An old streetcar rounds a flat corner of radius 9.1 m, at 16 km / h. What angle with the verti

step 1 So we have the free body diagram here for the mass M going straight down would of course be MG,

An old streetcar rounds a flat corner of radius 9.1 m, at...

Key Concepts

Resultant Force and Angle Calculation

In scenarios where two accelerations act perpendicularly—one due to gravity and one due to centripetal motion—the resultant effective acceleration is the vector sum of the two. The equilibrium angle, that is, the tilt of a hanging object, can be determined using trigonometry with tan(?) equal to the ratio of the centripetal acceleration to the gravitational acceleration.

Equilibrium in a Non-Inertial Frame

When observing a system in a non-inertial (accelerating) reference frame, such as a turning vehicle, fictitious forces (or pseudo forces) can be introduced to explain the apparent effects. For objects in such frames, the apparent equilibrium condition is reached when the vector sum of real forces and pseudo forces (e.g., due to centripetal acceleration) equals zero.

Centripetal Acceleration

This is the acceleration that is always directed toward the center of a circular path, responsible for keeping an object moving in a circle. It is calculated by the formula a = v²/r, where v is the speed of the object and r is the radius of the circle. This concept is key in analyzing situations involving circular motion.

Gravitational Acceleration

This is the acceleration due to gravity, acting vertically downward, independent of the object's horizontal motion. In many physics problems, including those involving circular motion, gravitational acceleration (g) is taken as a constant and is used to balance or compare with other accelerative effects.

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