   Chapter 3, Problem 25P

Chapter
Section
Textbook Problem

A bolt drops from the ceiling of a moving train car that is accelerating northward at a rate of 2.50 m/s2, (a) What is the acceleration of the bolt relative to the train car? (b) What is the acceleration of the bolt relative to the Earth? (c) Describe the trajectory of the bolt as seen by an observer fixed on the Earth.

(a)

To determine
The acceleration of the bolt relative to the train car.

Explanation

Let the reference frame be the positive x axis in the northward direction and the positive y axis vertically upward.

The accelerations relative to the Earth are,

aCE=2.50m/s2 in the +x direction

aBE=9.80m/s2 in the y direction

Here,

aCE is the acceleration of the car relative to Earth

aBE is the acceleration of the bolt relative to Earth

The relation between the accelerations is,

aBC=aBEaCE

aBE=aCE+aBC

Here,

aBC is the acceleration of the bolt relative to the car

The following diagram shows acceleration of car relative to Earth.

The x component of the velocity is,

(aBC)x=(aCE)x

Substitute 2

(b)

To determine
The acceleration of the bolt relative to the Earth.

(c)

To determine
The trajectory of the bolt as seen by an observer fixed on the Earth.

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