7 A box of mass 50 kg is at rest on a plane inclined at \(10 ^ { \circ }\) to the horizontal.
- Find an inequality for the coefficient of friction between the box and the plane.
In fact the coefficient of friction between the box and the plane is 0.19 .
- A girl pushes the box with a force of 50 N , acting down a line of greatest slope of the plane, for a distance of 5 m . She then stops pushing. Use an energy method to find the speed of the box when it has travelled a further 5 m .
The box then comes to a plane inclined at \(20 ^ { \circ }\) below the horizontal. The box moves down a line of greatest slope of this plane. The coefficient of friction is still 0.19 and the girl is not pushing the box.
- Find the acceleration of the box.