Question 2 please help

A high-speed flywheel in a motor is spinning at 450 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and

alexira [117]

Answer:

A) $\omega_f=17.503\ rad.s^{-1}$

B) $t=55.6822\ s$

C) $\theta=1312\ rad$

Explanation:

Given:

mass of flywheel, $m=40\ kg$

diameter of flywheel, $d=0.72\ m$

rotational speed of flywheel, $N_i=450\ rpm \Rightarrow \omega_i=\frac{450\times 2\pi}{60} =15\pi\ rad.s^{-1}$

duration for which the power is off, $t_0=35\ s$

no. of revolutions made during the power is off, $\theta=180\times 2\pi=360\pi\ rad$

<u>Using equation of motion:</u>

$\theta=\omega_i.t+\frac{1}{2} \alpha.t^2$

$360\pi=15\pi\times 35+\frac{1}{2} \times \alpha\times35^2$

$\alpha=-0.8463\ rad.s^{-2}$

Negative sign denotes deceleration.

A)

Now using the equation:

$\omega_f=\omega_i+\alpha.t$

$\omega_f=15\pi-0.8463\times 35$

$\omega_f=17.503\ rad.s^{-1}$ is the angular velocity of the flywheel when the power comes back.

B)

Here:

$\omega_f=0\ rad.s^{-1}$

Now using the equation:

$\omega_f=\omega_i+\alpha.t$

$0=15\pi-0.8463\times t$

$t=55.6822\ s$ is the time after which the flywheel stops.

C)

Using the equation of motion:

$\theta=\omega_i.t+\frac{1}{2} \alpha.t^2$

$\theta=15\pi\times 55.68225-0.5\times 0.8463\times 55.68225^2$

$\theta=1312\ rad$ revolutions are made before stopping.

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5 What is the angular displacement at the end of the 25-mm-diameter shaft and the linear displacement of point A of Figure P5.5

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5 What is the angular displacement at the end of the 25-mm-diameter shaft and the linear displacement of point A of Figure P5.5

<h3>What is displacement ?</h3>

A displacement is a vector in geometry and mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It calculates the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.

The final location xf of a point relative to its beginning position xi, or a relative position (derived from the motion), is another way to express a displacement. The difference between the end and beginning positions can be used to define the equivalent displacement vector

To learn more about displacement from the given link:

brainly.com/question/321442

#SPJ4

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When a fork is placed in a hot piece of lasagna, thermal energy is transferred up the fork by...

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Because it's placed in the lasagna, the thermal energy is transferred by conduction. Remember, convection is transfer of heat through fluids (liquids and gases), and radiation is just transfer of heat through air.

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What three assumptions about particles in a gas are made by the kinetic theory?

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The simplest kinetic model is based on the assumptions that: (1) the gas is composed of a large number of identical molecules moving in random directions, separated by distances that are large compared with their size; (2) the molecules undergo perfectly elastic collisions (no energy loss) with each other and with the walls of the container, but otherwise do not interact; and (3) the transfer of kinetic energy between molecules is heat.

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An archeologist on a dig finds a fragment of an ancient

marin [14]

Answer:

19792.96488 years

Explanation:

$\tau_{\dfrac{1}{2}}$ = Half life of carbon-14 atom = 5730 years

Disintegration is given by

$\lambda=\dfrac{ln2}{\tau_{\dfrac{1}{2}}}\\\Rightarrow \lambda=\dfrac{ln2}{5730}\\\Rightarrow \lambda=0.00012\ /years$

The distintegration constant

$0.093N_0=N_0e^{-\lambda t}\\\Rightarrow 0.093N_0=N_0e^{-0.00012 t}\\\Rightarrow ln\dfrac{1}{0.093}=0.00012t\\\Rightarrow t=\dfrac{ ln\dfrac{1}{0.093}}{0.00012}\\\Rightarrow t=19792.96488\ years$

The age of the basket is 19792.96488 years

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