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.

A.To what angle can he tilt the cabinet before it tips over?
Express your answer using two significant figures.

Answer 1

`\boxed {16}^(\circ)}`

Step-by-step explanation:

Normally, the angle from one corner to the center of gravity is expressed as

`Tan\theta=\frac {P}{B}` where P and B are perpendicular and base point of the cabinet.

Using the free body diagram attached then

`\theta=tan ^(-1) \frac {52}{15}=73.90^(\circ)`

The angle made by the vertical line will be
`90-\theta` hence
`90^(\circ)-73.90^(\circ)=\boxed {16}^(\circ)}`

Answer 2

Angle, he tilt the cabinet before it tips over is 16.09 degrees

Step-by-step explanation:

Center of gravity:

It is a point around which body is free to rotate in all direction.'

For Angle calculations:

`Tan \theta=(H)/(W)`

where:

H is the perpendicular/height

W is the base/width

In our Case:

H=52 inches

W=15 inches

`Tan\theta=(52)/(15)\\\theta=Tan^(-1)((52)/(15))\\\theta=73.90^o`

This is angle at the corner

Total angle is: (Figure is attached)

`\theta+a=90`

`a=90-73.90\\a=16.09^o`

Angle, he tilt the cabinet before it tips over is 16.09 degrees