Conservation of Energy Question?

Elsie Resner: Let m = massand v = speed at height h be given.Total mechanical energy = potential energy + kinetic energy= mgh + (1/2)mv^2which is conserved.If H = maximum height reached, then mechanical energy at that height= mgH ... [because at max. ht. velocity and hence kinetic energy is zero]By the law of conservation of energy,mgH = mgh + (1/2)mv^2=> Max. Ht. H = (2gh + v^2) / g= 2h + v^2/g....Show more

Hal Palowoda: The gravitational potential energy (I assume that is what you mean) is equal to the mass times the acceleration due to gravity times the height above the ground .PE = mgh where g = 9.8 m/sThe kinetic energy is one half the objects mass times the square of the velocity.KE = 1/2*mv^2The law of conservation of energy states that the combination of PE + KE for an object must total the same amount no matter where it is in its trajectory. For instance, if you you hold a ball 1 meter off the ground and throw it up in the air (with some velocity) then! it has PE equal to the height from which you threw it plus KE from the velocity you threw it. Once it gets to the top of its trajectory (where it turns from going up to coming back down) the velocity is Zero so ALL the energy is now PE. When it finally gets back down to your hand then you know it has to have the same exact velocity it had when you threw it, because the PE is back to 1 meter. If you let it go past your hand you can figure out how fast it will be going when it hits the ground because all the energy has to become kinetic (the ground is where PE is zero).Thus if you have the object's mass, speed and height at ANY given point in its travel, you can figure out everything else about it.I hope this helps...Show more