**Understanding Terminal Speed in Liquids**Particles in liquids achieve terminal speed very quickly. This experiment demonstrates how to measure the time taken for a particle to descend a certain distance and use this information to calculate a constant, β.**Scenario:**Suppose a steel ball bearing (mass = 0.86 grams) is dropped in a container of motor oil. It takes 12 seconds to fall 0.60 meters.**Experiments:**(a) **Estimate the Terminal Speed, \( v_{\text{term}} \):**Assume the ball bearing reaches terminal speed almost immediately.- **Solution:** \( v_{\text{term}} \approx 0.050 \, \text{m/s} \)(b) **Calculate β:**- **Solution:** \( \beta = 0.17 \, \text{kg/s} \)(c) **Determine the Speed of the Ball Bearing 11 ms After Being Dropped:**- **Solution:** \( 0.044 \, \text{m/s} \)This experiment and calculations help understand the behavior of particles in liquids and the factors affecting their motion.

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Particles in liquids achieve terminal speed very quickly. One can measure the time it takes for a particle to fall a certain distance and then calculate the constant B. Suppose a steel ball bearing (mass-0.86 grams) is dropped in a container of motor oil. It takes 12 s to fall 0.60 m. (a) Estimate the terminal speed, Vie, assuming the ball bearing reaches terminal speed almost immediately. (answer: Vier 0.050 m/s) (b) Calculate B. (answer: 0.17 kg/s) (c) What is the speed of the ball bearing 11 ms after it is dropped? (answer: 0.044 m/s)

Particles in liquids achieve terminal speed very quickly. One can measure the time it takes for a particle to fall a certain distance and then calculate the constant B. Suppose a steel ball bearing (mass-0.86 grams) is dropped in a container of motor oil. It takes 12 s to fall 0.60 m. (a) Estimate the terminal speed, Vie, assuming the ball bearing reaches terminal speed almost immediately. (answer: Vier 0.050 m/s) (b) Calculate B. (answer: 0.17 kg/s) (c) What is the speed of the ball bearing 11 ms after it is dropped? (answer: 0.044 m/s)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

**Understanding Terminal Speed in Liquids**

Particles in liquids achieve terminal speed very quickly. This experiment demonstrates how to measure the time taken for a particle to descend a certain distance and use this information to calculate a constant, β.

**Scenario:**
Suppose a steel ball bearing (mass = 0.86 grams) is dropped in a container of motor oil. It takes 12 seconds to fall 0.60 meters.

**Experiments:**

(a) **Estimate the Terminal Speed, \( v_{\text{term}} \):**

Assume the ball bearing reaches terminal speed almost immediately.

- **Solution:** \( v_{\text{term}} \approx 0.050 \, \text{m/s} \)

(b) **Calculate β:**

- **Solution:** \( \beta = 0.17 \, \text{kg/s} \)

(c) **Determine the Speed of the Ball Bearing 11 ms After Being Dropped:**

- **Solution:** \( 0.044 \, \text{m/s} \)

This experiment and calculations help understand the behavior of particles in liquids and the factors affecting their motion.

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