Chapter 8, Problem 38RE

Frictional Force(See Problem 37.)Once the box begins to slide and accelerate, kinetic friction acts to slow the box with a coefficient of kinetic friction ${\mu }_k=\mathrm{0.1.}$ The raised end of the surface can be lowered to a poinit where the box continues sliding but does not accelerate. The critical angle at which this happens, ${\theta }_c{}^{\text{'}}$, can be found from the equation $\tan {\theta }_c{}^{\text{'}}={\mu }_k.$

What is the critical angle for the box?

If the box is $5\text{ft}$ from the pivot point, at what height will the box begin to slide?

Frictional Force A box sitting on a flat surface has a coefficient of static friction of ${\mu }_s=\mathrm{0.3.}$ If one end of the surface is raised, static friction prevents the box from sliding until the force of static friction is overcome. The critical angle at which the box begins to slide, ${\theta }_c,$ can be found from the equation $\tan {\theta }_c={\mu }_s.$

What is the critical angle for the box?

If the box is $5\text{ft}$ from the pivot point, at what height will the box begin to slide? See the figure.