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Nov 2023 p43 q3
4041
A block of mass 8 kg slides down a rough plane inclined at 30° to the horizontal, starting from rest. The coefficient of friction between the block and the plane is \(\mu\). The block accelerates uniformly down the plane at 2.4 m/s\(^2\).
(a) Draw a diagram showing the forces acting on the block.
(b) Find the value of \(\mu\).
(c) Find the speed of the block after it has moved 3 m down the plane.
Solution
(a) The diagram should show three forces: the gravitational force acting downwards, the normal force perpendicular to the plane, and the frictional force opposing the motion.
(b) Resolve forces perpendicular to the plane: \(R = 8g \cos 30^{\circ} = 40\sqrt{3} \approx 69.282\). Resolve forces parallel to the plane and apply Newton's second law: \(8g \sin 30^{\circ} - F = 8 \times 2.4\). This gives \(F = 20.8\). Use \(F = \mu R\) to find \(\mu\):