The normal and frictional components of the contact force exerted on the ring by the rod are \(R \mathrm {~N}\) and \(F\) N respectively. Find \(R\) and \(F\) in terms of \(T\).
The coefficient of friction between the rod and the ring is 0.7 . Find the value of \(T\) for which the ring is about to slip.
A man walks in a straight line from \(A\) to \(B\) with constant acceleration \(0.004 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). His speed at \(A\) is \(1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and his speed at \(B\) is \(2.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the time taken for the man to walk from \(A\) to \(B\), and find the distance \(A B\).
A woman cyclist leaves \(A\) at the same instant as the man. She starts from rest and travels in a straight line to \(B\), reaching \(B\) at the same instant as the man. At time \(t \mathrm {~s}\) after leaving \(A\) the cyclist's speed is \(k \left( 200 t - t ^ { 2 } \right) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(k\) is a constant. Find
(a) the value of \(k\),
(b) the cyclist's speed at \(B\).
Sketch, using the same axes, the velocity-time graphs for the man's motion and the woman's motion from \(A\) to \(B\).