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Modeling a Box as a Particle

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See attached file for full problem description. Need help on 2b, 3.

2. A box of mass m is placed on a plane, which is inclined at an angle a to the horizontal, where tan a The plane is rough and the coefficient of friction between the box and the plane is . The box is kept in equilibrium on the plane by applying a horizontal force of magnitude P to it, acting in a vertical plane containing a line of greatest slope of the plane, as shown above. Given that P has the smallest possible, value which will enable the box to remain in equilibrium,
a draw a diagram, showing all the forces acting on the box, and indicating clearly the direction in which they act,
b find P in terms of m and g.

3. A box of mass 50 kg rests on rough, horizontal ground. The coefficient of friction between the box and the ground is 0.6. A force of magnitude P Newtons is applied to the box at an angle of 15° to the horizontal, as shown above, and the box is now in limiting equilibrium. By modelling the box as a particle find, to 3 significant figures, the value of P.

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Modelling a box as a a particle is investigated and discussed in the solution.

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