An old streetcar rounds a flat corner of radius 10.5 m, at 16 km/h. What angle with the vertical

step 1 So in the question the radius of the corner is given as r is equal to 10 .5 meters and the speed

An old streetcar rounds a flat corner of radius 10.5 m, at...

Key Concepts

Centripetal Acceleration

Centripetal acceleration is the acceleration directed towards the center of a circular path that keeps an object moving along that path. It is calculated by v²/r, where v is the speed of the object and r is the radius of the circle. This acceleration is responsible for changing the direction of the object’s velocity without altering its speed.

Non-Inertial Reference Frame

In a non-inertial reference frame, such as that of a turning streetcar, fictitious forces appear to act on objects. These include forces like the centrifugal force, which is not a true force but results from the acceleration of the reference frame. This concept helps explain why objects like hanging straps appear to tilt outward when the vehicle is undergoing centripetal acceleration.

Equilibrium of Forces in an Accelerated System

When an object is in an accelerating system, such as a turning streetcar, the equilibrium position of a hanging object is determined by the vector sum of the gravitational force and the fictitious force due to acceleration. The object will align along the effective gravity direction, which combines the downward gravitational pull and the outward inertial effect resulting from the centripetal acceleration.

Vector Addition of Forces

The tilting of the hanging hand strap is determined by combining the gravitational acceleration (acting vertically) and the centripetal acceleration (acting horizontally). The effective acceleration vector is the result of this vector addition, and the angle of tilt is given by the arctan of the ratio of the horizontal centripetal acceleration to the vertical gravitational acceleration.

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