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anonymous
 one year ago
You push against a steamer trunk with a force of 800 N at an angle alpha with the horizontal . The trunk is on a flat floor and the coefficient of static friction between the trunk and floor is 0.55. The mass of the trunk is 87 kg. What is the largest value of alpha that will allow you to move the trunk?
anonymous
 one year ago
You push against a steamer trunk with a force of 800 N at an angle alpha with the horizontal . The trunk is on a flat floor and the coefficient of static friction between the trunk and floor is 0.55. The mass of the trunk is 87 kg. What is the largest value of alpha that will allow you to move the trunk?

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the situation of your problem is described by the subsequent drawing: dw:1438333970203:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the pressure on the floor has the subsequent magnitude: \[\Large mg + F\sin \theta \] whereas the driving force, has the subsequent magnitude: \[\Large F\cos \theta \] the trunk will move, if and only if the subsequent condition is checked: \[\Large F\cos \theta > \mu \left( {mg + F\sin \theta } \right)\] where \mu is the coefficient of static friction

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: after a simplification, we can write: \[\Large \cos \theta  \mu \sin \theta > \frac{{\mu mg}}{F}\] if we divide last condition by: \[\Large \sqrt {{\mu ^2} + 1} \] we get: \[\Large \frac{1}{{\sqrt {{\mu ^2} + 1} }}\cos \theta  \frac{\mu }{{\sqrt {{\mu ^2} + 1} }}\sin \theta > \frac{1}{{\sqrt {{\mu ^2} + 1} }}\frac{{\mu mg}}{F}\] which can be rewritten as follows: \[\Large \cos \left( {\theta  \varphi } \right) > \frac{1}{{\sqrt {{\mu ^2} + 1} }}\frac{{\mu mg}}{F}\] where \phi is such that: \[\Large \tan \varphi = \mu \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1oops.. I have made a typo, here is the right formula: \[\Large \cos \left( {\theta + \varphi } \right) > \frac{1}{{\sqrt {{\mu ^2} + 1} }}\frac{{\mu mg}}{F}\]
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