Question

need help with all portion in this problem please show all steps

2. A uniform sphere( Ice = {mR) rolls down an incline. (a) What should be the incline angle 8 if the linear acceleration of the center of the sphere is to be 0.2g, where g is acceleration due to gravity? (b) For this angle, what would be the acceleration of a frictionless block sliding down the incline? (6-points)

Answer 1

А h Acceleration of a body molling down an in an inclined plane at point a sphere have only poten Hou energy = mgh at sphere has both only kinette energy Kies Ima2+ t I wr Emnez translational kinetic energi energy me mass and to speed ! x 162 & Rotational kinetic energy I = moment of imeytira, wa angular Nelocity consen vation of energ ngh - I mv2t & 1 W2 The on, w - VR R = Radius of sphere 4 mgha tmn2 + 2 x 2 mm² v2 mgh Immat 1/2 mn ory (2 + 1 mw? = mgh ory N2 From nergy R2 - MN2 gh N2 sphere 7 gh again of a be acceleration of the then from Law of kinematics we can write From figure reza zal hal sino 2a 2 10 7 g 1 sine i az loxgsino 14 16 / g sino acceleration of sphere in an inclined plame of inclined angle o gsino 9028 ong 8: Sint (0.28) Inclined angle D: 16.269 I 002 7 sino a 740.2 5 20:28 - 16. 28° ewison fore mgcolo "ИЯ If n be mass of object and a be acceleration downata with which block sliding down then 'appy equating along x direction sino mg a-gsine a Iga ASM(16.26) a go&x 0.28 Q = 2.744 ms2 ma - accep Affom o the of objet a: 2.744 mg 2 m/s2 Scanned with CamScanner