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At the top of its drop hill, a 1,000 kg roller coaster has 200,000 J of total energy. If the top of the next hill is 13 meters, what is the kinetic energy of the roller coaster on this hill?

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3 answers

200,000-1000g13

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To find the kinetic energy of the roller coaster on the next hill, we need to consider the conservation of energy. The total mechanical energy of the roller coaster is the sum of its potential energy and kinetic energy.

Let's break down the problem step by step:

Step 1: Calculate the potential energy at the top of the first hill.
The potential energy can be calculated using the formula: PE = mgh, where PE is the potential energy, m is the mass of the roller coaster, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the hill. Plugging in the values, we have:
PE1 = (1000 kg) * (9.8 m/s^2) * (13 m)
PE1 = 127,400 J

Step 2: Calculate the kinetic energy at the top of the first hill.
Using the conservation of energy, we know that the total energy (TE) is the sum of potential energy (PE) and kinetic energy (KE). Thus, we can write:
TE1 = PE1 + KE1
KE1 = TE1 - PE1

Given that TE1 = 200,000 J, we can now calculate KE1:
KE1 = 200,000 J - 127,400 J
KE1 = 72,600 J

Step 3: Calculate the kinetic energy at the top of the next hill.
At the top of the next hill, the roller coaster will have converted all of its potential energy into kinetic energy. Therefore, the kinetic energy at the top of the next hill will be equal to the total energy at the top of the first hill:
KE2 = KE1
KE2 = 72,600 J

Therefore, the kinetic energy of the roller coaster at the top of the next hill is 72,600 J.