Potential and Kinetic Energy

Question 1: The equation for calculating gravitational potential energy of an object

Gravitational Potential Energy (GPE) = m × g × h

Where; 

M = mass of the object, which is usually given in kilograms 

G = Earth’s acceleration that results from the earth’s gravitational pull. The experimental value of Earth’s acceleration is 9.8 m/s2

H = is the height above the Earth’s surface, which is usually given in meters

From the above formula, it is noted that the gravitational potential energy of an object depends on the mass of an object and its height above the surface of the Earth. The bigger the mass and the height of an object, the higher the gravitational potential energy. Gravitational potential energy is given in Joules.

Question 2: The equation for calculating an object's kinetic energy

Kinetic Energy (K.E) = 1/2× mass × velocity × velocity

K.E = 1/2 × m × v2 

Where;

m = the mass of the object in motion

v = the velocity of the object

From the equation, kinetic energy of an object increases with an increase in the mass of the object and an increase in the velocity of the object.

Question 3: Conversion of the maximum potential energy into kinetic energy

Part of the marble’s potential energy is converted into kinetic energy as it rolls down the coaster roller. However, part of this potential energy is converted into other forms of energy such as heat energy and sound energy as the roller moves and hits different corners and compartments of the coaster roller (Viegas, 2005). Besides, some of the marble’s potential energy is lost because of frictional force. The amount of potential energy that is converted into kinetic energy depends on the shape of the coaster roller, and the amount energy loss as friction and other forms of energy, such as heat and sound energy.

Question 4: Relationship between marble's kinetic energy and initial gravitational potential energy

The kinetic energy of the marble is usually lower than the maximum gravitational potential energy. The amount of potential energy that is converted into the kinetic energy depends on the maximum velocity that is attained by the marble as it moves down the roller. A marble achieves maximum velocity and kinetic energy if the coaster roller is smooth and has fewer bents.

References

Viegas, J. (2005).  Kinetic and potential energy: Understanding changes within physical systems . New York: Rosen Pub. Group.