A 30 kg mass and a 20 kg mass are joined by a light rigid rod and this system is free to rotate in the plane of the page about axis through

Question

A 30 kg mass and a 20 kg mass are joined by a light rigid rod and this system is free to rotate in the plane of the page about axis through A and perpendicular to the page. The 30 kg mass is 0.2 m from A and the 20-kg mass is 0.4 m from A. Treating the masses as point masses and assuming the system rotates at 5 rad/s about A, what is the total kinetic energy?

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Thanh Hà 5 months 2021-08-09T06:45:36+00:00 2 Answers 23 views 0

Answers ( )

    0
    2021-08-09T06:46:44+00:00

    55 J

    Explanation:

    Kinetic energy is given as: 0.5MV^2 where M is the mass and V is the speed of rotation. Since the masses are point masses, we calculate the point mass for each mass.

    M1 = 30*0.2^2 = 1.2kgm^2

    M2 = 20*0.4^2 = 3.2kgm^2

    V = 5 rad/s

    Calculating using the formula above, we obtain :

    0.5(1.2+3.2)5^2 =0.5*4.4*25 = 55 J

    0
    2021-08-09T06:46:56+00:00

    Answer:

      K = 55 J

    Explanation:

    Kinetic energy is a scalar therefore it is an additive quantity

           K = ½ I₁ w₁² + ½ I₂ w₂²

    The moment of inertia of a particular is

          I = m r²

          I₁ = 30 0.2² = 1.2   kg m²

          I₂ = 20 0.4² = 3.2  kg m²

    As the body is joined by a rigid rod they both have the same angular velocity

          K = ½ (I₁ + I₂) w²

    Let’s calculate

          K = ½ (1.2 + 3.2) 5²

           K = 55 J

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