Question

Under conditions of conservation of energy where the initial energy object is only gravitational 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.

What is the initial form of energy for the object in this scenario?
A. Kinetic energy
B. Thermal energy
C. Gravitational potential energy
D. Electrical energy

Answer 1

The initial energy of the object is gravitational potential energy, and the final velocity can be found using the Law of Conservation of Mechanical Energy, which results in the equation v = √(2gh).

Step-by-step explanation:

The initial form of energy for the object in the scenario described is gravitational potential energy (C). To calculate the final velocity of the object, we use the Law of Conservation of Mechanical Energy, which can be expressed as KEi + PEi = KEf + PEf. Here, the initial kinetic energy (KEi) is zero since the object starts from rest, and the final potential energy (PEf) is taken as zero at the lowest point. Let m be the mass of the object, g be the acceleration due to gravity, h be the height from which it falls, and v be the final velocity. The initial potential energy (PEi) is mgh and the final kinetic energy (KEf) is ½mv². The conservation of energy equation simplifies to mgh = ½mv², which, when solved for v, gives the equation for final velocity: v = √(2gh).