a eollee coaster car starts from rest at the top of the hill. if the roller coaster loses 10% of its potential energy due to non-conservative forces as it descends, what is its kinetic energy at the bottom of the hill? Assume that the mass of the car is 2500kg.
Answer (1)
Answer:Here's how to solve this problem: 1. Understand the Concepts - Potential Energy (PE): Energy stored due to an object's position or height.- Kinetic Energy (KE): Energy possessed by an object due to its motion.- Conservation of Energy: In an ideal system, total energy (PE + KE) remains constant. However, non-conservative forces (like friction) can cause energy loss. 2. Set Up the Problem - Initial PE: Let's assume the initial potential energy at the top of the hill is PE₀.- Energy Loss: 10% of PE₀ is lost due to non-conservative forces.- Final KE: We need to find the kinetic energy (KE) at the bottom of the hill. 3. Apply the Conservation of Energy Principle (with Energy Loss) - Initial Total Energy: PE₀- Final Total Energy: KE + (90% of PE₀) (Since 10% is lost) Since energy is conserved (except for the loss), we can set these equal: PE₀ = KE + 0.9 * PE₀ 4. Solve for KE - Subtract 0.9 * PE₀ from both sides: 0.1 * PE₀ = KE 5. Since we don't know the initial height (and thus PE₀), we can express the answer in terms of PE₀: KE = 0.1 * PE₀ Answer: The kinetic energy of the roller coaster car at the bottom of the hill is 10% of its initial potential energy (PE₀). Important Note: To get a numerical answer for KE, you would need to know the initial height of the hill to calculate the initial potential energy (PE₀).
