Need help with these questions if anyone can provide someinsight..... 1.) The in

Question

Need help with these questions if anyone can provide someinsight.....

1.) The instantaneous velocity of a particle is given as v = 6i -5jm/s. At this instant the radius of curvature of the particle's pathis 7.0m, and the speed of the particle is decreasing at the rate of3 m/s^2. Write the expression for the particle's velocity andacceleration using unit vectors En and Et.

2.) An airplane has a mass of 250,000 kg and four engines whicheach produce a constant thrust of 190,000 N during takeoff.Calculate the length of the runway required if the takeoff is 225km/h. Neglect friction and air resistance.

3.) A coin is placed on the horizontal surface of a rotation diskat a distance r from the disk's center. If the disk start from restwith an angular acceleration alpha, determine an expression for thenumber of revolutions N through which the disk turns before thecoin begins to slide. The coefficient of static friction betweenthe disk and the coin is Uk.

Any help is appreciated!

Explanation / Answer

1.)the instantaneous velocity of the particle is v = [(6)2 + (-5)2]1/2 = 7.8m/s the speed of the particle is v1 = (2 * r * a)1/2 r = 7.0 m and a = -3 m/s2 or v1 = (2 * 7.0 * 3)1/2 = 6.4 m/s the time taken to decrease the speed of the particle is v = v1 + at or t = (v - v1/a) or t = (7.8 - 6.4/3) = 0.47 s 2.)the centripetal force acting on the airplane is F = (m * v2/r) or r = (m * v2/F) m = 250,000 kg,v = 225 km/h = 225 * (1000/3600) m/s = 62.5 m/sand F = 190000 N 3.)we know that w2 - wo2 =2 wo = 0 or w2 = 2 ---------(1) the linear velocity of the coin on the disk is v = (2 * s * r * g)1/2------------(2) the linear velocity is given by v = r * w or w = (v/r) ------------(3) from (1) and (3) we get (v/r)2 = 2 or (v2/r2) = 2 or v2 = 2 * r2-------------(4) from (2) and (4) we get 2 * r2 = 2 * s *r * g or = k * (g/r) or 2 * N = s * (g/r) or N = (1/2) * s * (g/r) s is the coefficient of static friction,g isthe acceleration due to gravity and has a value of 9.8m/s2 and r is the distance from the disk's center.

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