Physics, 03.12.2019 18:31 KP1998

Consider a father pushing a child on a playground merry-go-round. the system has a moment of inertia of 84.4 kg · m2. the father exerts a force on the merry-go-round perpendicular to its 1.50 m radius to achieve a torque of 375 n · m.(a) calculate the rotational kinetic energy (in j) in the merry-go-round plus child when they have an angular velocity of 29.2 rpm. j(b) using energy considerations, find the number of revolutions the father will have to push to achieve this angular velocity starting from rest. revolutions(c) again, using energy considerations, calculate the force (in n) the father must exert to stop the merry-go-round in seven revolutions. n

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Answer from: emmazhu1106

A)The rotational kinetic energy is ≈ 9.9962 J

B)The number of revolutions to achieve that angular velocity = 0.0085

C)Force to stop it = 0.15152N

Explanation:

Given :

The system has a moment of inertia of $84.4kgm^{2}$ Radius R = 1.50m

Torque exerted = 375Nm

Rotational kinetic energy :

$E = \frac{1}{2} Iw^{2}$

where,

is the rotational kinetic energy (J)

is the moment of inertia $(Kgm^{2})$

is the angular velocity $(rads^{-1})$

⇒ $I=84.4\\w=29.2rpm=\frac{29.2}{60} rps=0.4867 rads^{-1}$

⇒ $E = \frac{1}{2} Iw^{2}\\E=\frac{1}{2} *84.4*(0.4867)^{2}\\E=9.9962 J$

Thus the energy is ≈ 9.9962 J

B) Work done by the torque = The change in rotational kinetic energy

$T\alpha = \frac{1}{2} Iw^{2} - \frac{1}{2} Iw_{o}^{2}$

where ,

is the torque exerted $\alpha$ is the angle traversed w_o

is the initial angular velocity.

Thus,

$375*\alpha =\frac{1}{2} *84.4*(0.4867)^{2}-\frac{1}{2} *84.4*0\\\alpha =0.026657 rad\\=\frac{0.026657}{\pi } rev\\=0.0085 rev$

The number of revolutions = 0.0085

7 revolutions :

$=7*2\pirad\\=14\pirad$

$T\alpha = \frac{1}{2} Iw^{2} - \frac{1}{2} Iw_{o}^{2}$

$T*14\pi =9.9962\\T= 0.2273 Nm\\F=\frac{T}{R} =\frac{0.2273}{1.5} \\F=0.15152N$

Force = 0.15152N

Answer from: Quest

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.

Answer from: Quest

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this. hope that you like the video and that it explains more in detail to you.

that is the link.

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Consider a father pushing a child on a playground merry-go-round. the system has a moment of inertia...

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