2)For the normal force in the figure to have the same magnitude at all points on

Question

2)For the normal force in the figure to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose, for example, that the track has a radius of 3.4 m and that the driver goes past point 1 at the bottom with a speed of 16 m/s. What speed must she have at point 3, so that the normal force at the top has the same magnitude as it did at the bottom?
m/s

A jet flying at 132 m/s banks to make a horizontal circular turn. The radius of the turn is 3810 m, and the mass of the jet is 1.88 times 10 5 kg. Calculate the magnitude of the necessary lifting force. L = For the normal force in the figure to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose, for example, that the track has a radius of 3.4 m and that the driver goes past point 1 at the bottom with a speed of 16 m/s. What speed must she have at point 3, so that the normal force at the top has the same magnitude as it did at the bottom?

Explanation / Answer

1. The lifting force has to be enough to keep the plane flying and to produce a centripetal force that will allow the jet to make the turn. So, there will be two components for the lifting force:

Lift Vertical component= F_y = mass of jet * gravity

Lift Horizontal component= F_x = mass of jet * Velocity^2 / Radius of turn

where F_x is calculated from standard relations used in circular motion. The total lift force is then

F_total = SQRT ( F_x^2 + F_y^2)

Plug in the numeric data into the equations above and that is your answer.

2.

Normal force at bottom = mg + m . v^2 / R = m(9.8 + 16^2 / 3.4)
= 85.1 m

Normal force at top = (m . v^2 / R )

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