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Question Number 102553 by aurpeyz last updated on 09/Jul/20
Commented by aurpeyz last updated on 09/Jul/20
pls help
$$\mathrm{pls}\:\mathrm{help} \\ $$
Commented by aurpeyz last updated on 09/Jul/20
Commented by Rio Michael last updated on 10/Jul/20
Force = μF_N + mg sin θ ⇒ F = (0.4)(10 × 9.8)N + (10)(9.8)sin 60N
$$\mathrm{Force}\:=\:\mu{F}_{{N}} \:+\:\mathrm{mg}\:\mathrm{sin}\:\theta \\ $$$$\Rightarrow\:{F}\:=\:\left(\mathrm{0}.\mathrm{4}\right)\left(\mathrm{10}\:×\:\mathrm{9}.\mathrm{8}\right){N}\:+\:\left(\mathrm{10}\right)\left(\mathrm{9}.\mathrm{8}\right)\mathrm{sin}\:\mathrm{60}{N} \\ $$
Answered by mr W last updated on 10/Jul/20
F cos θ−mg sin θ≥μ(mg cos θ+F sin θ) F (cos θ−μ sin θ)≥mg(μcos θ+sin θ) ⇒F≥((mg(μ cos θ+sin θ))/(cos θ−μ sin θ)) ⇒F≥((mg(μ+tan θ))/(1−μ tan θ)) ⇒F≥((10×9.81(0.4+(√3)))/(1−0.4×(√3)))=681 N
$${F}\:\mathrm{cos}\:\theta−{mg}\:\mathrm{sin}\:\theta\geqslant\mu\left({mg}\:\mathrm{cos}\:\theta+{F}\:\mathrm{sin}\:\theta\right) \\ $$$${F}\:\left(\mathrm{cos}\:\theta−\mu\:\mathrm{sin}\:\theta\right)\geqslant{mg}\left(\mu\mathrm{cos}\:\theta+\mathrm{sin}\:\theta\right) \\ $$$$\Rightarrow{F}\geqslant\frac{{mg}\left(\mu\:\mathrm{cos}\:\theta+\mathrm{sin}\:\theta\right)}{\mathrm{cos}\:\theta−\mu\:\mathrm{sin}\:\theta} \\ $$$$\Rightarrow{F}\geqslant\frac{{mg}\left(\mu+\mathrm{tan}\:\theta\right)}{\mathrm{1}−\mu\:\mathrm{tan}\:\theta} \\ $$$$\Rightarrow{F}\geqslant\frac{\mathrm{10}×\mathrm{9}.\mathrm{81}\left(\mathrm{0}.\mathrm{4}+\sqrt{\mathrm{3}}\right)}{\mathrm{1}−\mathrm{0}.\mathrm{4}×\sqrt{\mathrm{3}}}=\mathrm{681}\:{N} \\ $$
Commented by aurpeyz last updated on 10/Jul/20
your solution is great Sir. pls explain the first line of the solution. i will understand the rest
$$\mathrm{your}\:\mathrm{solution}\:\mathrm{is}\:\mathrm{great}\:\mathrm{Sir}.\:\mathrm{pls}\:\mathrm{explain}\:\mathrm{the}\:\mathrm{first}\:\mathrm{line}\:\mathrm{of}\:\mathrm{the}\:\mathrm{solution}.\:\mathrm{i}\:\mathrm{will}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{rest} \\ $$
Commented by aurpeyz last updated on 10/Jul/20
with this solution it seem like there is a force action at Θ degrees to the plane
$$\mathrm{with}\:\mathrm{this}\:\mathrm{solution}\:\mathrm{it}\:\mathrm{seem}\:\mathrm{like}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{force}\:\mathrm{action}\:\mathrm{at}\:\Theta\:\mathrm{degrees}\:\mathrm{to}\:\mathrm{the}\:\mathrm{plane} \\ $$
Commented by mr W last updated on 10/Jul/20
Commented by aurpeyz last updated on 10/Jul/20
where F is the horizontal force right? so i will just have to resolve to get the answers like hou did
$$\mathrm{where}\:\mathrm{F}\:\mathrm{is}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{force}\:\mathrm{right}?\:\mathrm{so}\:\mathrm{i}\:\mathrm{will}\:\mathrm{just}\:\mathrm{have}\:\mathrm{to}\:\mathrm{resolve}\:\mathrm{to}\:\mathrm{get}\:\mathrm{the}\:\mathrm{answers}\:\mathrm{like}\:\mathrm{hou}\:\mathrm{did} \\ $$
Commented by aurpeyz last updated on 10/Jul/20
Sir Pls check Q. 102194. what will be the direction of the friction?
$$\mathrm{Sir}\:\mathrm{Pls}\:\mathrm{check}\:\mathrm{Q}.\:\mathrm{102194}.\:\mathrm{what}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{friction}? \\ $$
Commented by mr W last updated on 10/Jul/20
in this question you should move the object up to the plane and the friction is always in the opposite direction to the movement the object tries to make. in this case it is downwards. but in Q102194 you don′t need to move up the object, you just need to prevent it to move down, in that case the friction is upwards, because the object tries to move downwards.
$${in}\:{this}\:{question}\:{you}\:{should}\:{move} \\ $$$${the}\:{object}\:{up}\:{to}\:{the}\:{plane}\:{and}\:{the} \\ $$$${friction}\:{is}\:{always}\:{in}\:{the}\:{opposite} \\ $$$${direction}\:{to}\:{the}\:{movement}\:{the}\:{object} \\ $$$${tries}\:{to}\:{make}.\:{in}\:{this}\:{case}\:{it}\:{is} \\ $$$${downwards}. \\ $$$${but}\:{in}\:{Q}\mathrm{102194}\:{you}\:{don}'{t}\:{need}\:{to}\:{move} \\ $$$${up}\:{the}\:{object},\:{you}\:{just}\:{need}\:{to} \\ $$$${prevent}\:{it}\:{to}\:{move}\:{down},\:{in}\:{that}\:{case} \\ $$$${the}\:{friction}\:{is}\:{upwards},\:{because}\:{the} \\ $$$${object}\:{tries}\:{to}\:{move}\:{downwards}. \\ $$
Commented by aurpeyz last updated on 10/Jul/20
i understand you Sir. thanks alot.
$$\mathrm{i}\:\mathrm{understand}\:\mathrm{you}\:\mathrm{Sir}.\:\mathrm{thanks}\:\mathrm{alot}.\: \\ $$
Commented by aurpeyz last updated on 11/Jul/20
Sir cam you recomend a textbook for me Sir. that will help me with all of this?
$$\mathrm{Sir}\:\mathrm{cam}\:\mathrm{you}\:\mathrm{recomend}\:\mathrm{a}\:\mathrm{textbook}\:\mathrm{for}\:\mathrm{me}\:\mathrm{Sir}.\:\mathrm{that}\:\mathrm{will}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{all}\:\mathrm{of}\:\mathrm{this}? \\ $$
Commented by mr W last updated on 11/Jul/20
no sir. not because i don′t want to tell you, but because i don′t know such a book, not because i don′t find the books good enough, but because i have never read such a book since i left the school.
$${no}\:{sir}.\:{not}\:{because}\:{i}\:{don}'{t}\:{want}\:{to}\:{tell} \\ $$$${you},\:{but}\:{because}\:{i}\:{don}'{t}\:{know}\:{such}\:{a} \\ $$$${book},\:{not}\:{because}\:{i}\:{don}'{t}\:{find}\:{the} \\ $$$${books}\:{good}\:{enough},\:{but}\:{because}\:{i}\:{have} \\ $$$${never}\:{read}\:{such}\:{a}\:{book}\:{since}\:{i}\:{left} \\ $$$${the}\:{school}. \\ $$
Commented by aurpeyz last updated on 11/Jul/20
okay Sir
$$\mathrm{okay}\:\mathrm{Sir} \\ $$

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