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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.

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opudodennis

Answer:

[tex]\boxed {16}^{\circ}}[/tex]

Explanation:

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

[tex]Tan\theta=\frac {P}{B}[/tex] where P and B are perpendicular and base point of the cabinet.

Using the free body diagram attached then

[tex]\theta=tan ^{-1} \frac {52}{15}=73.90^{\circ}[/tex]

The angle made by the vertical line will be [tex]90-\theta[/tex] hence [tex]90^{\circ}-73.90^{\circ}=\boxed {16}^{\circ}}[/tex]

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zainsubhani

Answer:

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

Explanation:

Center of gravity:

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

For Angle calculations:

[tex]Tan \theta=\frac{H}{W}[/tex]

where:

H is the perpendicular/height

W is the base/width

In our Case:

H=52 inches

W=15 inches

[tex]Tan\theta=\frac{52}{15}\\\theta=Tan^{-1}(\frac{52}{15})\\\theta=73.90^o[/tex]

This is angle at the corner

Total angle is: (Figure is attached)

[tex]\theta+a=90[/tex]

[tex]a=90-73.90\\a=16.09^o[/tex]

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

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