4 Some tiles on a roof are being replaced. Each tile has a mass of 2 kg and the coefficient of friction between it and the existing roof is 0.75 . The roof is at \(30 ^ { \circ }\) to the horizontal and the bottom of the roof is 6 m above horizontal ground, as shown in Fig. 4.
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\caption{Fig. 4}
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- Calculate the limiting frictional force between a tile and the roof.
A tile is placed on the roof. Does it slide? (Your answer should be supported by a calculation.)
- The tiles are raised 6 m from the ground, the only work done being against gravity. They are then slid 4 m up the roof and placed at the point A shown in Fig. 4.
(A) Show that each tile gains 156.8 J of gravitational potential energy.
(B) Calculate the work done against friction per tile.
(C) What average power is required to raise 10 tiles per minute from the ground to A ? - A tile is kicked from A directly down the roof. When the tile is at \(\mathrm { B } , x \mathrm {~m}\) from the edge of the roof, its speed is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). It subsequently hits the ground travelling at \(9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). In the motion of the tile from B to the ground, the work done against sliding and other resistances is 90 J .
Use an energy method to find \(x\).