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A merry-go-round with a rotational inertia of 600 kg m2 and a radius of 3.0 m is initially at rest. A 20 kg boy approaches the m

nekit [7.7K]

Answer:

The velocity of the merry-go-round after the boy hops on the merry-go-round is 1.5 m/s

Explanation:

The rotational inertia of the merry-go-round = 600 kg·m²

The radius of the merry-go-round = 3.0 m

The mass of the boy = 20 kg

The speed with which the boy approaches the merry-go-round = 5.0 m/s

$F_T \cdot r = I \cdot \alpha = m \cdot r^2 \cdot \alpha$

Where;

$F_T$ = The tangential force

I = The rotational inertia

m = The mass

α = The angular acceleration

r = The radius of the merry-go-round

For the merry go round, we have;

$I_m \cdot \alpha_m = I_m \cdot \dfrac{v_m}{r \cdot t}$

$I_m$ = The rotational inertia of the merry-go-round

$\alpha _m$ = The angular acceleration of the merry-go-round

$v _m$ = The linear velocity of the merry-go-round

t = The time of motion

For the boy, we have;

$I_b \cdot \alpha_b = m_b \cdot r^2 \cdot \dfrac{v_b}{r \cdot t}$

Where;

$I_b$ = The rotational inertia of the boy

$\alpha _b$ = The angular acceleration of the boy

$v _b$ = The linear velocity of the boy

t = The time of motion

When the boy jumps on the merry-go-round, we have;

$I_m \cdot \dfrac{v_m}{r \cdot t} = m_b \cdot r^2 \cdot \dfrac{v_b}{r \cdot t}$

Which gives;

$v_m = \dfrac{m_b \cdot r^2 \cdot \dfrac{v_b}{r \cdot t} \cdot r \cdot t}{I_m} = \dfrac{m_b \cdot r^2 \cdot v_b}{I_m}$

From which we have;

$v_m = \dfrac{20 \times 3^2 \times 5}{600} = 1.5$

The velocity of the merry-go-round, $v_m$ , after the boy hops on the merry-go-round = 1.5 m/s.

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Which one of the following activities is considered part of health care operations? A. Administering a stress test B. Reviewing

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<span>B. Reviewing the competency of health care workers</span> is considered part of health care operations

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Weight of the mass is the tension in the string if the turntable is held fixed, with the mass hanging from the pulley

Weight is a force that acts at all times on all objects near Earth. The Earth pulls on all objects with a force of gravity downward toward the center of the Earth. Weight (symbolized w ) is a quantity representing the force exerted on a particle or object by an acceleration field, particularly the gravitational field of the Earth at the surface.

The tension force is defined as the force that is transmitted through a rope, string or wire when pulled by forces acting from opposite sides. The tension force is directed over the length of the wire and pulls energy equally on the bodies at the ends.

The direction of tension is the pull which is given the name tension. Thus, the tension will point away from the mass in the direction of the string/rope. In case of the hanging mass, the string pulls it upwards, so the string/rope exerts an upper force on the mass and the tension will be in the upper side.

Tension will act opposite the the weight of the mass attached in order to maintain equilibrium .

To learn more about weight here

brainly.com/question/2293244

#SPJ4

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The approximate rotation period of the Moon is: A. 1 day B. 1 week C. I month D. Infinite, since the Moon does not rotate, but k

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Answer:

C. 1 month

Explanation:

The moon orbits around the earth once in a time of 27.322 days and it also takes about 27 days to orbit around its own axis. Due to this the moon is not seem to be spinning and it always seems still to observer who is observing from the Earth.

The moon takes about almost 1 month to make 1 revolution around the Earth . It also takes approximately the same time to make one rotation about its axis. This is why we always see the same face of the moon.

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