The speed of trainee in
is
and in
is
.
Explanation:
The radius of horizontal circle is
.and the force is equal to
times the weight of trainee.
Our aim is to obtain the velocity or speed of trainee in both
and
.
The weight of the trainee is calculated as,
![W=mg](https://tex.z-dn.net/?f=W%3Dmg)
The force is equal to 7.8 times the weight of trainee and is shown below.
![F=7.8mg](https://tex.z-dn.net/?f=F%3D7.8mg)
The expression for centripetal force is shown below.
......(1)
The radius of circle is
.
The centripetal force is equal to the force exerted by trainee.
So, substitute
for
and
for
in equation (1) to obtain the value of velocity in
.
![\begin{aligned}7.8mg&=\frac{{m{v^2}}}{{11}}\\7.8g&=\frac{{{v^2}}}{{11}}\\{v^2}&=85.8g\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D7.8mg%26%3D%5Cfrac%7B%7Bm%7Bv%5E2%7D%7D%7D%7B%7B11%7D%7D%5C%5C7.8g%26%3D%5Cfrac%7B%7B%7Bv%5E2%7D%7D%7D%7B%7B11%7D%7D%5C%5C%7Bv%5E2%7D%26%3D85.8g%5C%5C%5Cend%7Baligned%7D)
The acceleration due to gravity is
.
Now, the velocity is calculated as,
![\begin{gathered}{v^2}=85.8\left({9.8}\right)\\=840.84\\v=\sqrt{840.84}\\=28.99\\\approx29{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%7Bv%5E2%7D%3D85.8%5Cleft%28%7B9.8%7D%5Cright%29%5C%5C%3D840.84%5C%5Cv%3D%5Csqrt%7B840.84%7D%5C%5C%3D28.99%5C%5C%5Capprox29%7B%5Ctext%7B%20%7D%7D%7B%7B%5Ctext%7Bm%7D%7D%5Cmathord%7B%5Cleft%2F%7B%5Cvphantom%7B%7B%5Ctext%7Bm%7D%7D%7B%5Ctext%7Bs%7D%7D%7D%7D%5Cright.%5Ckern-%5Cnulldelimiterspace%7D%7B%5Ctext%7Bs%7D%7D%7D%5C%5C%5Cend%7Bgathered%7D)
Therefore, the velocity of trainee in
is approximately
.
The expression for angular velocity in
is shown below.
... (2)
The obtained velocity is
, so substitute
for
and
for
in equation (2) to obtain the angular velocity.
![\begin{aligned}\omega&=\frac{29}{2\pi(11)}\\&=0.419\\&\approx0.42\text{ rev/s}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Comega%26%3D%5Cfrac%7B29%7D%7B2%5Cpi%2811%29%7D%5C%5C%26%3D0.419%5C%5C%26%5Capprox0.42%5Ctext%7B%20rev%2Fs%7D%5Cend%7Baligned%7D)
Therefore, the angular velocity in
is
.
Thus, the speed of trainee in
is
and in
is
.
Learn More:
1. Linear momentum <u>brainly.com/question/11947870</u>
2. Motion and velocity <u>brainly.com/question/6955558
</u>
3. Centripetal Force <u>brainly.com/question/7420923</u>
Answer Details:
Grade: High School
Subject: Physics
Chapter: Circular Motion
Keywords:
Device, astronauts, jet, pilots, rotation, trainee, horizontal, force, weight, fast, m/s, rev/s, tangential, velocity, speed, angular, centripetal.