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Nov 2018 p41 q6
4046
A particle is projected from a point P with initial speed u m s-1 up a line of greatest slope PQR of a rough inclined plane. The distances PQ and QR are both equal to 0.8 m. The particle takes 0.6 s to travel from P to Q and 1 s to travel from Q to R.
Show that the deceleration of the particle is \(\frac{2}{3}\) m s-2 and hence find u, giving your answer as an exact fraction.
Given that the plane is inclined at 3° to the horizontal, find the value of the coefficient of friction between the particle and the plane.
Solution
(i) Using the equation of motion \(s = ut + \frac{1}{2}at^2\) for the segment PQ:
\(0.8 = 0.6u + \frac{1}{2}a(0.6)^2\)
\(0.8 = 0.6u + 0.18a\)
For the segment QR:
\(0.8 = (u + a \times 0.6) \times 1 + \frac{1}{2}a \times 1^2\)