Question Number 227521 by mr W last updated on 07/Feb/26
Commented by mr W last updated on 08/Feb/26
As shown in the figure, 100 wooden blocks, each with weight 5 N, are clamped by two forces of magnitude F from the left and right. All contact surfaces have the same roughness. What is the friction force between block No. 27 and block No. 28?
Commented by MrAjder last updated on 08/Feb/26
It should be 250N - it's not hard for readers to verify on their own
Commented by MrAjder last updated on 08/Feb/26
yes
Commented by mr W last updated on 08/Feb/26
$${the}\:{question}\:{is}\:{to}\:{find}\:{the}\:{friction} \\ $$$${force}\:{between}\:{block}\:{no}.\:\mathrm{27}\:{and}\:{block} \\ $$$${no}.\:\mathrm{28}.\:{do}\:{you}\:{want}\:{to}\:{say}\:{that}\:{this} \\ $$$${force}\:{is}\:\mathrm{250}\:{N}? \\ $$
Commented by mr W last updated on 08/Feb/26
$${total}\:{weight}\:{of}\:{all}\:{blocks}\:{is}\:\mathrm{500}\:{N}. \\ $$$${since}\:{all}\:{blocks}\:{are}\:{identical},\:{the} \\ $$$${center}\:{of}\:{gravity}\:{of}\:{them}\:{lies}\:{in}\:{the} \\ $$$${middle}.\:\:{the}\:{friction}\:{force}\:{on}\:{the} \\ $$$${left}\:{and}\:{on}\:{the}\:{right}\:{should}\:{be} \\ $$$${equal}.\:{each}\:{of}\:{them}\:{is}\:{then} \\ $$$$\mathrm{500}/\mathrm{2}=\mathrm{250}{N}. \\ $$$${the}\:{friction}\:{force}\:{between}\:{block}\:\mathrm{1} \\ $$$${and}\:{block}\:\mathrm{2}\:{must}\:{be}\:\mathrm{5}\:{N}\:\left(={weight}\:{of}\right. \\ $$$$\left.{block}\:\mathrm{1}\right)\:{less}\:{than}\:\mathrm{250}\:{N}.\:{etc}.\: \\ $$$${the}\:{friction}\:{force}\:{between}\:{block}\:\mathrm{27}\: \\ $$$${and}\:\mathrm{28}\:{is}\:\mathrm{27}×\mathrm{5}{N}\:{less}\:{than}\:\mathrm{250}\:{N}.\:{so} \\ $$$${the}\:{correct}\:{answer}\:{is} \\ $$$$\mathrm{250}−\mathrm{27}×\mathrm{5}=\mathrm{115}\:{N}. \\ $$
Commented by mr W last updated on 08/Feb/26
$${then}\:{wrong} \\ $$
Commented by MrAjder last updated on 08/Feb/26
So, sir, do you already know the correct answer? Can you write down the process?？
Commented by fantastic2 last updated on 08/Feb/26
$${why}\:{flagged}\:{as}\:{inappropiate} \\ $$
Commented by mr W last updated on 08/Feb/26
$${or}\:{in}\:{other}\:{way}: \\ $$$${the}\:{friction}\:{force}\:{between}\:{block}\:\mathrm{27} \\ $$$${and}\:\mathrm{28}\:{is}\:{the}\:{same}\:{as}\:{that}\:{between} \\ $$$${block}\:\mathrm{73}\:{and}\:\mathrm{74},\:{due}\:{to}\:{symmetry}. \\ $$$${they}\:{together}\:{carry}\:{the}\:{weight}\:{from} \\ $$$${blocks}\:{no}.\:\mathrm{28}\:{to}\:\mathrm{73}. \\ $$$$\Rightarrow{f}_{\mathrm{27}−\mathrm{28}} ={f}_{\mathrm{73}−\mathrm{74}} =\frac{\mathrm{46}×\mathrm{5}}{\mathrm{2}}=\mathrm{115}\:{N} \\ $$
Commented by mr W last updated on 08/Feb/26
