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Feb/Mar 2020 p42 q2
3985
A particle P of mass 0.4 kg is on a rough horizontal floor. The coefficient of friction between P and the floor is \(\mu\). A force of magnitude 3 N is applied to P upwards at an angle \(\alpha\) above the horizontal, where \(\tan \alpha = \frac{3}{4}\). The particle is initially at rest and accelerates at 2 m/s\(^2\).
(a) Find the time it takes for P to travel a distance of 1.44 m from its starting point.
(b) Find \(\mu\).
Solution
(a) Using the equation of motion \(s = ut + \frac{1}{2} a t^2\), where \(u = 0\), \(s = 1.44\) m, and \(a = 2\) m/s\(^2\):
\(1.44 = 0 + \frac{1}{2} \times 2 \times t^2\)
\(1.44 = t^2\)
\(t = \sqrt{1.44} = 1.2 \text{ s}\)
(b) Resolve forces vertically to find the normal reaction \(R\):