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in Motion of System of Particles and Rigid Bodies by (48.2k points)
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The 747 boing plane is landing at a speed of 70 m s-1 . Before touching the ground, the wheels are not rotating. How long a skid mark do the wing wheels leave (assume their mass is 100 kg which is distributed uniformly, radius is 0.7 m, and the coefficient of friction with the ground is 0.5)?

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The types of the plane will leave a skid mark if the speed of the types in contact with ground is lesser than the velocity of the plane. The condition for this is –

v > ω

(When the type attained an angular velocity of V/R) The types will stop the skidding and starts the rolling. 

The forces acting on the wheel after the plane touches down are, 

N – P Normal force W – weight 

The wheel is not accelerating means N = ω 

The torque about the center of the wheel is \(\tau\)= RF = µωR

The angular acceleration is

According to equation of motion, time taken to stop the skidding by the wheel is,

The six mark will have a length of 

l = vt = 70 x 0.03 = 2.1 m 

Note:

The 747 is resting on the runway, supported by 16 wheels under the wing, and 2 under the nose total length is 68.63 m. The normal force experienced by plane through its 16 wheels is ω = 232 KN.

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