A jet pilot takes his aircraft in a vertical loop, as shown in the figure(Figure

Question

A jet pilot takes his aircraft in a vertical loop, as shown in the figure(Figure 1) .

If the jet is moving at a speed of 1140km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 7.0 g's. Express your answer to two significant figures and include the appropriate units.

Part B Calculate the 75-kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and at the top of the circle (assume the same speed). Express your answers using two significant figures separated by a comma.

Explanation / Answer

Given that

if the jet is moving at a speed of (v) =1140km/h at the lowest point of the loop then (v) =316.667m/s

The centripetal acceleration at the lowest point does not exceed 7.0 g's means (ac) =7*9.81m/s2 =68.67m/s2

We know that centripetal force is given by

Fc =mv2/r ===>mac =mv2/r

Then ac =v2/r

Therefore to determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 7.0 g's is r =v2/ac =(316.667)2/68.67=1460.285m.

B)

The total centripetal force Fc =Fg+Fn

Now Fc =mac =mv2/r =75*(316.667)2/1460.285 =5150.261N

The force of gravity is given by Fg =mg =75(9.81) =735.75N

The normal force acting is given by Fn =Fc-Fg =5150.261-735.75 =4414.511N

With the above force the seat pushes up on him

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