Another Example: A Skateboarder on a Ramp Problem: A skateboarder starts descending a curved ramp from the top. What is their speed upon exiting the ramp? Assume the ramp's vertical height is 4.0 m, and neglect friction. Solution: Sketch the situation and identify key positions. h Initial Position, yi = 4.0 m Reference Level Final position, yf = 0 Choosing the reference level at the final position: yf = 0 yi = 4.0 m vi = 0 vf =? Applying the conservation of energy: 1 2 mv2 f + mgyf = 1 2 mv2 i + mgyi Simplifying: 1 2 mv2 f + 0 = 0 + mgyi Canceling m: v 2 f = 2gyi Solving for vf : vf = p 2gyi = 2 9.8 4.0 = 8.9 m/s 4 3 Using Energy Concepts in the Presence of Friction Friction and drag forces are present in nearly every physical scenario. While they may be negligible in certain cases, they often play a significant role in energy dissipation. When friction, drag force, or the coefficient of friction is provided, we must account for the thermal energy dissipated due to the influence of these