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A solid steel sphere of radius 1.50cm and density of 8045 kg/m³ was launched on a...

A solid steel sphere of radius 1.50cm and density of 8045 kg/m³ was launched on a horizontal frictionless surface. The sphere was launched using a spring gun which possessed a spring with a force constant of 35.6 N/m. The spring was compressed 30.0 cm and the sphere was launched. At the end of the frictionless surface (that was 0.955 m above the floor), the sphere rolled (no slipping) up a 25° ramp with height of 1.15m and then launched off of the ramp. The coefficient of rolling friction between the sphere and ramp was 0.0500. What was the speed of the sphere at the end of the frictionless surface (when it was sliding - not rolling) ? What was the translational speed of the sphere at the very beginning of the ramp (when it transitioned to perfect rolling (no slipping))? What was the sphere's rotational speed (in revolutions per minute) at the very top of the ramp? Ignoring drag, at what horizontal distance from the end of the ramp did the sphere strike the floor? What was the greatest height the sphere achieved (above the floor)?

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