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Alexeev081 [22]
3 years ago
7

Calculate the moment of inertia and the rotational kinetic energy for the following objects spinning about a central axis (in un

its of Joules): a solid sphere with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec. a thin spherical shell with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec. a solid cylinder with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec. a hoop with a mass of 200 grams and a radius of 5.0 cm rotating with an angular speed of 2.5 rad/sec.
Physics
1 answer:
Helga [31]3 years ago
6 0

Answer:

a) K = 6.25 10⁻⁴ J , b)  K = 10.41  10⁻⁴ J , c)  K = 7.81 10⁻⁴ J , d)  K = 15.625 10⁻⁴ J

Explanation:

The moment of inertia is

         I = ∫ r² dm

For high symmetry bodies it is tabulated.

The rotational kinetic energy is

         K = ½ I w²

Let's calculate the values ​​of the given bodies

a) solid sphere

         I = 2/5 M R²

         I = 2/5 0.200 0.05²

         I = 2 10⁻⁴ kg m²

        K = ½ 2 10⁻⁴ 2.5²

        K = 6.25 10⁻⁴ J

b) spherical shell

        I = 2/3 M R²

        I = 2/3 0.200 0.05²

        I = 3.33 10⁻⁴ kg m²

        K = ½ 3.33 10-4 2.5²

        K = 10.41  10⁻⁴ J

c) solid cylinder

        I = ½ M R²

        I = ½ 0.200 0.05²

        I = 2.5 10⁻⁴ kg m²

       K = ½ 2.5 10-4 2.5²

       K = 7.81 10⁻⁴ J

d) hoop

       I = M R²

       I = 0.200 0.05²

       I = 5 10⁻⁴ kg m²

      K = ½ 5 10⁻⁴ 2.5²

      K = 15.625 10⁻⁴ J

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. Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank f
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Time taken by A and B is 1.2 hr.

Explanation:

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Time taken by tank when B+C are open = 2 hr

If we treat as filling of tank is a work then

Work = time x rate

Lets take work is 1 unit

1 = 1(1/a+1/b+1/c)          ---------1

1 = 1.5(1/a+1/c)           ----------2

1 = 2(1/b+1/c)             --------3

From equation 1 and 3

1=1(1/a+1/2)

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Form equation 2

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From equation 3

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So time taken by

A is alone to fill tank is 2 hr

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Answer:

27.44 J

Explanation:

We can find the energy at the top of the slide by using the potential energy equation:

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At the top of the slide, the swimmer has 0 kinetic energy and maximum potential energy.

The swimmer's mass is given as 7.00 kg.

The acceleration due to gravity is 9.8 m/s².

The (vertical) height of the water slide is 0.40 m.

Substitute these values into the potential energy equation:

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Since there is 0 kinetic energy at the top of the slide, the total energy present is the swimmer's potential energy.

Therefore, the answer is 27.44 J of energy when the swimmer is at the top of the slide.

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