To solve this problem, we will start by defining each of the variables given and proceed to find the modulus of elasticity of the object. We will calculate the deformation per unit of elastic volume and finally we will calculate the net energy of the system. Let's start defining the variables
Yield Strength of the metal specimen

Yield Strain of the Specimen

Diameter of the test-specimen

Gage length of the Specimen

Modulus of elasticity



Strain energy per unit volume at the elastic limit is



Considering that the net strain energy of the sample is




Therefore the net strain energy of the sample is 
Kinetic energy: the energy of motion
Work: the change in kinetic energy
Power: the rate of work done
Explanation:
The kinetic energy of an object is the energy possessed by the object due to its motion. Mathematically, it is given by:

where
m is the mass of the object
v is its speed
The work done an object is the amount of energy transferred; according to the energy-work theorem, it is equal to the change in kinetic energy of an object:

where
is the final kinetic energy
is the initial kinetic energy
Finally, the power is the rate of work done per unit time. Mathematically, ti can be expressed as

where
W is the work done
t is the time elapsed
Learn more about kinetic energy, work and power:
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Answer:
a)
, b)
, c) 
Explanation:
a) The initial potential energy is:


b) The efficiency of the bounce is:


c) The final speed of Danielle right before reaching the bottom of the hill is determined from the Principle of Energy Conservation:





3.125 meters diving 10 and 3.2 the angel does not have a value in the equation but if you were to use it in a real life setting it will