Acar on a roller coaster starts at zero speed at an elevation above the ground of 26 m. it coasts down a slope, and then climbs a hill. the top of the hill is at an elevation of 16 m. what is the speed of the car at the top of the hill? neglect any frictional effects. [hint: use conservation of mechanical energy]

v = 14 m / s

Explanation:

For this exercise Let's use the concepts of mechanical energy. Let's write in two points, the highest one where energy is potential and the lowest one where energy is potential and kinetic part pate

initial. Highest  

       Em₀ = U = mg y₁

final. top  on the hill

      = K + U = ½ m v² + mg y₂

As there is no rubbing

      Em₀ =

      mg y₁ = ½ m v² + mg y₂

      v = √ 2g (y₁ -y₂)

Let's calculate

    v = √ 2 9.8 (26 - 16)

    v = 14 m / s

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.