College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**Understanding Propulsion in Microorganisms**

Microorganisms in water need to constantly exert propulsion forces to maintain their movement due to their small size. This differs from larger objects, which can rely on inertia. For microorganisms, these forces are applied through mechanisms like rotating flagella or beating cilia.

**Drag Forces and Equations**

For small particles in a liquid, the quadratic model of drag typically used for larger objects is not suitable. Instead, a linear drag force is experienced, represented by:

\[ \overrightarrow{D} = b\overrightarrow{v} \]

Here, \( \overrightarrow{D} \) is the drag force, \( \overrightarrow{v} \) is velocity, and \( b \) is a constant dependent on factors like the object's shape and the liquid's viscosity. Specifically, for a sphere with radius \( R \):

\[ b = 6\pi \eta R \]

where \( \eta \) represents the liquid's viscosity. At 20°C, water’s viscosity is \( 1.0 \times 10^{-3} \text{N} \cdot \text{s/m}^2 \).

**Application and Calculation**

To evaluate the propulsion force for microorganisms:

1. **Calculation for Paramecium (Part C)**
   - Determine the acceleration the propulsion force could provide to a paramecium if no drag is present.
   - Enter results to two significant figures, including units.

2. **Calculation for E.coli Bacterium (Part D)**
   - Determine the acceleration the propulsion force could provide to E.coli if no drag is present.
   - Enter results to two significant figures, with appropriate units.

Both calculations assume the density of these organisms equals that of water, \( 1000 \text{kg/m}^3 \).

This understanding aids in grasping how microorganisms adapt their movement strategies in a fluid environment, highlighting the unique challenges faced due to their small size.
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Transcribed Image Text:**Understanding Propulsion in Microorganisms** Microorganisms in water need to constantly exert propulsion forces to maintain their movement due to their small size. This differs from larger objects, which can rely on inertia. For microorganisms, these forces are applied through mechanisms like rotating flagella or beating cilia. **Drag Forces and Equations** For small particles in a liquid, the quadratic model of drag typically used for larger objects is not suitable. Instead, a linear drag force is experienced, represented by: \[ \overrightarrow{D} = b\overrightarrow{v} \] Here, \( \overrightarrow{D} \) is the drag force, \( \overrightarrow{v} \) is velocity, and \( b \) is a constant dependent on factors like the object's shape and the liquid's viscosity. Specifically, for a sphere with radius \( R \): \[ b = 6\pi \eta R \] where \( \eta \) represents the liquid's viscosity. At 20°C, water’s viscosity is \( 1.0 \times 10^{-3} \text{N} \cdot \text{s/m}^2 \). **Application and Calculation** To evaluate the propulsion force for microorganisms: 1. **Calculation for Paramecium (Part C)** - Determine the acceleration the propulsion force could provide to a paramecium if no drag is present. - Enter results to two significant figures, including units. 2. **Calculation for E.coli Bacterium (Part D)** - Determine the acceleration the propulsion force could provide to E.coli if no drag is present. - Enter results to two significant figures, with appropriate units. Both calculations assume the density of these organisms equals that of water, \( 1000 \text{kg/m}^3 \). This understanding aids in grasping how microorganisms adapt their movement strategies in a fluid environment, highlighting the unique challenges faced due to their small size.
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