekor qiladi.

$$R=\frac{mv^{2}}{F-gm}$$

R qiymati 0 teng bo‘lmaydi.

$$R=\frac{mv^{2}}{F-gm}\text{, }R\neq 0$$

F uchun yechish

$$F=\frac{m\left(v^{2}+Rg\right)}{R}$$

$$R\neq 0$$