A ball is hanging from a long string that is tied to the...

Name: Problem 29, Chapter 4: University Physics with Modern Physics
Uploaded: 2019-05-22T01:16:28-08:00
Duration: 2 min 15 s
Channel: Farhanul Hasan
Description: A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity and (b) the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity and (b) the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

A ball is hanging from a long string that is tied to the ceiling of a train car traveling eastward on horizontal tracks. An observer inside the train car sees the ball hang motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a uniform velocity and
(b) the train is speeding up uniformly. Is the net force on the ball zero in either case? Explain.

Key Concepts

Pseudo Forces

Pseudo forces, also known as fictitious forces, arise in non?inertial reference frames when the observer is accelerating. They are not due to physical interactions but are needed to apply Newton’s laws from the perspective of an accelerating observer. In scenarios where the train accelerates, a pseudo force appears in the free-body diagram opposite to the direction of acceleration.

Free?Body Diagrams

A free-body diagram is a graphical representation of all the forces acting on an object, isolated from its environment. It includes vectors showing the direction and relative magnitude of forces like gravity, tension, friction, and any applied or inertial forces. This tool is essential in analyzing the equilibrium or acceleration of the object in various scenarios.

Inertial vs. Non?Inertial Reference Frames

An inertial reference frame is one in which an object with no net force moves at a constant velocity, meaning Newton’s laws hold without modifications. In contrast, a non?inertial reference frame is accelerating, so observers within it must introduce fictitious or pseudo forces to correctly apply Newton’s laws. Understanding the difference between these frames is crucial when analyzing motion from different perspectives, such as inside a train car under acceleration.

Newton’s Laws of Motion

Newton’s laws, particularly the second law (F_net = ma), form the foundation for analyzing the motion of objects. They help in determining whether an object is in equilibrium (net force zero) or accelerating. In any free-body diagram, these laws are applied to sum forces vectorially and relate them to the object’s acceleration.

Equilibrium and Net Force Analysis

Equilibrium occurs when the sum of forces acting on an object is zero, meaning there is no acceleration relative to the chosen reference frame. In an inertial frame (or from the viewpoint of an observer incorporating pseudo forces in a non?inertial frame), the free-body diagram can show either equilibrium or an unbalanced force leading to acceleration. Understanding how to sum these forces helps determine whether the net force is zero or if the object is accelerating.

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