A solid cylinder with a mass of 2.72 kg and a radius of 0.083 m starts from rest at a height of 4.20 m and rolls down a 88.7 ◦ slope. What i

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A solid cylinder with a mass of 2.72 kg and a radius of 0.083 m starts from rest at a height of 4.20 m and rolls down a 88.7 ◦ slope. What is the translational speed of the cylinder when it leaves the incline? The acceleration of gravity is 9.81 m/s 2 . Answer in units of m/s.

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Bình An 4 years 2021-08-28T23:55:32+00:00 1 Answers 3 views 0

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  1. niczorrrr
    0
    2021-08-28T23:56:58+00:00
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    Explanation:

    According to the law of conservation of energy
    ,    

                 Potential energy = kinetic energy

       mgh = \frac{1}{2} \times mv^{2} + \frac{1}{2} \times I \times \omega^{2}

                      I = \frac{mr^{2}}{2}

              \omega = \frac{v}{r}

         mgh = [\frac{1}{2} \times mv^{2}] + [\frac{1}{2} \times (\frac{mr^{2}}{2}) \frac{v^{2}}{r^{2}}]

         mgh = [\frac{1}{2} \times mv^{2}] + [\frac{1}{4} \times mv^{2}]

                 g \times h = \frac{3}{4} \times v^{2}

                 9.8 \times 4.2 = \frac{3}{4} \times v^{2}

                      v = 7.4 m/s

    thus, we can conclude that the translational speed of the cylinder when it leaves the incline is 7.4 m/s.

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