Question

determining the potential and kinetic energy of a roller coaster
complete these sentences.
if a roller coaster train has a potential energy of 1,500 j and a kinetic energy of 500 j as it starts to travel downhill, its total energy is □ j.
once the roller coaster train gets closer to the bottom of the hill, its kinetic energy increases to 1,100 j, and its potential energy decreases to □ j.
when the train reaches the bottom of the track and is traveling along the ground, its kinetic energy is □ j.

Explanation:

Step1: Calculate total energy initially

Total energy is the sum of potential energy (PE) and kinetic energy (KE). So, \( \text{Total Energy} = \text{PE} + \text{KE} \). Given \( \text{PE} = 1500 \, \text{J} \) and \( \text{KE} = 500 \, \text{J} \), we have \( 1500 + 500 = 2000 \, \text{J} \).

Step2: Find potential energy at lower hill

Total energy is conserved (assuming no energy loss). So, \( \text{PE} = \text{Total Energy} - \text{KE} \). Total energy is 2000 J, \( \text{KE} = 1100 \, \text{J} \), so \( 2000 - 1100 = 900 \, \text{J} \).

Step3: Find kinetic energy at bottom

At the bottom, potential energy is 0 (height is 0, \( \text{PE} = mgh \), \( h = 0 \)). So, \( \text{KE} = \text{Total Energy} - \text{PE} = 2000 - 0 = 2000 \, \text{J} \).

Answer:

First blank: 2000
Second blank: 900
Third blank: 2000