Physics Problem Set: Kinetic Energy, Angular Velocity, and Harmonic Waves, Exams of Physics

Download Physics Problem Set: Kinetic Energy, Angular Velocity, and Harmonic Waves and more Exams Physics in PDF only on Docsity! Problem 2: A uniform hoop of mass m=0.2kg and radius r=0.6m rolls without slipping on a horizontal surface. Its linear acceleration is uniform, a=0.5m/s^2. If it starts from rest, find its total kinetic energy after 5 seconds. The hoop will have translational and rotational kinetic energy. K(trans) = (1/2)mv^2 K(rot) = (1/2)Iw^2 Since v=at we have after 5s v=2.5m/s. So K(trans) = (1/2)*0.2* 2.5^2 J = 0.625 J. w = v/r is the angular velocity of a rolling hoop. Its moment of inertia is I = mr^2. So K(rot) = (1/2)Iw^2 = 0.625 J. K(trans) + K(rot) = 1.25 J. Problem 6: From the Web material: Consider a transverse harmonic wave traveling in the positive x-direction. The displacement y of a particle in the medium is given as a function of x and t by y=Asin(kx-t+). For a transverse harmonic wave traveling in the negative x-direction we have y=Asin(kx+t+). In this problem is  zero. You have to watch for the + or – sign. From the notes: Consider a transverse harmonic wave traveling in the positive x-direction. The displacement y of a particle in the medium is given as a function of x and t by y(x,t) = Asin(kx -t +). For a transverse harmonic wave traveling in the negative x-direction we have y(x,t) = Asin(kx +t +). Here k is the wavenumber, k = 2/, and = 2/T = 2f is the angular frequency of the wave.  is called the phase constant. The speed v of the wave can be expressed in terms of these quantities. v =f = /k. Here y = (0.1m)sin(0.4x+5t). The + sign indicates that the wave is traveling in the negative x direction and k = 0.4,  = 5, and  = 0. v = /k. Problem 11: Angular momentum L = I. Given: m = 2kg, r = 0.15m,  = 12/s. I = (1/2)mr2 = 1kg (0.15m)2. Problem 12:  = r  F. Magnitude:  = rFsin.