Question

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)

Answer 1

`"7.65 kg wt"`

Explanation:

Let speed of aeroplane at lowest and highest point be `"v"_i` and `"v"_f` respectively

From conservation of energy

`1/2cancel"m""v"_i^2 = cancel"m""g(2R)" + 1/2cancel"m""v"_f^2`

`"v"_f^2 = "v"_i^2 - "4gR"`

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

`color(white)(v_f) = sqrt(("100 m/s")^2 - ("4 × 9.8 m/s"^2 × "200 m"))`

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

`color(white)(v_f) = sqrt(10^4(1 - 0.784))\ "m/s"`

`color(white)(v_f) = sqrt(2160)\ "m/s"`

At highest position

• weight `"mg"` acts downwards
• centripetal force `"mv"^2/"r"` acts upwards

Normal force (`"F"_n`) is

`"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]`

`color(white)(F_n) = "75 kg × 1 m/s"^2`

`color(white)(F_n) = "75 N"`

It’s asked to find the force in `"kg wt"`

So,

`"F"_n = "75 N"/"9.8 N/kg wt" = "7.65 kg wt"`