Respuesta :

AL2006
                                                           M g h  =  1/2 m v²

What you have here is the first step in solving a couple of
very interesting questions.

Question #1). 
I just lifted this thing and put it on the high shelf, so now it has
some potential energy.
How fast would it have to be moving to have the same amount
of kinetic energy ?

Question #2).
This thing is moving down the street, so it has some kinetic energy. 
How high would it have to be to have the same amount of potential
energy ?

The first step in solving either of those questions would be to SAY that
the potential energy is equal to the kinetic energy:

                                                M g h  =  1/2 m v²
                                                 (PE)   =    (KE)

The first thing I want to do to this equation
is to divide each side by ' m ' :         
                                                     g h  =  1/2 v²
There it is !
- If you know the height of the shelf (h) you can find the
speed (v) to give the equivalent KE.
- If you know the speed, you can find the height for the
equivalent PE.
-- And the mass of the object doesn't matter !

This question that you posted says: 
I know the height of the shelf.  It's ' h ' .  I know how much potential energy
the object on that shelf has.  How fast would it need to move to have the
same amount of kinetic energy ?

Solve this equation for ' v ' :     g h  =  1/2 v²

Multiply each side by  2 :       2 g h  =         v²

Square root each side:             v  =  √(2 g h)     
________________________________________

If the object were moving down the street with speed = v, you would
know its kinetic energy.  How high would you have to lift it so that it
had the same amount of potential energy ?      

Solve this equation for ' h ' :     g h  =  1/2 v²

Divide each side by ' g ' :            h  =  v² / 2g

Is that cool or what !
rahulsharma789888

The solution for v by using the equation mgh = 1/2mv² would be v = √(2gh)

What is mechanical energy?

Total kinetic energy and total potential energy, which reflect all the energy that is stored in the system but is still in motion, are combined to form mechanical energy.

The sum of all the kinetic and potential energy held in the system is known as total mechanical energy.

ME = KE + PE

The total potential energy of the body

PE = mgh

m is the mass of the object

h is the height

g is the acceleration due to gravity

Similarly, The total kinetic energy of the object

KE = 1/2mv²

m is the mass of the object

v is the velocity of the object

As given in the problem we have to solve for velocity by equating the th total potential energy with the total kinetic energy

mgh = 1/2mv²

v = √(2gh)

Thus ,The solution for v by using the equation mgh = 1/2mv² would be v = √(2gh)

Learn more about mechanical energy from here

brainly.com/question/12319302

#SPJ2

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