**Problem Statement:**A 50 cm diameter, 400 g beach ball is dropped with a 4 mg ant riding on top. The ball experiences air resistance, but the ant does not. What is the magnitude of the normal force exerted on the ant when the ball’s speed is 2 m/s? The drag coefficient \( C \) is 0.5, and the air density \( \rho \) is 1.2 kg/m\(^3\).**Solution Explanation:**1. **Parameters:** - Diameter of the ball: 50 cm - Mass of the ball: 400 g - Mass of the ant: 4 mg - Speed of the ball: 2 m/s - Drag coefficient \( C = 0.5 \) - Air density \( \rho = 1.2 \) kg/m\(^3\)2. **Drag Force Calculation:** - Convert diameter to meters: 0.5 m - Cross-sectional area \( A \) of the ball: \[ A = \pi \left(\frac{0.5}{2}\right)^2 \] - Drag Force \( F_d \): \[ F_d = \frac{1}{2} \cdot C \cdot \rho \cdot A \cdot v^2 \]3. **Normal Force on the Ant:** - As the ant does not experience air resistance, the only forces acting on it are: - Its weight: \( m_{ant} \cdot g \) - The normal force exerted by the ball - The ant experiences the same acceleration as the ball. - Using Newton's Second Law to solve for the normal force \( N \) on the ant when the forces balance: \[ N = m_{ant} \cdot g - F_d \]4. **Result:** - Plug in the calculated drag force and ant's weight to find \( N \).This solution approach outlines the necessary steps to determine the normal force exerted on the ant. The calculations are a simple illustration of Newtonian physics principles, particularly focusing on dynamics in the presence of air resistance.

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A 50 cm diameter 400g beach ball is dropped with a 4mg ant riding the top. The ball experiences air resistance, but the ant does not; What is the magnitude of the normal force exerted on the ant when the ball's speed is 2m/s? (C= 0.5, p = 1.2 kg/m^3)

A 50 cm diameter 400g beach ball is dropped with a 4mg ant riding the top. The ball experiences air resistance, but the ant does not; What is the magnitude of the normal force exerted on the ant when the ball's speed is 2m/s? (C= 0.5, p = 1.2 kg/m^3)

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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