Calculating the Force of Friction Acting on a Bike Rider: An Application of Newton’s Laws

Newton's laws of motion provide a fundamental framework for understanding how forces affect the movement of objects. In this article, we will explore the application of these laws to determine the force of friction acting on a bike rider. We will perform a detailed step-by-step calculation to find the exact force due to friction, ensuring a clear and comprehensive understanding.

Problem Description

A bike rider with a mass of 86.2 kg and their bike accelerate from rest to 3.15 m/s over a distance of 7.83 meters while exerting a 98.4 N force. The question is to determine the force that pushes back against the bike rider due to friction and other resistive forces. The unit of force is Newton (N).

Principles and Formulas

The forces acting on the bike rider include the applied force (due to the rider’s effort) and the frictional force (opposing the motion due to various resistive factors). We can use Newton’s second law of motion and the principle of conservation of energy to find the force of friction.

Newton's Second Law of Motion

Newton's second law states that the net force applied to an object is equal to the mass of the object multiplied by its acceleration: F_{net} m cdot a.

Conservation of Energy

The kinetic energy (KE) gained by the bike rider can be expressed as: KE frac{1}{2}mv^2. This kinetic energy is due to the work done by the applied force over a distance: Work F_{applied} cdot s frac{1}{2}mv^2.

Step-by-Step Calculation

Calculate the Acceleration

The first step is to determine the acceleration of the bike rider. We use the kinematic equation: v^2 u^2 2as, where: v 3.15 , text{m/s} u 0 , text{m/s} (since the bike starts from rest) s 7.83 , text{m} Rearrange the equation to solve for acceleration a:

a frac{v^2 - u^2}{2s} frac{3.15^2 - 0^2}{2 times 7.83}

Calculating this:

a frac{9.9225}{15.66} approx 0.633 , text{m/s}^2

Calculate the Net Force

Next, we calculate the net force using Newton's second law: F_{net} m cdot a. Here, m 86.2 , text{kg} and a 0.633 , text{m/s}^2.

F_{net} 86.2 times 0.633 approx 54.66 , text{N}

Calculate the Frictional Force

Finally, we use the equation for net force to solve for the frictional force: F_{friction} F_{applied} - F_{net}. Given F_{applied} 98.4 , text{N} and F_{net} approx 54.66 , text{N}, we have:

F_{friction} 98.4 - 54.66 approx 43.74 , text{N}

Conclusion

The force that pushes back against the bike rider due to friction and other resistive forces is approximately 43.74 N. This calculation demonstrates the application of Newton’s laws and the principle of work and energy in practical scenarios involving motion and forces.

Understanding these principles is crucial for comprehending the forces at play in various physical situations. Whether you are a physics student, an engineer, or anyone interested in mechanics, mastering these concepts provides valuable insights into the behavior of moving objects.