Equations for Kinetic and Potential Energy (KE/PE):
KE = ½mv², where 'm' is the mass of the object, and 'v' is the velocity at which said object is going.
PE = mgh, where 'm' is the mass of the object, 'g' is force of gravity, and 'h' is the height.
Substitutions and Solutions:
KE = ½ × 0.59965 × v²
For the kinetic energy of this motion, the prime value to be used is when the cart is at the end of the ramp, as this provides the highest point of kinetic energy of the cart at any one moment during the roll.
After analyzing the tracker video, we find that the velocity is 1.58, and now we can plug this in to our above formula and get the result:
KE = 0.74848313 Joules, or approximately three quarters of a Joule.
PE = 0.59965 × 9.8 × h
For the potential energy of this system, however, the peak value can be found when the cart is located at the top of the ramp, because of the height is at it's max, and a push will turn that to kinetic energy.
After calculating the height of the ramp with the textbooks, which is 0.18, we can substitute values in the above equation to receive:
PE = 1.0577826 Joules, or just about one Joule of energy.
KE = ½mv², where 'm' is the mass of the object, and 'v' is the velocity at which said object is going.
PE = mgh, where 'm' is the mass of the object, 'g' is force of gravity, and 'h' is the height.
Substitutions and Solutions:
KE = ½ × 0.59965 × v²
For the kinetic energy of this motion, the prime value to be used is when the cart is at the end of the ramp, as this provides the highest point of kinetic energy of the cart at any one moment during the roll.
After analyzing the tracker video, we find that the velocity is 1.58, and now we can plug this in to our above formula and get the result:
KE = 0.74848313 Joules, or approximately three quarters of a Joule.
PE = 0.59965 × 9.8 × h
For the potential energy of this system, however, the peak value can be found when the cart is located at the top of the ramp, because of the height is at it's max, and a push will turn that to kinetic energy.
After calculating the height of the ramp with the textbooks, which is 0.18, we can substitute values in the above equation to receive:
PE = 1.0577826 Joules, or just about one Joule of energy.
The Law of Conservation of Energy
States specifically for this lab that all of the potential energy was stored in the cart when not in motion at the top of the ramp, and this gross energy was not lost in thin air; rather, it proves that the equivalent amount of this energy converted to both heat and kinetic energy as it rolled down the ramp.
But with the Law of Conservation of Energy, shouldn't the amount of Joules be equivalent?
The answer to this is yes, actually, because there are more outlets of energy, such as heat (the most common way for something to transfer, NOT LOSE, energy), and sound. Heat can be found as the cart's wheels cause friction with the wooden ramp, and sound is discovered with the noise created by the cart while rolling down the ramp. Therefore, the amount of total energy in this system does remain at an equilibrium, as it is only transferred into other forms.
States specifically for this lab that all of the potential energy was stored in the cart when not in motion at the top of the ramp, and this gross energy was not lost in thin air; rather, it proves that the equivalent amount of this energy converted to both heat and kinetic energy as it rolled down the ramp.
But with the Law of Conservation of Energy, shouldn't the amount of Joules be equivalent?
The answer to this is yes, actually, because there are more outlets of energy, such as heat (the most common way for something to transfer, NOT LOSE, energy), and sound. Heat can be found as the cart's wheels cause friction with the wooden ramp, and sound is discovered with the noise created by the cart while rolling down the ramp. Therefore, the amount of total energy in this system does remain at an equilibrium, as it is only transferred into other forms.
Explanations for Numeric Values and Change Over Time
Barring the erred lapses of the Tracker program, the kinetic energy is constantly increasing along with the cart moving down the ramp in sync, as it is equally accelerating. The potential energy, which has no graph included, technically doesn't need one anyways, because the cart is moving, not resting, so it has zero potential energy, as it would need to be stationary.