Conservation of Energy in Rolling Motion Video Lessons

Concept

# Problem: A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15 degrees, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4 MR2 for a solid sphere and g = 9.8m/s2)a. 4.7m/sb. 4.1 m/sc. 3.4 m/sd. 2.4m/s

###### FREE Expert Solution

Let's consider the law of conservation of energy.

$\overline{)\begin{array}{rcl}\mathbf{P}\mathbf{E}& {\mathbf{=}}& {\mathbf{K}}_{\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{n}\mathbf{s}}\mathbf{+}{\mathbf{K}}_{\mathbf{r}\mathbf{o}\mathbf{t}}\end{array}}$, where PE is the potential energy, Ktranslational is the translational kinetic energy, and Krot is the rotational kinetic energy.

But, PE = mgh

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###### Problem Details

A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15 degrees, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: I = 0.4 MR2 for a solid sphere and g = 9.8m/s2)

a. 4.7m/s

b. 4.1 m/s

c. 3.4 m/s

d. 2.4m/s