a 70 kg block rests on the earth's surface. How much energy is required to move the block very far from the earth, ending up at rest again?
Using conservation of energy
Efinal=Einitial + Work
Neglecting rest mass energies
Uf+Kf=Ui+Ki+W
Starting and ending at rest so
Kf=Ki=0
Therefore
W=Uf-Ui
Using Gravitational potential energy
U=-Gm1m2/r
When r is very large
Uf=0
So
W=Gm1m2/r
To calculate the energy required to move the block very far from the earth, we need to consider the work done against the force of gravity. Here's how you can calculate it:
1. Determine the gravitational potential energy at the initial and final positions of the block. The formula to calculate gravitational potential energy is given by:
Potential Energy = mass × gravitational acceleration × height
2. Since moving the block far from the Earth requires us to consider infinite distances, we can approximate the height to infinity. In this case, the potential energy at the initial position is 0, as the block is on the Earth's surface.
3. The potential energy at the final position can be calculated as follows:
Potential Energy = mass × gravitational acceleration × height
Since height is approximated to infinity, the potential energy at the final position is also infinite.
4. The difference in potential energy between the initial and final positions is the energy required to move the block very far from the Earth. Therefore, the energy required is infinite.
This means that an infinite amount of energy is needed to move the block very far from the Earth's surface. The laws of physics prevent us from achieving this in reality, as it would violate the conservation of energy.