Answer:
Minimum height of metal = 5 inches
Explanation:
Volume of the cylindrical metal = πR²H = 125π
cancelling out π on both sides
R²H = 125
Hence it can be deduced that R² = 25 and H = 5
Hence minimum height of metal = 5 inches
1) The total mechanical energy of the rock is:

where U is the gravitational potential energy and K the kinetic energy.
Initially, the kinetic energy is zero (because the rock starts from rest, so its speed is zero), and the total mechanical energy of the rock is just gravitational potential energy. This is equal to

where

is the mass,

is the gravitational acceleration and

is the height.
Putting the numbers in, we find the potential energy

2) Just before hitting the ground, the potential energy U is zero (because now h=0), and all the potential energy of the rock converted into kinetic energy, which is equal to:

where v is the speed of the rock just before hitting the ground. Since the mechanical energy of the rock must be conserved, then the kinetic energy K before hitting the ground must be equal to the initial potential energy U of the rock:

3) For the work-energy theorem, the work W done by the gravitational force on the rock is equal to the variation of kinetic energy of the rock, which is:
Answer:
Spring cannot return to its original, since a part of its deformation is <u>plastic</u>, not <u>elastic</u>.
Explanation:
Physically speaking, stress is equal to the axial force divided by effective transversal area of spring. In addition, springs have usually a linear relationship between stress and strain in <u>elastic region</u>, since they are made of ductile materials. Axial force is directly proportional to axial stress, which is also directly proportional to axial strain.
Then, if force is greater than force associated with elastic limit of the spring, then spring cannot return to its original, since a part of its deformation is <u>plastic</u>, not <u>elastic</u>.