A man uses the inclined plane to lift a solid load through a vertical height from the inclined plane makes an angle of 30 degrees with the horizontal. If the efficiency of the inclined plane is 75%. Calculate effort needed to move the load up the inclined plane at constant velocity.

Kazi inayofaa ($W_{out}$) inatokana na kuinua mzigo dhidi ya mvuto.
Tunatumia formula $W_{out} = mgh$, ambapo $m$ ni uzito, $g$ ni mvutano wa mvuto ($9.8 \text{ m/s}^2$), na $h$ ni urefu.

$$W_{out} = (50 \text{ kg})(9.8 \text{ m/s}^2)(4 \text{ m})$$ $$W_{out} = 1960 \text{ J}$$

Umbali ($d$) kwenye ndege iliyoinama unahusiana na urefu ($h$) na angle ya kuinama ($\theta$) kupitia $\sin \theta = \frac{h}{d}$.

$$d = \frac{h}{\sin \theta}$$ $$d = \frac{4 \text{ m}}{\sin 30^\circ}$$

Tunajua $\sin 30^\circ = 0.5$.

$$d = \frac{4 \text{ m}}{0.5}$$ $$d = 8 \text{ m}$$

Ufanisi ($\eta$) unafafanuliwa kama uwiano wa kazi inayofaa kwa kazi ya kuingiza: $\eta = \frac{W_{out}}{W_{in}}$. Ufanisi umetolewa kama $75\%$, ambayo ni 0.75 kama desimali.

$$0.75 = \frac{1960 \text{ J}}{W_{in}}$$ $$W_{in} = \frac{1960 \text{ J}}{0.75}$$ $$W_{in} \approx 2613.33 \text{ J}$$

Kazi ya kuingiza ($W_{in}$) pia inaweza kuhesabiwa kama nguvu inayohitajika (Effort, $E$) ikizidishwa na umbali uliosafirishwa kwenye ndege iliyoinama ($d$). Hivyo, $W_{in} = E \times d$.

$$2613.33 \text{ J} = E \times 8 \text{ m}$$ $$E = \frac{2613.33 \text{ J}}{8 \text{ m}}$$ $$E \approx 326.67 \text{ N}$$