Question

Thanks so much ahead of time!

A spherical shell of radius 0.43 m and mass 27 kg initially rolls without slipping towards an incline at a linear speed of 9.1 m/s. If the ball rolls up an incline (inclined 35 degrees above the horizontal) without sliding. How high will it go? A professor holding a spinning wheel used for a demonstration brings the wheel to a stop by applying a constant, tangential friction force to the edge (his hand). The wheel has moment of inertia 1.56 kg m2 and a radius of 0.45 m. The initial angular velocity is 6.1 rad/s. The wheel rotates 4.0 turns as it slows to a stop. Find an expression for the applied force in terms of the given variables, and then compute its magnitude A hanging bucket of mass M-2.0 kg is tied to a rope that is wrapped around a frictionless pulley that has mass m = 1.0 kg and radius R-0.50 m. What is the numerical value of the angular acceleration of the pulley after the bucket is released? The pulley may be considered a uniform disk. ly L-千凵 むごMR2

Answer 1

Spherical shell = I rightdoublearrow 2/3 MR^2 V = rw rightdoublearrow 2/3 times 27 times (0.43)^2 rightdoublearrow 3.3282 kg m^2 Initial kinetic energy = Final potential energy 1/2 mv^2 + 1/2 I w^2 = mgh 1/2 mv^2 + 1/2 times 2/3 MR^2 times v^2/R^2 = Mgh removing M. v^2/2 + v^2/3 = gh gh = 5v^2/6 h = 5v^2/6 g h = 5 times (9.1)^2/6 times 9.8 rightdoublearrow 7.041 m Height reached will be 7.01 m