The reel shown in the figure below has radius R and moment ofinertia I. One end of the block of mass m is connected to a springof force constant k, and the other end is fastened to a cordwrapped around the reel. The reel axle is frictionless, and thecoefficient of friction between the block and the incline is μk.The reel is wound counterclockwise so that the spring stretches adistance d from its unstretched position and the reel is thenreleased from rest. (a) Derive an expression for the angular speedof the reel when the spring is again unstretched. (b) Evaluate theangular speed numerically at this point, taking I = 1.00 kg m2, R =0.300 m, k = 50.0 N / m, m =0.500 kg, d = 0.200 m, μk = 0.100, andθ = 37.0º.
The reel shown in the figure below has radius R and moment of inertia I. One end of the block of mass m is connected to a spring of force constant k, and the other end is fastened to a cord wrapped around the reel. The reel axle is frictionless, and the coefficient of friction between the block and the incline is ?k. The reel is wound counterclockwise so that the spring stretches a distance d from its unstretched position and the reel is then released from rest. (a) Derive an expression for the angular speed of the reel when the spring is again unstretched. (b) Evaluate the angular speed numerically at this point, taking I = 1.00 kg m2, R = 0.300 m, k = 50.0 N / m, m =0.500 kg, d = 0.200 m, muk = 0.100, and ? = 37.0 degree.
