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MakcuM [25]
3 years ago
8

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provid

e a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 309-mile trip in a typical midsize car produces about 2.96 x 109 J of energy. How fast would a 10.1-kg flywheel with a radius of 0.437 m have to rotate to store this much energy? Give your answer in rev/min.
Physics
1 answer:
Kisachek [45]3 years ago
6 0

Answer:

\dot n = 748178.306\,rpm

Explanation:

A flywheel stores mechanical energy in the form of rotational kinetic energy:

K = \frac{1}{2}\cdot I \cdot \omega^{2}

The expression is simplified by considering the flywheel as a solid disk:

K = \frac{1}{4}\cdot m\cdot r^{2}\cdot \omega^{2}

The final speed of the flywheel is:

\Delta E = \frac{1}{4}\cdot m \cdot r^{2}\cdot \omega^{2}

\omega = \sqrt{\frac{4\cdot \Delta E}{m\cdot r^{2}} }

\omega = \frac{2}{r}\cdot \sqrt{\frac{\Delta E}{m} }

\omega = \frac{2}{0.437\,m}\cdot \sqrt{\frac{2.96\times 10^{9}\,J}{10.1\,kg} }

\omega \approx 78349.049\,\frac{rad}{s}

The final speed in revolutions per minute is:

\dot n = \frac{60\cdot \omega}{2\pi}

\dot n = \frac{60\cdot (78349.049\,\frac{rad}{s} )}{2\pi}

\dot n = 748178.306\,rpm

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pogonyaev

Answer:

Explanation:

3.75 * 10^-7

=3.75 * 1/10^7

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8 0
3 years ago
A hawk is flying horizontally at 18.0 m/s in a straight line, 230 m above the ground. A mouse it has been carrying struggles fre
Lisa [10]

Answer:

a) vd = 47.88 m/s

b) θ = 80.9°

c) t = 6.8 s

Explanation:

In the situation of the problem, you can assume that the trajectory of the hawk and the trajectory of the mouse form a rectangle triangle.

One side of the triangle is the horizontal trajectory of the hawk after 2.00s of flight, the other side of the triangle is the distance traveled by the mouse when it is falling down. And the hypotenuse is the trajectory of the hawk when it is trying to recover the mouse.

(a) In order to calculate the diving speed of the hawk, you first calculate the hypotenuse of the triangle.

One side of the triangle is c1 = (18.0m/s)(2.0s) = 36m

The other side of the triangle is c2 = 230m - 3m = 227 m

Then, the hypotenuse is:

h=\sqrt{(36m)^2+(227m)^2}=229.83m    (1)

Next, it is necessary to calculate the falling down time of the mouse, this can be done by using the following formula:

y=y_o+v_ot+\frac{1}{2}gt^2    (2)

yo: initial height = 230m

vo: initial vertical speed of the mouse = 0m/s

g: gravitational acceleration = -9.8m/s^2

y: final height of the mouse = 3 m

You replace the values of the parameters in (2) and solve for t:

3=230-4.9t^2\\\\t=\sqrt{\frac{227}{4.9}}=6.8s

The hawk traveled during 2.00 second in the horizontal trajectory, hence, the hawk needed 6.8s - 2.0s = 4.8 s to travel the distance equivalent to the hypotenuse to catch the mouse.

You use the value of h and 4.8s to find the diving speed of the hawk:

v_d=\frac{229.83m}{4.8s}=47.88\frac{m}{s}

The diving speed of the Hawk is 47.88m/s

(b) The angle is given by:

\theta=cos^{-1}(\frac{c_1}{h})=cos^{-1}(\frac{36m}{229.83m})=80.9 \°

Then angle between the horizontal and the trajectory of the Hawk when it is descending is 80.9°

(c) The mouse is falling down during 6.8 s

4 0
3 years ago
A radio station broadcasts its music with waves at a frequency of 7.34 x 10²Hz. These radio waves travel at a speed of 3.00x 10%
Lorico [155]

Answer:

See below

Explanation:

<u>I will use   3 x 10^8 m/s for speed or wave</u>

speed = wavelength * frequency

3 x 10^8  = w * 7.34 x 10^2     <====== are you sure this isn't KILO Hz ?

w = <u>408719. 3 meters   </u>

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2 years ago
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