How Does Young's Modulus Factor into Calculating Pendulum Swing Velocity?

In summary, the problem is missing information about the point of release of the pendulum, which is necessary to calculate the tension in the wire and ultimately find the velocity of the ball at its lowest point. This information could be the angle at which the pendulum is released, such as 45 degrees or 10 degrees, etc. Without this data, it is not possible to solve the problem.
  • #1
Abhishekdas
208
0
Young's modulus question...

Homework Statement


A sphere of radius 10 cm and mass 25 kg is attached to the lower ends of a steel wire which is suspended from the ceiling of a room. the point of the support is 521 cm above the floor. When the sphere is set swinging as a simple pendulum, its lowest point just grazes the floor. Calculate the velocity of the ball at its lowest point.


Homework Equations





The Attempt at a Solution


I think some information is missing here...Either th strain or the initial length or change in length should be given so that i can calculate tension and hence equate it to mv2/r + mg...
 
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  • #2


What's missing is the point of release of the pendulum.
 
  • #3


Hi...PhanthomJay...

What is the use of the point of release? I thought if i had the tension in the wire somehow my job was done...As i said equate it to mv^2/r + mg...
 
  • #4


Yes, and you don't have the tension, so, as you say, the problem is missing information, like is the pendulum released when it's 45 degrees from the negative y axis, or is it 10 degrees, or 5 degrees, etc. ? That is the missing data.
 
  • #5


Ya...right...
 

What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of the stiffness or rigidity of a material. It is defined as the ratio of stress (force per unit area) to strain (change in length per unit length) in a material that is being elastically deformed. It is denoted by the symbol E and has units of pascals (Pa).

How is Young's modulus calculated?

Young's modulus is calculated by dividing the stress applied to a material by the strain that results from that stress. This can be expressed mathematically as E = stress/strain. The strain is typically measured in units of length, such as meters (m), and the stress is measured in units of force per area, such as newtons per square meter (N/m2).

What factors affect Young's modulus?

Young's modulus is affected by several factors, including the type of material, its composition, and its microstructure. Generally, materials with stronger interatomic bonds and a more ordered microstructure tend to have a higher Young's modulus. Temperature and pressure can also affect Young's modulus, as they can cause changes in the structure and arrangement of atoms in a material.

What is the significance of Young's modulus?

Young's modulus is a fundamental property of materials that is used to characterize their mechanical behavior. It is an important factor in determining the strength and stiffness of a material, which can impact its suitability for different applications. For example, materials with a high Young's modulus may be more suitable for structural components, while materials with a lower Young's modulus may be better for flexible applications.

Can Young's modulus change over time?

Yes, Young's modulus can change over time due to various factors such as temperature, stress, and strain. Some materials may also exhibit time-dependent behavior, known as viscoelasticity, which can cause their Young's modulus to change over time. Additionally, external factors such as exposure to chemicals or radiation can also affect Young's modulus.

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