How do you use this equation?
mgh+1/2mvh=mgh+1/2mv^2+Fd
How you use it depends upon the problem you are trying to solve.
It looks like you are trying to use conservation of energy to solve a problem of height and velocity of an object moving in a gravitational field, with a work or drag term (Fd) included. However the mvh on the left would have to be mv^2. Even more important, the v's and h's on the right and left sides shoule have different subscripts, since they would apply to different times along the trajectory.
The equation you mentioned is the principle of conservation of mechanical energy. It relates the initial and final mechanical energies of a system.
To use this equation, you need to understand the variables involved:
- "m" represents the mass of an object.
- "g" represents the acceleration due to gravity, which is approximately 9.8 m/s^2 on Earth.
- "h" represents the height or vertical displacement of the object.
- "v" represents the velocity of the object.
- "F" represents the force acting on the object.
- "d" represents the displacement of the object in the direction of the force.
Here are the steps to use this equation:
1. Determine the initial and final states of the system: You need to identify the initial and final states of the object to assess its mechanical energy.
2. Calculate the initial mechanical energy (mgh+1/2mvh): You multiply the mass (m) by the acceleration due to gravity (g) and the vertical displacement (h). Then, you add half of the mass times the square of the initial velocity (1/2mvh).
3. Calculate the final mechanical energy (mgh+1/2mv^2+Fd): Similarly, you calculate the mass (m) times the acceleration due to gravity (g) and the vertical displacement (h). Then, you add half of the mass times the square of the final velocity (1/2mv^2). Finally, you add the work done by the force (F) acting on the object multiplied by the displacement (d) in the direction of the force.
4. Compare the initial and final mechanical energy: If the initial mechanical energy is equal to the final mechanical energy, it means mechanical energy is conserved.
So, to use this equation, you need to know the relevant variables and apply the steps explained above to determine if mechanical energy is conserved in a given situation.