A roller-coaster car has a mass of 1300 kg when fully loaded...

Name: Problem 48, Chapter 6: Principles of Physics
Uploaded: 2022-03-19T12:24:00-08:00
Duration: 5 min 30 s
Channel: Sandeep Kumar Dhania
Description: A roller-coaster car has a mass of 1300 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 20 m, its speed is not changing. At the top of the hill, what are the (a) magnitude FN and (b) direction (up or down) of the normal force on the car from the track if the car’s speed is v 11 m/s? What are (c) FN and (d) the direction if v 14 m/s?

A roller-coaster car has a mass of 1300 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 20 m, its speed is not changing. At the top of the hill, what are the (a) magnitude FN and (b) direction (up or down) of the normal force on the car from the track if the car’s speed is v 11 m/s? What are (c) FN and (d) the direction if v 14 m/s?

A roller-coaster car has a mass of 1300 kg when fully loaded
with passengers. As the car passes over the top of a circular hill of
radius 20 m, its speed is not changing. At the top of the hill, what
are the (a) magnitude FN and (b) direction (up or down) of the
normal force on the car from the track if the car’s speed is v 11
m/s? What are (c) FN and (d) the direction if v 14 m/s?

Key Concepts

Centripetal Acceleration

In circular motion, an object moving along a curved path requires an acceleration directed toward the center of the circle, known as centripetal acceleration. This acceleration is given by the formula a = v²/r, where v is the speed of the object and r is the radius of the circle. It is this inward acceleration that necessitates a net inward force.

Free-Body Diagram Analysis

Analyzing the forces acting on an object using a free-body diagram is essential when dealing with dynamics. For a roller coaster car at the top of a circular hill, the diagram typically shows the gravitational force (weight) acting downward and the normal force from the track acting upward. The net force, determined by these components, must equal the mass times the centripetal acceleration required for circular motion.

Normal Force

The normal force is the perpendicular contact force exerted by a surface on an object. At the crest of a circular hill, the normal force works against part of the gravitational force to provide the necessary net force for inward (downward) centripetal acceleration. Its magnitude can be less than the full weight of the object, and in cases where the speed is high, the normal force may even act downward if the centripetal force requirement exceeds the gravitational force.

Gravitational Force

Gravitational force (or weight) is the force exerted by the Earth on a mass, calculated as mg, where m is the mass and g is the acceleration due to gravity. At the top of a hill, gravity always acts downward and is one of the primary forces considered in achieving the necessary centripetal force for circular motion. Its interplay with the normal force determines whether the contact force is upward or may effectively act downward if the speed increases.

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