Large objects have inertia and tend to keep moving-Newton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag given by the equation, Ď= (CpAv², direction opposite the motion), fails for very small particles. Instead, small object moving in a liquid experiences a linear drag force, D= (bu, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6R, where is the viscosity of the liquid. Water at 20°C has viscosity 1.0 x 10-³ N-s/m². The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, 1000 kg/m³. Part C Compute the acceleration that the propulsion force could give the paramecium if there were no drag Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) a= Submit Part D Value a 4 Value Compute the acceleration that the propulsion force could give the E.coli bacterium if there were no drag. Express your answer to two significant figures and include the appropriate units. ▸ View Available Hint(s) Units 4 → ? Units ?
Large objects have inertia and tend to keep moving-Newton's first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag given by the equation, Ď= (CpAv², direction opposite the motion), fails for very small particles. Instead, small object moving in a liquid experiences a linear drag force, D= (bu, direction opposite the motion), where b is a constant. For a sphere of radius R, the drag constant can be shown to be b = 6R, where is the viscosity of the liquid. Water at 20°C has viscosity 1.0 x 10-³ N-s/m². The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, 1000 kg/m³. Part C Compute the acceleration that the propulsion force could give the paramecium if there were no drag Express your answer to two significant figures and include the appropriate units. ► View Available Hint(s) a= Submit Part D Value a 4 Value Compute the acceleration that the propulsion force could give the E.coli bacterium if there were no drag. Express your answer to two significant figures and include the appropriate units. ▸ View Available Hint(s) Units 4 → ? Units ?
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37bce96e-1ddb-43d2-a9d4-e40e4a58cae5%2Fce504c17-e917-4345-9a6a-a7aaa8eda340%2Fxwoa7kn_processed.png&w=3840&q=75)
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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