A uniform, solid sphere of radius 4.50 cm and mass 4.50 kg starts with a purely translational speed of 2.00 m/s at the top of an inclined plane. The surface of the incline is 1.00 m long, and is tilted at an angle of 29.0 ∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed v 2 at the bottom of the ramp.

3.58 m/s

Explanation:

Data:

The plot can be drawn to present the information in the question.

Then the calculations:

mass = 4.50 kg

translational speed = 2 m/s

radius = 4.50 cm

angle  = 29.0 °

Energy at the top of the incline, is calculated as follows:

The next item is the moment of inertia of the solid:

  =

Then the final velocity, is given by:

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.