- A particle \(P\) of mass 0.4 kg is attached to one end of a light elastic string, of natural length 0.8 m and modulus of elasticity 0.6 N . The other end of the string is fixed to a point \(A\) on a rough horizontal table. The coefficient of friction between \(P\) and the table is \(\frac { 1 } { 7 }\)
The particle \(P\) is projected from \(A\), with speed \(1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), along the surface of the table.
After travelling 0.8 m from \(A\), the particle passes through the point \(B\) on the table.
- Find the speed of \(P\) at the instant it passes through \(B\).
The particle \(P\) comes to rest at the point \(C\) on the table, where \(A B C\) is a straight line.
- Find the total distance travelled by \(P\) as it moves directly from \(A\) to \(C\).
- Show that \(P\) remains at rest at \(C\).