6 In this question the box should be modelled as a particle.
A box of mass mkg is placed on a rough slope which makes an angle of \(\alpha\) with the horizontal.
- Show that the box is on the point of slipping if \(\mu = \tan \alpha\), where \(\mu\) is the coefficient of friction between the box and the slope.
A box of mass 5 kg is pulled up a rough slope which makes an angle of \(15 ^ { \circ }\) with the horizontal. The box is subject to a constant frictional force of magnitude 3 N . The speed of the box increases from \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at a point A on the slope to \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at a point B on the slope with B higher up the slope than A . The distance AB is 10 m .
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The pulling force has constant magnitude P N and acts at a constant angle of \(25 ^ { \circ }\) above the slope, as shown in the diagram. - Use the work-energy principle to determine the value of P .