Mechanical energy is the sum of both potential and kinetic energy. Thus, we must find both the potential and kinetic energy first.
The equation for gravitational potential energy is PE=MGH, or potential energy=Mass*gravitational acceleration*height. Since initial potential energy is equal to final kinetic energy, we can also equal our potential energy equation to the kinetic energy equation, or Kinetic Energy=1/2mass*velocity^2.
MGHinitial=1/2mv^2final.
Now, insert the values that we know. First, lets insert the mass.
(1)GHinitial=1/2(1)v^2final.
Now substitute gravitational acceleration and height into the potential energy equation.
1(9.8)(10)=1/2(1)V^2
98=1/2(1)v^2
Since KE is equal to PE, we know that both KE and PE are 98. So to solve for mechanical energy, multiply 98 by 2.
98*2=196.
The mechanical energy is 196.
Hope this helps!
