The following is a simple method of measuring coefficients of friction. Suppose

Question

The following is a simple method of measuring coefficients of friction. Suppose a block is placed on a rough surface inclined relative to the horizontal as shown in the figure. The incline angle is increased until the block starts to move. Show that you can obtain ?s by measuring the critical angle ?c at which this slipping just occurs.

An un-tethered block sits on a flatbed truck as it accelerates up an incline that makes an angle of 15? with respect to the horizontal. If the truck speeds up at a rate less than 2.20 m/s2, the block remains on the truck. If the truck speeds up at a rate equal to or greater than this value, however, the block slides off the truck. What is the coefficient of static friction between the truck and the block?
?s =

Explanation / Answer

part 1; lets write equations mgsin?-Fs=0 Fs=µN=µmgcos? --> mgsin?=µmgcos? --> µ=tg? part 2: ma=Fs-mgsin? Fs=µN=µmgcos? --> ma=µmgcos?-mgsin? --> µ=(gsin?+a)/gcos?=0.5

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