Brain is trying to pull Julie on a sled across a flat snowy field. Brain pulls on a rope attached to the sled. Brian's pulling force is directed forward and upward at an angle of 30 degrees above horizontal. Julie's mass is 50 kg, and the sled's mass is 8 kg. If the coefficient of static friction between the sled runners and the snow is 0.10, how much force must Brain exert on the rope to start moving the sled?

Question

summersnow8 · Answer

W = mg 
W= (58) (9.81) 
W= 569 N 

$$F= \mu _{s} R$$
$$\mu _{s} = .1 $$
R = 58? or 569 N ?

summersnow8 · Answer

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summersnow8 · Answer

the answer should be 62 N

anonymous · Answer

you started out correctly
the friction on the runners will be 0.1x569 =56.9Newtons

anonymous · Answer

so now the horizontal component of the pulling force has to be at least 56.9N

summersnow8 · Answer

@ProfBrainstorm how do i find the answer though? it is suppose to be 62

summersnow8 · Answer

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anonymous · Answer

okay, so if we call the pulling force along the direction of the rope F, what will it's component in the horizontal direction be, in terms of F and the 30 degree angle ?

summersnow8 · Answer

@ProfBrainstorm tht would mean F= CAH --> F= 56.9/ cos(30), but that doesnt give me 62

anonymous · Answer

I get an answer of 65.7 N
who says it should be 62 ?

summersnow8 · Answer

the book

anonymous · Answer

well based on the numbers given here I'm fairly sure the answer is 65.7
did you put the correct numbers in the question ?
It could be a typo error in the book, it happens.

summersnow8 · Answer

Yeah I am sure, this is the problem I see in my book, and the answer is 62 N in the back of the book

anonymous · Answer

The answer in the book is wrong

summersnow8 · Answer

@ProfBrainstorm haha, okay, thanks for all your help!