# Problem: A solid sphere of mass 2.5kg and radius 0.15m starts from rest at the top of a ramp inclined 25 degrees and rolls to the bottom without slipping. The upper end of the ramp is 0.85m higher than the lower end. a. What is the translational kinetic energy of the sphere when it reaches the bottom of the ramp? b. What is the rotational kinetic energy of the sphere when it reaches the bottom of the ramp?

###### FREE Expert Solution

Potential energy:

$\overline{){\mathbf{P}}{\mathbf{E}}{\mathbf{=}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

The kinetic energy at the bottom:

$\overline{){{\mathbf{K}}}_{\mathbf{b}\mathbf{o}\mathbf{t}\mathbf{t}\mathbf{o}\mathbf{m}}{\mathbf{=}}{{\mathbf{K}}}_{\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{n}\mathbf{s}\mathbf{l}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{a}\mathbf{l}}{\mathbf{+}}{{\mathbf{K}}}_{\mathbf{r}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{a}\mathbf{l}}}$

Translational kinetic energy is given by:

Rotational kinetic energy is given by:

$\overline{){{\mathbf{K}}}_{{\mathbf{rotational}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{I}}{{\mathbf{\omega }}}^{{\mathbf{2}}}}$

92% (404 ratings) ###### Problem Details

A solid sphere of mass 2.5kg and radius 0.15m starts from rest at the top of a ramp inclined 25 degrees and rolls to the bottom without slipping. The upper end of the ramp is 0.85m higher than the lower end.

a. What is the translational kinetic energy of the sphere when it reaches the bottom of the ramp?

b. What is the rotational kinetic energy of the sphere when it reaches the bottom of the ramp?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Conservation of Energy in Rolling Motion concept. You can view video lessons to learn Conservation of Energy in Rolling Motion. Or if you need more Conservation of Energy in Rolling Motion practice, you can also practice Conservation of Energy in Rolling Motion practice problems.