Question

eₚ = 40 j
a roller coaster car sits on top of a hill with 40 j of potential energy. as it goes down the hill, it has 15 j of potential energy, 20 j of kinetic energy, and some thermal energy.
eₚ = 15 j
eₖ = 20 j
how much thermal energy is present?
10 j 20 j
5 j 40 j

Explanation:

Step1: Recall energy conservation

The initial total energy is the potential energy at the top, \( E_{initial} = E_{p,initial} = 40\space J \).

Step2: Calculate final total energy

The final energy is the sum of potential, kinetic, and thermal energy: \( E_{final} = E_{p,final} + E_{k,final} + E_{thermal} \).

Step3: Apply energy conservation

Since energy is conserved (ignoring external factors, initial energy equals final energy), we have \( 40 = 15 + 20 + E_{thermal} \).

Step4: Solve for thermal energy

Simplify the equation: \( E_{thermal} = 40 - 15 - 20 = 5\space J \).

Answer:

5 J (corresponding to the option "5 J")