A cube and a hollow sphere are released from the top of aninclined plane. The cu

Question

A cube and a hollow sphere are released from the top of aninclined plane. The cube slides along the incline while thesphere starts rolling down smoothly (v=R). The top of theinclined plane is at height 2.5 m above the ground. Both cube andsphere have the same mass M. The sphere has a radius of R. 1. What is the speed of the sphere when it reaches the ground.Moment of inertia is 2/3MR2. 2. What is the speed of the cube when it reaches theground? A cube and a hollow sphere are released from the top of aninclined plane. The cube slides along the incline while thesphere starts rolling down smoothly (v=R). The top of theinclined plane is at height 2.5 m above the ground. Both cube andsphere have the same mass M. The sphere has a radius of R. 1. What is the speed of the sphere when it reaches the ground.Moment of inertia is 2/3MR2. 2. What is the speed of the cube when it reaches theground?

Explanation / Answer

(a). Height h = 2.5 m Mass of the sphere M = M from law of conservation of energy , potential energy atheight h = kinetic energy at the bottom                    M g h = ( 1/ 2) M v ^ 2  * [ 1 + ( k / r ) ^2] Since its both rolling and trnaslating                       2gh= v ^ 2 * [ 1 + ( 2/ 3) ]                             =v ^ 2 * ( 5/ 3 )                        v ^ 2 = [ 6gh / 5 ]                            v = 5.422 m / s Mass of the sphere M = M from law of conservation of energy , potential energy atheight h = kinetic energy at the bottom                    M g h = ( 1/ 2) M v ^ 2  * [ 1 + ( k / r ) ^2] Since its both rolling and trnaslating                       2gh= v ^ 2 * [ 1 + ( 2/ 3) ]                             =v ^ 2 * ( 5/ 3 )                        v ^ 2 = [ 6gh / 5 ]                            v = 5.422 m / s (b). Height h = 2.5 m Mass of the cube M = M from law of conservation of energy , potential energy atheight h = kinetic energy at the bottom                    M g h = ( 1/ 2) M v ^ 2     Since itsonly sliding                           v = [ 2gh ]                             = 7 m / s

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