16 A particle of mass 2 kg slides down a plane inclined at \(20 ^ { \circ }\) to the horizontal. The particle has an initial velocity of \(1.4 \mathrm {~ms} ^ { - 1 }\) down the plane. Two models for the particle's motion are proposed.
In model A the plane is taken to be smooth.
- Calculate the time that model A predicts for the particle to slide the first 0.7 m .
- Explain why model A is likely to underestimate the time taken.
In model B the plane is taken to be rough, with a constant coefficient of friction between the particle and the plane.
- Calculate the acceleration of the particle predicted by model B given that it takes 0.8 s to slide the first 0.7 m .
- Find the coefficient of friction predicted by model B , giving your answer correct to 3 significant figures.
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