Textbook Question
During each heartbeat, approximately 70 cm³ of blood is pushed from the heart at an average pressure of 105 mm-Hg. Calculate the power output of the heart, in watts, assuming 70 beats per minute.
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19. Fluid Mechanics
Intro to Pressure
5:52 minutesProblem 48a
Textbook Question
What is the maximum tension possible in a 1.00-mm-diameter nylon tennis racket string?
Verified step by step guidance1
Determine the cross-sectional area of the string. The string is cylindrical, so the cross-sectional area can be calculated using the formula: , where is the radius of the string. Since the diameter is given as 1.00 mm, the radius is half of that: m.
Look up the tensile strength of nylon, which is the maximum stress it can withstand before breaking. Tensile strength is typically given in units of Pascals (Pa). For nylon, this value is approximately Pa (this value may vary slightly depending on the specific type of nylon).
Calculate the maximum force (tension) the string can withstand using the relationship between stress and force: , where is the tensile strength, is the force, and is the cross-sectional area. Rearrange this formula to solve for : .
Substitute the values for tensile strength and cross-sectional area into the formula. Use the tensile strength of nylon ( Pa) and the area calculated in step 1.
Perform the multiplication to find the maximum tension. Ensure that the units are consistent throughout the calculation (e.g., using meters for radius and Pascals for tensile strength). The result will give the maximum tension in Newtons (N) that the string can withstand.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Tension in Strings
Tension is the force transmitted through a string, rope, or cable when it is pulled tight by forces acting from opposite ends. In the context of a tennis racket string, the maximum tension is determined by the material properties of the string and the forces applied during play. Understanding how tension behaves under different conditions is crucial for analyzing the performance of the racket.
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Material Properties
The maximum tension a string can withstand is influenced by its material properties, such as tensile strength and elasticity. Nylon, commonly used in tennis racket strings, has specific characteristics that define how much force it can handle before breaking. Knowing these properties helps in determining the safe operating limits of the string during use.
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Cross-Sectional Area
The cross-sectional area of a string plays a significant role in its ability to withstand tension. For a cylindrical string, the area can be calculated using the diameter, which affects the distribution of stress within the material. A larger cross-sectional area generally allows for greater tension capacity, making it essential to consider when evaluating the maximum tension in the racket string.
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