Answer: A bookcase weighing 1500 N rests on a horizontal

Chapter 11, Problem 97CP

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A bookcase weighing 1500 N rests on a horizontal surface for which the coefficient of static friction is \(\mu_{s}=0.40\) The bookcase is \(1.80 \mathrm{~m}\) tall and \(2.00 \mathrm{~m}\) wide; its center of gravity is at its geometrical center. The bookcase rests on four short legs that are each \(0.10 \mathrm{~m}\) from the edge of the bookcase. A person pulls on a rope attached to an upper corner of the bookcase with a force \(\overrightarrow{\mathrm{F}}\) that makes an angle  with the bookcase (Fig. P11.97).

(a) If \(\theta=90^{\circ}\) so \(\overrightarrow{\mathrm{F}}\) is horizontal, show that as is increased from zero, the bookcase will start to slide before it tips, and calculate the magnitude of \(\overrightarrow{\mathrm{F}}\) that will start the bookcase sliding.

(b) If \(\theta=0^{\circ}\) so \(\overrightarrow{\mathrm{F}}\) is vertical, show that the bookcase will tip over rather than slide, and calculate the magnitude of \(\overrightarrow\F\) that will cause the bookcase to start to tip.

(c) Calculate as a function of  the magnitude of \(\overrightarrow{\mathrm{F}}\) that will cause the bookcase to start to slide and the magnitude that will cause it to start to tip. What is the smallest value that \(\theta\) can have so that the bookcase will still start to slide before it starts to tip?

Equation Transcription:

°

°

   

Text Transcription:

\mu_s = 0.40

s=0.40

1.80 m

2.00 m

0.10 m

\overrightarrow\F

\theta=90^\circ

Vec F

F

\theta=0^\circ

\overrightarrow\F

\overrightarrow\F

\overrightarrow\F