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19.02.2022 19:26
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Adisk and a hoop roll without slipping down the incline plane, starting from rest

Adisk and a hoop roll without slipping down the incline plane, starting from rest at height h=0.55m above the level surface. using the laws of energy conservation find the speeds of the objects at the bottom of the incline.
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katrinadoughty9356
katrinadoughty9356
4,9(35 marks)

v = \sqrt{\frac{1.1g}{(1 + \frac{1}{r^2})}}

Explanation:

By the law of energy conservation, the potential energy can be converted to kinetic energy and rotational energy as it rolling downhill

E_p = E_k + E_r

mgh = 0.5mv^2 + 0.5m\omega^2

Also velocity of the disk is its angular velocity times its radius:

gh = 0.5v^2 + \frac{v^2}{2r^2}

gh = (\frac{v^2}{2})(1 + \frac{1}{r^2})

v^2 = \frac{2gh}{(1 + \frac{1}{r^2}})

v = \sqrt{\frac{2gh}{(1 + \frac{1}{r^2})}}

v = \sqrt{\frac{1.1g}{(1 + \frac{1}{r^2})}}

deanblackstone
deanblackstone
4,8(19 marks)

Earth and Uranus

Explanation: hope this helps

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