Fourth Test, Page 3 of 6 Dec 1, 2017 4. (12 points) A car is doing laps in a cir

Question

Fourth Test, Page 3 of 6 Dec 1, 2017 4. (12 points) A car is doing laps in a circular track of radius 122m, at a rate of one lap every 31.4s. The centripetal acceleration the car experiences is close to A. B. V5g C. 59 D. 25g E. 5. (12 points) Three objects, a solid cyllinder, a solid sphere and a spherical shell, all with identical mass and radius, are set to roll without slipping, with identical initial speed, up an inclined ramp. Rank from highest to lowest, the height the objects reach when they come to a complete stop on the incline. A. Spherical Shell, Solid Cyllinder, Solid Sphere B. Solid Cyllinder, Solid Sphere, Spherical Shell C. Solid Sphere, Spherical Shell, Solid Cyllinder D. Solid Cyllinder, Spherical Shell, Solid Sphere E. Solid Sphere, Solid Cyllinder, Spherical Shell without slipping from a heisht of 50m down an incline. The speed of the shell when it reaches the bottom of the incline is 6. (12 points) A cylindrical shell, of mass(M = 15 kg), radius (R = 10. nn is set to roll M-161 A. 15.1% B. 7.0s C. 10.1% D. 2.0s E. 3.0m/s

Explanation / Answer

4. Acceleration = w^2*R = (2*pi/T)^2 * 122 = 4.88

5. Moment of inertia of solid cylinder = .5 mr^2

Moment of inertia of solid sphere = (2/5) mr^2

Moment of inertia of spherical shell = (2/3) mr^2

Height depends on moment of inertia as:

mgH = .5 mv^2 + .5*I*w^2

So, shell>cylinder>sphere

So, the order is

6.

Moment of inertia I = mr^2

mgh = .5mv^2 + .5*I*w^2 = .5 mv^2 + .5mv^2 = mv^2

v = sqrt(gH) = sqrt (9.8*5) = 7 m/sec

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