Question

A standard four-drawer filing cabinet is 52 inches high and 15 inches wide. If it is evenly loaded, the center of gravity is at the center of the cabinet. A worker is tilting a filing cabinet to the side to clean under it.

Part A

To what angle can he tilt the cabinet before it tips over?

Express your answer using two significant figures.

Answer 1

Concepts and reason

This question is based on the concepts of the coordinate system and center of the gravity.

Calculate the angle from one corner to the center of gravity and calculate angle in which worker tilts the cabinet before it tips over.

Fundamentals

Center of the gravity is single point in which the body may rotate freely in all direction. It is also defined as center of the mass.

The expression for is,

Here, is the perpendicular and is the base of the cabinet.

Diagram of cabinet is given as,

The expression for angle from one corner to the center of gravity is,

Here, is the high of the cabinet and is the width of the cabinet.

Rearrange the equation for .

Substitute for and for in the above equation.

Angle made by it with vertical line is,

$x+0=90° $

Rearrange the above expression for x.

Substitute for in the above equation.

Ans:

Worker can rotate the cabinet before it tips over.