In an amusement park a box is attached to a rod of length 25 m and rotates in a vertical circle.

Name: Problem 18, Chapter 2: Physics for the IB Diploma
Uploaded: 2021-06-28T09:49:51-08:00
Duration: 1 min 19 s
Channel: Prabhu Ramji
Description: In an amusement park a box is attached to a rod of length 25 m and rotates in a vertical circle. The park claims that the centripetal acceleration felt by the occupants sitting firmly in the box is 4 g . How many revolutions per minute does the machine make?

step 1 This question covers the concept of the centipotile acceleration and we are going to use this eq

Question

In an amusement park a box is attached to a rod of length $25 \mathrm{m}$ and rotates in a vertical circle. The park claims that the centripetal acceleration felt by the occupants sitting firmly in the box is $4 g .$ How many revolutions per minute does the machine make?

   In an amusement park a box is attached to a rod of length $25 \mathrm{m}$ and rotates in a vertical circle. The park claims that the centripetal acceleration felt by the occupants sitting firmly in the box is $4 g .$ How many revolutions per minute does the machine make?

Physics for the IB Diploma

K. A. Tsokos 5th Edition

Chapter 2, Problem 18

Instant Answer

Solved by Expert Prabhu Ramji

06/28/2021

Step 1

Step 1: We know that the centripetal acceleration $a_c$ is given by the formula $a_c = 4\pi^2f^2r$, where $f$ is the frequency of rotation and $r$ is the radius of the circle. Show more…

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In an amusement park a box is attached to a rod of length $25 \mathrm{m}$ and rotates in a vertical circle. The park claims that the centripetal acceleration felt by the occupants sitting firmly in the box is $4 g .$ How many revolutions per minute does the machine make?

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Key Concepts

Angular Frequency and Unit Conversion

Angular frequency measures how fast an object rotates or revolves, usually given in radians per second. Converting this to revolutions per minute involves understanding the relationships between the angular values (2? radians equals one revolution) and time units (60 seconds equals one minute).

Uniform Circular Motion

Uniform circular motion describes the motion of an object moving at a constant speed along a circular path. Despite the constant speed, the object experiences continuous acceleration due to the change in the direction of its velocity, which is provided by the centripetal acceleration.

Centripetal Acceleration

This concept refers to the acceleration directed towards the center of a circular path that a body must have in order to change its velocity direction and remain in circular motion. It is calculated using the formula a_c = v² / R, where v is the tangential speed and R is the radius of the circle.

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