Question

At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 2.80 m/s, and an 76.6-kg person feels a 341-N force pressing against his back. What is the radius of a chamber?

Answer 1

Answer:1.76 m

Explanation:

Given

speed of wall=2.8 m/s

mass of person m =76.6 kg

Person feels a force of 341 N

centrifugal force is given by

$F_c=\frac{mv^2}{r}$

$341=\frac{76.6\times 2.8^2}{r}$

$r=\frac{76.6\times 7.84}{341}$

$r=1.76 m$

Answer 2

The radius of a chamber is 1.76 m

$\texttt{ }$

Further explanation

Centripetal Acceleration can be formulated as follows:

$\large {\boxed {a = \frac{ v^2 } { R } }$

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

$\texttt{ }$

Centripetal Force can be formulated as follows:

$\large {\boxed {F = m \frac{ v^2 } { R } }$

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

$\texttt{ }$

Given:

speed = v = 2.80 m/s

mass of person = m = 76.6 kg

force = F = 341 N

Asked:

radius of chamber = R = ?

Solution:

$F = m \frac{v^2}{R}$

$F \div m = \frac{v^2}{R}$

$R = mv^2 \div F$

$R = 76.6 \times 2.80^2 \div 341$

$\boxed{R \approx 1.76 \texttt{ m}}$

$\texttt{ }$

Learn more

• Impacts of Gravity : https://brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
• The Acceleration Due To Gravity : https://brainly.com/question/4189441

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion