Physics, 04.04.2020 11:26 look26goingjbgy

A 210-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.600 rev/s in 2.00 s

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Answer from: jessieeverett432

The value of the constant force is $\bf{296.88~N}$ .

Explanation:

Given:

Mass of the merry-go-round, m = 210~Kg

Radius of the horizontal disk, r = 1.5~m

Time required, t = 2.00~s

Angular speed, $\omega = 0.600~rev/s$

Torque on an object is given by

$\tau = F.r = I.\alpha~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)$

where is the moment of inertia of the object, $\alpha$ is the angular acceleration and is the force on the disk.

The moment of inertia of the horizontal disk is given by

$I = \dfrac{1}{2}mr^{2}$

and the angular acceleration is given by

$\alpha = \dfrac{2\pi \omega}{t}$

Substituting all these values in equation (1), we have

$F &=& \dfrac{I\alpha}{r}\\&=& \dfrac{\pi m r \omega}{t}\\&=& \dfarc{\pi(210~Kg)(1.5~m)(0.600~rev/s)}{2.00~s}\\&=& 296.88~N$

Answer from: Quest

what is the actual question though?

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

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A 210-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in...

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