Menu Close

Question-210809

Tinku Tara 0 Comments
Pin




Question Number 210809 by mr W last updated on 19/Aug/24
Commented by mr W last updated on 19/Aug/24
can the boy lift himself?
$${can}\:{the}\:{boy}\:{lift}\:{himself}? \\ $$
Commented by Ghisom last updated on 19/Aug/24
if we use a machine coiling the rope instead of a boy pulling it, it will work. there should be no difference.
$$\mathrm{if}\:\mathrm{we}\:\mathrm{use}\:\mathrm{a}\:\mathrm{machine}\:\mathrm{coiling}\:\mathrm{the}\:\mathrm{rope}\:\mathrm{instead} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{pulling}\:\mathrm{it},\:\mathrm{it}\:\mathrm{will}\:\mathrm{work}.\:\mathrm{there} \\ $$$$\mathrm{should}\:\mathrm{be}\:\mathrm{no}\:\mathrm{difference}. \\ $$
Commented by mr W last updated on 19/Aug/24
yes. i agree with you. if a hand winch is mounted on the box, people may sag that the boy can lift himself. it′s a popular type of lift which you may see in many construction sites. it is the same when the boy pulls the rope.
$${yes}.\:{i}\:{agree}\:{with}\:{you}.\:{if}\:{a}\:{hand}\:{winch} \\ $$$${is}\:{mounted}\:{on}\:{the}\:{box},\:{people}\:{may} \\ $$$${sag}\:{that}\:{the}\:{boy}\:{can}\:{lift}\:{himself}. \\ $$$${it}'{s}\:{a}\:{popular}\:{type}\:{of}\:{lift}\:{which}\:{you} \\ $$$${may}\:{see}\:{in}\:{many}\:{construction}\:{sites}. \\ $$$${it}\:{is}\:{the}\:{same}\:{when}\:{the}\:{boy}\:{pulls}\: \\ $$$${the}\:{rope}. \\ $$
Commented by mr W last updated on 19/Aug/24
Answered by mr W last updated on 19/Aug/24
Commented by mr W last updated on 19/Aug/24
say the mass of the boy is m_1 =50kg, the mass of the box including the pulley set is m_2 =20kg. let′s say the box rests on a scale. when the boy doesn′t pull the rope, the scale shows just the total weight of all things, i.e. 70 kg (or 700 N). now the boy pulls the rope with a force T. as shown above, N_1 =T+m_1 g 2T+N_2 =N_1 +m_2 g=T+m_1 g+m_2 g ⇒N_2 =(m_1 +m_2 )g−T we see, the more the boy pulls the rope, the less the scale shows. when the boy pulls with a force (m_1 +m_2 )g, the box will lose contact with the scale. now when he gives a little more force, they will begin to move upwards. therefore the boy can lift himself!
$${say}\:{the}\:{mass}\:{of}\:{the}\:{boy}\:{is}\:{m}_{\mathrm{1}} =\mathrm{50}{kg}, \\ $$$${the}\:{mass}\:{of}\:{the}\:{box}\:{including}\:{the} \\ $$$${pulley}\:{set}\:{is}\:{m}_{\mathrm{2}} =\mathrm{20}{kg}. \\ $$$${let}'{s}\:{say}\:{the}\:{box}\:{rests}\:{on}\:{a}\:{scale}. \\ $$$${when}\:{the}\:{boy}\:{doesn}'{t}\:{pull}\:{the}\:{rope}, \\ $$$${the}\:{scale}\:{shows}\:{just}\:{the}\:{total}\:{weight} \\ $$$${of}\:{all}\:{things},\:{i}.{e}.\:\mathrm{70}\:{kg}\:\left({or}\:\mathrm{700}\:{N}\right). \\ $$$${now}\:{the}\:{boy}\:{pulls}\:{the}\:{rope}\:{with}\:{a} \\ $$$${force}\:{T}.\:{as}\:{shown}\:{above}, \\ $$$${N}_{\mathrm{1}} ={T}+{m}_{\mathrm{1}} {g} \\ $$$$\mathrm{2}{T}+{N}_{\mathrm{2}} ={N}_{\mathrm{1}} +{m}_{\mathrm{2}} {g}={T}+{m}_{\mathrm{1}} {g}+{m}_{\mathrm{2}} {g} \\ $$$$\Rightarrow{N}_{\mathrm{2}} =\left({m}_{\mathrm{1}} +{m}_{\mathrm{2}} \right){g}−{T} \\ $$$${we}\:{see},\:{the}\:{more}\:{the}\:{boy}\:{pulls}\:{the}\:{rope}, \\ $$$${the}\:{less}\:{the}\:{scale}\:{shows}.\:{when}\:{the} \\ $$$${boy}\:{pulls}\:{with}\:{a}\:{force}\:\left({m}_{\mathrm{1}} +{m}_{\mathrm{2}} \right){g},\: \\ $$$${the}\:{box}\:{will}\:{lose}\:{contact}\:{with}\:{the} \\ $$$${scale}.\:{now}\:{when}\:{he}\:{gives}\:{a}\:{little} \\ $$$${more}\:{force},\:{they}\:{will}\:{begin}\:{to}\:{move} \\ $$$${upwards}. \\ $$$${therefore}\:{the}\:{boy}\:{can}\:{lift}\:{himself}! \\ $$
Commented by BHOOPENDRA last updated on 19/Aug/24
You are right Mr.W sir Appreciate Thankyou
$${You}\:{are}\:{right}\:{Mr}.{W}\:{sir}\:{Appreciate}\:{Thankyou} \\ $$
Commented by mr W last updated on 19/Aug/24
thanks for your contribution too!
$${thanks}\:{for}\:{your}\:{contribution}\:{too}! \\ $$

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *