Under conditions of conservation of energy where the initial energy object is only gravitiational potential energy and the final energy is only kinetic, write an equation to calculate the final velocity of the object. Ignore all friction. Show all work
Your answer:
To calculate the final velocity of an object under conditions of conservation of energy, where the initial energy is only gravitational potential energy and the final energy is only kinetic, we can use the principle of conservation of energy.
The principle of conservation of energy states that the total energy of a closed system remains constant. In this case, as there is no friction or external forces acting on the object, we can assume it is a closed system.
The initial energy of the object is gravitational potential energy, given by the equation:
E_initial = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance the object is raised from a reference point.
The final energy of the object is kinetic energy, given by the equation:
E_final = 1/2 * mv^2
where m is the mass of the object and v is the final velocity of the object.
According to the principle of conservation of energy, the initial energy equals the final energy:
E_initial = E_final
Substituting the values of the initial and final energy, we have:
mgh = 1/2 * mv^2
To solve for the final velocity v, we can rearrange the equation as follows:
mgh = 1/2 * mv^2
Canceling out the masses on both sides:
gh = 1/2 * v^2
Multiply both sides by 2:
2gh = v^2
Taking the square root of both sides:
sqrt(2gh) = v
Therefore, the equation to calculate the final velocity of the object is:
v = sqrt(2gh)
This equation allows you to calculate the final velocity of an object when only considering gravitational potential energy and kinetic energy, assuming no friction or external forces.
P.E. = K.E.
m * g * h = 1/2 * m * v^2
divide by m and multiply by 2 ... 2 * g * h = v^2
take square root ... v = √(2 * g * h)