Question

at the highest point of the roller coaster the potential energy is 10 joules. assuming there is no loss of energy what would be the kinetic energy at the lowest point of the roller coaster? 10 jpoules 5 joules 0 joules 12 joules

Explanation:

Step1: Apply the principle of conservation of mechanical energy

The total mechanical energy \(E = E_p+E_k\) (potential energy + kinetic energy) is conserved when there is no energy loss. At the highest point, the roller - coaster has only potential energy \(E_{p1}=10\space J\) and \(E_{k1} = 0\space J\) (assuming it is at rest or has minimum speed at the very top for the sake of potential - energy dominance consideration). At the lowest point, the potential energy \(E_{p2}=0\space J\) (taking the lowest point as the zero - potential level).

Step2: Use the conservation formula \(E_1=E_2\)

By the law of conservation of mechanical energy \(E_1 = E_2\), where \(E_1=E_{p1}+E_{k1}\) and \(E_2=E_{p2}+E_{k2}\). Substituting the values: \(10 + 0=0+E_{k2}\)

Answer:

10 Joules