The Power of Kinetic Energy: Reaching New Heights

How does kinetic energy play a role in determining the stopping point of a bike rider on a hill?

Given that a bike rider and his bike have a combined mass of 95 kg and the rider is riding at a speed of 7.5 m/s on a flat road, how much higher than the bottom of the hill is the stopping point?

Answer:

The stopping point is approximately 2.86 meters higher than the bottom of the hill.

The kinetic energy of the bike and rider is given by:

K = (1/2) * m * v^2

where m is the combined mass of the bike and rider, and v is their speed. Plugging in the given values, we get:

K = (1/2) * 95 kg * (7.5 m/s)^2 = 2671.875 J

When the rider reaches the bottom of the hill, all of their kinetic energy will have been converted to potential energy, as they are no longer moving. The potential energy at the bottom of the hill is zero, so the total potential energy at the stopping point is equal to the initial kinetic energy of the rider.

The potential energy at a height h is given by:

U = m * g * h

where g is the acceleration due to gravity (9.8 m/s^2). Setting U equal to K and solving for h, we get:

h = K / (m * g)

Plugging in the given values, we get:

h = 2671.875 J / (95 kg * 9.8 m/s^2) ≈ 2.86 meters

Understanding the concept of kinetic energy can help us appreciate the forces at play in various physical scenarios. It showcases how energy can be transformed from one form to another, ultimately determining the outcomes of dynamic systems. By delving deeper into the principles of kinetic energy, we can unlock new heights and possibilities in our understanding of the world around us.