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A bowling ball of mass 7.29 kg and radius 11.0 cm rolls without slipping down a lane at 3.00 m/s. Calculate the total kinetic energy.

Sagot :

We have the next information

m=7.29 kg

v=3 m/s

r=11cm=0.11m

We can find the kinetic energy using the next formula

[tex]KE=\frac{1}{2}mv^2+\frac{1}{2}Iw^2[/tex]

I is the moment of inertia

w is the angular velocity

First, we need to calculate the moment of inertia

[tex]I=\frac{2}{5}mr^2[/tex][tex]I=\frac{2}{5}(7.29)(0.11)^2=0.0353kgm^2[/tex]

Then for the angular velocity

[tex]\omega=\frac{v}{r}[/tex]

[tex]\omega=\frac{3}{0.11}=27.28[/tex]

then we will substitute the values in the kinetic energy formula

[tex]KE=\frac{1}{2}(7.29)(3)^2+\frac{1}{2}(0.0353)(27.28)^2[/tex][tex]KE=45.9J[/tex]

The total kinetic energy is 45.9 J

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