How Do Gravitational Potential and Kinetic Energy Relate in Energy Conservation?

[okgo]

Homework Statement

Homework Equations

Wgravity = mgh
KE=1/2mv²

The Attempt at a Solution

I know the gravitational potential energy is different because mgh accounts for mass.
But the book says that B is correct. I don't know why because isn't the less mass you have the faster you go? 2KE/m=v²

 

[LowlyPion]

Homework Equations

Wgravity = mgh
KE=1/2mv²

The Attempt at a Solution

I know the gravitational potential energy is different because mgh accounts for mass.
But the book says that B is correct. I don't know why because isn't the less mass you have the faster you go? 2KE/m=v²

Step back a bit and look at the equations.

PE = KE at the bottom.

m*g*h = 1/2*m*v²

v² = 2*g*h

The mass has canceled out.

 

[nlightner]

.

I would like to clarify that the concept of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another. In this case, the equations for gravitational potential energy and kinetic energy are both valid and do not contradict each other.

The equation Wgravity = mgh represents the potential energy an object has due to its position in a gravitational field, where m is the mass, g is the acceleration due to gravity, and h is the height. This equation does not take into account the velocity of the object, as it is solely based on its mass and position.

On the other hand, the equation KE=1/2mv2 represents the kinetic energy of an object, where m is the mass and v is the velocity. This equation takes into account the velocity of the object and shows that the kinetic energy increases as the velocity increases.

Therefore, the two equations are not contradictory, but rather they represent different forms of energy that an object can possess. In the case of a falling object, the potential energy is converted into kinetic energy as the object gains speed. This is in line with the principle of conservation of energy, where the total energy of the system (object + Earth) remains constant.

As for the statement about the less mass you have, the faster you go, it is important to note that this is only true if the other variables, such as height or force, remain constant. In the case of a falling object, the acceleration due to gravity (g) remains constant, so the mass of the object does not affect its velocity. However, if other factors such as air resistance are taken into account, the mass of the object can play a role in its velocity.

In conclusion, the equations for gravitational potential energy and kinetic energy are both valid and do not contradict each other. They represent different forms of energy and are both important in understanding the concept of conservation of energy.