### Physics Problem: Calculating the Mass of a Speed Skater**Problem Statement:**A speed skater goes around a turn that has a radius of 34 meters. The skater has a speed of 14 meters per second and experiences a centripetal force of 450 Newtons. What is the mass of the skater?To solve this problem, we will use the formula for centripetal force:\[ F = \frac{mv^2}{r} \]Where:- \( F \) is the centripetal force- \( m \) is the mass of the skater- \( v \) is the speed- \( r \) is the radius**Given:**- \( F = 450 \, \text{N} \)- \( v = 14 \, \text{m/s} \)- \( r = 34 \, \text{m} \)**Solution Steps:**1. Rearrange the formula to solve for the mass \( m \):\[ m = \frac{Fr}{v^2} \]2. Substitute the given values into the equation:\[ m = \frac{450 \, \text{N} \times 34 \, \text{m}}{(14 \, \text{m/s})^2} \]3. Perform the calculations:\[ m = \frac{450 \times 34}{14^2} \]\[ m = \frac{15300}{196} \]\[ m \approx 78.06 \, \text{kg} \]Therefore, the mass of the skater is approximately \( 78.06 \) kilograms.

Radius, R = 34 mSpeed, V = 14 m/sForce, F = 450 N

Answered: A speed skater goes around a turn that…

A speed skater goes around a turn that has a radius of 34 m. The skater has a speed of 14 m/s and experiences a centripetal force of 450 N. What is the mass of the skater?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

### Physics Problem: Calculating the Mass of a Speed Skater

**Problem Statement:**

A speed skater goes around a turn that has a radius of 34 meters. The skater has a speed of 14 meters per second and experiences a centripetal force of 450 Newtons. What is the mass of the skater?

To solve this problem, we will use the formula for centripetal force:

\[ F = \frac{mv^2}{r} \]

Where:
- \( F \) is the centripetal force
- \( m \) is the mass of the skater
- \( v \) is the speed
- \( r \) is the radius

**Given:**
- \( F = 450 \, \text{N} \)
- \( v = 14 \, \text{m/s} \)
- \( r = 34 \, \text{m} \)

**Solution Steps:**

1. Rearrange the formula to solve for the mass \( m \):

\[ m = \frac{Fr}{v^2} \]

2. Substitute the given values into the equation:

\[ m = \frac{450 \, \text{N} \times 34 \, \text{m}}{(14 \, \text{m/s})^2} \]

3. Perform the calculations:

\[ m = \frac{450 \times 34}{14^2} \]

\[ m = \frac{15300}{196} \]

\[ m \approx 78.06 \, \text{kg} \]

Therefore, the mass of the skater is approximately \( 78.06 \) kilograms.

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