# An aeroplane flying in the sky dives with a speed of 100 m/s in vertical circle of radius 200m.weight of the pilot sitting in it is 75kg. The force with which the pilot presses his seat when aeroplane is at highest position ?(in kg wt)

May 30, 2018

$\text{7.65 kg wt}$

#### Explanation:

Let speed of aeroplane at lowest and highest point be ${\text{v}}_{i}$ and ${\text{v}}_{f}$ respectively

$\frac{1}{2} {\cancel{\text{m""v"_i^2 = cancel"m""g(2R)" + 1/2cancel"m""v}}}_{f}^{2}$

$\text{v"_f^2 = "v"_i^2 - "4gR}$

"v"_f = sqrt( "v"_i^2 - "4gR")

$\textcolor{w h i t e}{{v}_{f}} = \sqrt{\left(\text{100 m/s")^2 - ("4 × 9.8 m/s"^2 × "200 m}\right)}$

color(white)(v_f) = sqrt(10^4 - (0.784 × 10^4))\ "m/s"

$\textcolor{w h i t e}{{v}_{f}} = \sqrt{{10}^{4} \left(1 - 0.784\right)} \setminus \text{m/s}$

$\textcolor{w h i t e}{{v}_{f}} = \sqrt{2160} \setminus \text{m/s}$

At highest position

• weight $\text{mg}$ acts downwards
• centripetal force $\text{mv"^2/"r}$ acts upwards

Normal force (${\text{F}}_{n}$) is

$\text{F"_n = "mv"_f^2/"r" - "mg}$

color(white)(F_n) = "m"["v"_f^2/"r" - "g"]

color(white)(F_n) = "75 kg"[(sqrt(2160)\ "m/s")^2/"200 m" - "9.8 m/s"^2]

color(white)(F_n) = "75 kg"["10.8 m/s"^2 - "9.8 m/s"^2]

$\textcolor{w h i t e}{{F}_{n}} = {\text{75 kg × 1 m/s}}^{2}$

$\textcolor{w h i t e}{{F}_{n}} = \text{75 N}$

It’s asked to find the force in $\text{kg wt}$

So,

$\text{F"_n = "75 N"/"9.8 N/kg wt" = "7.65 kg wt}$