Standard +0.3 This is a straightforward application of circular motion with friction providing the centripetal force. Students need to recognize that F = μR provides the maximum friction, set this equal to mv²/r, and solve for r. The calculation is direct with given values, requiring only one key insight and basic algebraic manipulation.
5 Tom is travelling on a train which is moving at a constant speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) on a horizontal track. Tom has placed his mobile phone on a rough horizontal table. The coefficient of friction between the phone and the table is 0.2 .
The train moves round a bend of constant radius. The phone does not slide as the train travels round the bend.
Model the phone as a particle moving round part of a circle, with centre \(O\) and radius \(r\) metres.
Find the least possible value of \(r\).
5 Tom is travelling on a train which is moving at a constant speed of $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ on a horizontal track. Tom has placed his mobile phone on a rough horizontal table. The coefficient of friction between the phone and the table is 0.2 .
The train moves round a bend of constant radius. The phone does not slide as the train travels round the bend.
Model the phone as a particle moving round part of a circle, with centre $O$ and radius $r$ metres.
Find the least possible value of $r$.
\hfill \mbox{\textit{AQA M2 2013 Q5 [4]}}