# Law of conservation of energy

1. Feb 28, 2008

### annabelx4

1. The problem statement, all variables and given/known data

Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth.

In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy.

In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the object's kinetic energy and its gravitational potential energy . The law of conservation of energy for such cases implies that the sum of the object's kinetic energy and potential energy does not change with time. This idea can be expressed by the equation

K_i + U_1 + W_other = K_2 + U_2 ,

where "i" denotes the "initial" moment and "f" denotes the "final" moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem.

What is the speed of the object at the height of ?
Express your answer in terms of and . Use three significant figures in the numeric coefficient.

2. Relevant equations

K_i + U_1 + W_other = K_2 + U_2

3. The attempt at a solution

(1/2) mv^2 + 0 + 0 = (1/2) mv^2 + mg (v^2 / 4g)

so when I solve for v it = 0

mv^2 = 2(0)

v = 0

What did I do wrong?

2. Feb 28, 2008

### blochwave

So you're assuming it launches from the ground, so Ki=1/2*mVi^2

then at some other point it will have slowed down of course, so Kf=1/2*m*Vf^2, and the potential energy will be U=mgh

You tried to solve for h as a function of its velocity(which at that point will be the same Vf) as in the kinetic energy equation but I don't believe you did it right

3. Feb 28, 2008

### Staff: Mentor

You need to find that appropriate expression for the gravitational potential energy, U_1 and U_2, as functions of r, where r is the radius from the center of the mass responsible for the gravitational field.

http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html#gpt