Question Number 201107 by behi834171 last updated on 29/Nov/23
$${two}\:{weels},\:{those}\:{have}\:{the}\:{same}\:{materials}, \\ $$$${with}\:{radii}:\boldsymbol{{r}}_{\mathrm{1}} =\mathrm{4}\:{and}\:\boldsymbol{{r}}_{\mathrm{2}} =\mathrm{14} \\ $$$${are}\:{starting}\:{to}\:{move}\:{on}\:{a}\:{surface},{with} \\ $$$${the}\:{same}\:{velocity},{from}:\boldsymbol{{x}}=\mathrm{0}\:{to}\:\boldsymbol{{x}}=\mathrm{20}. \\ $$$${the}\:{surface}\:{has}\:{no}\:{friction}. \\ $$$${wich}\:{one}\:{arrives}\:{faster}? \\ $$$${any}\:{informations}\:{needed}? \\ $$
Commented by mr W last updated on 29/Nov/23
$${no}\:{friction}\:{means}\:{that}\:{the}\:{wheels} \\ $$$${don}'{t}\:{rotate}.\:{we}\:{have}\:{two}\:{objects}: \\ $$$${a}\:{bigger}\:{one}\:{and}\:{a}\:{smaller}\:{one},\:{both} \\ $$$${start}\:{with}\:{the}\:{same}\:{velocity}.\:{they} \\ $$$${need}\:{the}\:{same}\:{time}\:{to}\:{cover}\:{the} \\ $$$${same}\:{distance}.\:{your}\:{question}\:“{which} \\ $$$${one}\:{arrives}\:{faster}?''\:{can}\:{not}\:{be} \\ $$$${answered},\:{because}\:{you}\:{didn}'{t}\:{tell}\:{if} \\ $$$${they}\:{moved}\:{the}\:{same}\:{distance}\:{or}\:{not}. \\ $$$${from}\:{x}=\mathrm{0}\:{and}\:{x}=\mathrm{20}\:{to}\:{where}? \\ $$
Commented by behi834171 last updated on 29/Nov/23
$${hello}\:{dear}\:{master}\:. \\ $$$${thanks}\:{for}\:{your}\:{time}\:{and}\:{attention}. \\ $$$${you}\:{are}\:{right}. \\ $$$${now}\:{we}\:{assume}\:{that}\:{the}\:{surface}\:{has}\: \\ $$$${the}\:{friction},{same}\:{to}\:{both}\:{objects}. \\ $$$${the}\:{passed}\:{distance}\:{is}, \\ $$$${also}\:{the}\:{same}\:{for}\:{two},{i}.{e}.\:\mathrm{20}\:{units}. \\ $$$$ \\ $$$$ \\ $$
Commented by mr W last updated on 29/Nov/23
$${if}\:{they}\:{start}\:{with}\:{the}\:{same}\:{velocity} \\ $$$${and}\:{they}\:{move}\:{the}\:{same}\:{distance}, \\ $$$${then}\:{they}\:{need}\:{the}\:{same}\:{time},\: \\ $$$${despite}\:{their}\:{different}\:{masses}\:{and} \\ $$$${sizes}. \\ $$
Commented by mr W last updated on 30/Nov/23
Commented by mr W last updated on 30/Nov/23
$${when}\:{a}\:{wheel}\:{starts}\:{to}\:{roll}\:{on}\:{a} \\ $$$${horizontal}\:{surface}\:{with}\:{velocity}\:{v}, \\ $$$${it}\:{will}\:{keep}\:{this}\:{speed}.\:{if}\:{two}\:{wheels} \\ $$$${with}\:{different}\:{radii}\:{and}\:{different} \\ $$$${masses}\:{start}\:{with}\:{the}\:{same}\:{velocity}, \\ $$$${they}\:{will}\:{rotate}\:{differently}\:{fast},\: \\ $$$${depending}\:{on}\:{their}\:{radii},\:{but}\:{they} \\ $$$${move}\:{forwards}\:{with}\:{the}\:{same} \\ $$$${velocity}\:{v}.\:{to}\:{cover}\:{the}\:{same}\: \\ $$$${distance}\:{s}\:{they}\:{need}\:{the}\:{same}\:{time}\: \\ $$$${t}=\frac{{s}}{{v}}. \\ $$$${certainly}\:{to}\:{bring}\:{these}\:{two}\:{wheels} \\ $$$${to}\:{start}\:{to}\:{move}\:{with}\:{the}\:{same} \\ $$$${velocity},\:{you}\:{need}\:{to}\:{do}\:{different} \\ $$$${amount}\:{of}\:{work}. \\ $$
Commented by behi834171 last updated on 04/Dec/23
$${thanks}\:{a}\:{lot}\:{sir}\:{for}\:{your}\:{time}\:{and}\:{favor}. \\ $$$${in}\:{fact},{i}\:{have}\:\:{no}\:{idea}. \\ $$$${please}\:{rewrite}\:{the}\:{quetion}\:{in}\:{good}\:{and} \\ $$$$\:{true}\:{conditions}\:,{and}\:{please}\:{post}\:{your} \\ $$$${answer}.\:{thank}\:{a}\:{lot},{again}. \\ $$