ME = 12mv^2 + mgh

Question

The total mechanical energy of an object with mass mm at height hh in a closed system can be written as ME = 12mv2 + mghME = 12mv^2 + mgh. Solve for v, the velocity of the object, in terms of the given quantities.

Answer 1

Nick,

 

I am sure you meant (1/2)mv², not 12mv² 

 

Let E = total mechanical energy

 

E = (1/2)mv² + mgh ⇒ 

 

v = √[(2/m)(E - mgh)]

 

 

Answer 2

Hi Nick,

 

This is a purely algebraic question. You just need to rearrange the variables so that you can get v.

 

ME = (1/2)mv^2 + mgh

 

ME - mgh = (1/2)mv^2

 

v^2 = 2*(ME - mgh) / (m)

 

v = ± √[2*(ME - mgh) / (m)]

 

Hope this helps!