Solving Young Modulus of Metal: Density, Length, Hammer Pulse Time

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In summary, the conversation discusses finding the Young Modulus of a metal rod that is hit with a hammer. Using the given data of the length, time, and density of the metal, the equation v=[sq. root](E/D) is used to calculate the modulus. The conversation concludes with the realization that the equation was already known and just needed to be applied.
  • #1
lifeiseasy
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Homework Statement


A metal rod of length 1.0 m is hit with a hammer at one end. It takes 5.5x10^-4 s for the compression pulse generated to travel to the other end and reflected back to the end hit by the hammer. Find the Young Modulus of the metal.
(Given: density of the metal = 9.0x10^3 kg m^-3)


Homework Equations


E=FL/Ae
D=M/V

The Attempt at a Solution


D=M/V=M/(AxL) (L=1m)
I just don't know how to make use of the data given. Clueless. My head's going to explode!
 
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  • #2
You need the equation that relates the speed of sound in a solid to its Young Modulus and density. From that you can calculate the modulus simply and directly from the other two values you are given.
Do you have this equation in your book or lecture notes?
 
  • #3
Yes! Is it v=[sq. root](E/D)?

Ah, it's actually just substituting numbers into the equation... Why can't I think of this equation in the first place

Thanks a lot!
 

Related to Solving Young Modulus of Metal: Density, Length, Hammer Pulse Time

1. What is the Young Modulus of a metal?

The Young Modulus, also known as the modulus of elasticity, is a measure of the stiffness of a material. In other words, it is a measure of how much a material will deform when a force is applied to it.

2. How do you calculate the Young Modulus of a metal?

The Young Modulus can be calculated by dividing the stress (force per unit area) by the strain (change in length per unit length) of a material. The equation is E = σ/ε, where E is the Young Modulus, σ is stress, and ε is strain.

3. Why is density a factor in calculating the Young Modulus?

Density is a factor in calculating the Young Modulus because it affects the mass of the material, which in turn affects its resistance to deformation. Materials with higher densities tend to have higher Young Moduli and are less likely to deform under a given stress.

4. How does length affect the Young Modulus?

The length of a material affects its Young Modulus because it determines the amount of strain that occurs when a force is applied. Longer materials will generally experience more strain and have lower Young Moduli compared to shorter materials.

5. What is the significance of hammer pulse time in solving the Young Modulus?

Hammer pulse time is an important factor in solving the Young Modulus because it represents the duration of the force applied to the material. The longer the hammer pulse time, the greater the force applied and the more strain the material experiences, resulting in a lower Young Modulus.

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