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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?

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  1. Michele_Laino
    • one year ago
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    the situation of your problem is described by the subsequent drawing: |dw:1438333970203:dw|

  2. Michele_Laino
    • one year ago
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    the 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

  3. Michele_Laino
    • one year ago
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    hint: 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: \[\Large \tan \varphi = \mu \]

  4. Michele_Laino
    • one year ago
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    oops.. 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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