Question

Solve the question no. 4 ^_^​

Answer 1

$\underline{\boxed{\bold{Question}}}$  

↠ Propeller blades in aero-plane are 2 m long.

• When propeller is rotating with 1800 Rev/min, compute tangential velocity of the tips of blade.
• What is tangential at a point on the blade mid way between tips and axis

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Important\;Information}}}$  

↠ In the figure is shown a particle moving on a circular path. As it moves it  covers a distance s (arc length).

 

$\boxed{\bold{s=\theta R}}$

↠ Linear velocity "v" is always along the path. Its magnitude known as linear  speed is obtained by differentiating s with respect to time t.

$\boxed{\boxed{\bold{v=\omega R}}}$

↠ Hence this relation should be remembered.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Given}}}$

↠ Length of Blades = 2 Meters

↠ There are 1800 Rev/min

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\underline{\boxed{\bold{Answer}}}$

Let's Start !

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Let's simply the number of revolutions and convert it into radians.

$:\implies 1800\; Rev/min$

$:\implies 1800\; (2\pi ) \times \frac{1}{60}$

$:\implies 30\; (2\pi )$

$\boxed{\bold{\red{:\implies 60\pi\; Rad/sec}}}$

∴ ω = 60π rad/sec

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Now let's relation between v, ω, r.

i) Let's solve first part !

➢ ω = 60π rad/sec

➢ r = 2 meters

$\therefore v = \omega r$

$:\implies v = (60\pi )(2)$

$:\implies v = 120\pi\; m/s$

$:\implies v = 120\times 3.14\; m/s$

$:\implies v = 376.8 \;m/s$

$\boxed{\bold{\blue{:\leadsto v = 376.8\; m/s\; \approx 388\;m/s}}}$

ii) Let's solve second part !

➢ ω = 60π rad/sec

➢ r = 2/2 = 1 meters

$\therefore v = \omega r$

$:\implies v = (60\pi )(1)$

$:\implies v = 60\pi\; m/s$

$:\implies v = 60\times 3.14\; m/s$

$:\implies v = 188.4 \;m/s$

$\boxed{\bold{\blue{:\leadsto v = 188.4\; m/s}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Hope this helps u.../

【Brainly Advisor】

Answer 2

Explanation:

I hope this is help full to you