Physics, 19.11.2019 00:31 almaloney01

Aflywheel of mass 35.0 kg and diameter 60.0 cm spins at 400 rpm when it experiences a sudden power loss. the flywheel slows due to friction in its bearings during the 20.0 s the power is off. if the flywheel makes 200 complete revolutions during the power failure, (a) at what rate is the flywheel spinning when the power comes back on? (b) how long would it have taken for the flywheel to come to a complete stop?

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Answer from: nadarius2017

To solve this problem it is necessary to apply the concepts of displacement, speed and acceleration given by classical mechanics.

Our previously given values correspond to,

$\omega =400rpm = 400*\frac{2*pi}{60}= 41.9 rad/s$

$\theta=200 revs = 200*2*pi= 1257.14 rad$

By definition we know that angular displacement is defined by,

$\theta = \theta_0 +\omega_0*t+\frac{1}{2}\alpha t^2$

Here we know that there is no initial deployment so replacing the values we have to,

$1257.14 = 0+41.9*20+0.5*\alpha*20^2$

Solving for $\alpha$

$\alpha = 2.0957 rad/s^2$

From the acceleration description equations we know that,

$\omega_f = \omega_i+\alpha t$

$\omega_f = 41.9+2.0957*20 = 83.814 rad/s$

The moment the body reaches the final velocity 0, it will take a period of time and a couple of turns the point at which it stops, then

$\omega_f = \omega_i+\alpha t$

0=41.9-2.0957*t

$t = \frac{41.9}{2.0957} = 19.99 s$

The angular displacement will then be given by

$\theta = \omega_0*t-\frac{1}{2}\alpha t$

$\theta=41.9*19.99-0.5*2.0957*19.992$

$\theta= 418.86 rad$

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.

Answer from: Quest

The anwser is: wave a has a greater pitch and frequency.

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