A sledder has 800 J of potential energy and 200 J of kinetic energy at one point on a steep hill. How much kinetic energy will the sledder have at the bottom of the hill? (Assume negligible air resistance and friction.)
assuming that your potential energy is defined as zero at the bottom of the hill, all your energy is kinetic by the time you get there. 800 + 200 = 1000
Pert of this problem statement is missing though. In potentials, all you can define is differences. You have to define some point as zero.
Well, that sledder is really going for the energy roller coaster ride! So, let's calculate it. At the top of the hill, the sledder has 800 J of potential energy. As the sledder descends down the hill, all that potential energy is converted into kinetic energy. Therefore, at the bottom of the hill, the sledder will have a total of 1000 J of kinetic energy. More speed, more fun, right? Just make sure to hold on tight!
To solve this problem, we can make use of the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed from one form to another.
Given that the sledder has 800 J of potential energy and 200 J of kinetic energy at one point on the hill, we can assume that the total mechanical energy of the sledder remains constant throughout the ride.
Therefore, the total mechanical energy (E) at the top of the hill is the sum of potential energy (PE) and kinetic energy (KE):
E = PE + KE
= 800 J + 200 J
= 1000 J
Since we assume negligible air resistance and friction, the total mechanical energy of the sledder will remain constant. As the sledder goes downhill, the potential energy will decrease, and the kinetic energy will increase.
At the bottom of the hill, all the potential energy will be converted into kinetic energy.
Therefore, the kinetic energy at the bottom of the hill will be equal to the total mechanical energy (1000 J) minus the potential energy:
Kinetic energy at the bottom = Total mechanical energy - Potential energy
= 1000 J - 800 J
= 200 J
Hence, the sledder will have 200 J of kinetic energy at the bottom of the hill.
To find the amount of kinetic energy the sledder will have at the bottom of the hill, we need to consider the principle of conservation of energy. The total mechanical energy, which is the sum of potential energy and kinetic energy, remains constant in the absence of external forces like friction or air resistance.
Given that the potential energy at the initial point is 800 J and the kinetic energy at that same point is 200 J, the total mechanical energy at that point is 800 J + 200 J = 1000 J.
Since there is no loss of mechanical energy in this scenario, the total mechanical energy at the bottom of the hill will also be 1000 J. However, at the bottom of the hill, all the potential energy will be converted into kinetic energy.
Therefore, the sledder will have 1000 J of kinetic energy at the bottom of the hill.