A bicyclist (Fig. 5-41) travels in a circle of radius 25 m at a constant speed of 8.7 m / s. T

step 1 So we're going to be looking at problem 36 from chapter 5 of the physics 5th. The question says

A bicyclist (Fig. 5-41) travels in a circle of radius 25 m...

A bicyclist (Fig. 5-41) travels in a circle of radius $25 \mathrm{~m}$ at a constant speed of $8.7 \mathrm{~m} / \mathrm{s}$. The combined mass of the bicycle and rider is $85 \mathrm{~kg}$. Calculate the force - magnitude and angle with the vertical- exerted by the road on the bicycle.

Key Concepts

Circular Motion

Circular motion refers to the movement of an object along the circumference of a circle. In such motion, even if the speed remains constant, the direction of the velocity vector changes continuously. This change in direction constitutes an acceleration, known as centripetal acceleration, that is always directed towards the center of the circle.

Centripetal Force

Centripetal force is the net force that causes an object to undergo circular motion. It is not a separate kind of force but results from the vector sum of forces acting on the object, which, in many cases, includes friction and the normal force. This force is crucial for maintaining circular motion and is calculated by multiplying the mass of the object by its centripetal acceleration (v²/r).

Newton's Second Law

Newton's Second Law is fundamental in linking forces to the motion of particles. It states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In problems involving circular motion, this law is applied to determine the net force required to provide the needed centripetal acceleration as well as to analyze equilibrium conditions in the vertical direction.

Force Decomposition

Force decomposition involves breaking a force into components along specific directions, typically perpendicular and parallel to a chosen reference axis. In problems involving circular motion on an inclined or non-vertical force application, the overall contact force (such as the force exerted by the road) is decomposed into vertical and horizontal components. This allows one to use equilibrium in the vertical direction and relate the horizontal component to the centripetal force required for circular motion.

Free-Body Diagram

A free-body diagram is a graphical representation that shows all the forces acting on an object. It is a crucial tool in physics and engineering that helps in visualizing and analyzing the forces contributing to an object’s motion or equilibrium. By isolating the bicyclist and diagramming the gravitational force, normal force, frictional force, and other possible forces, one can set up equations to solve for unknowns such as the magnitude and direction of the net force.

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