State Newton's Laws of Motion and deduce the equation \(P=mf\). A particle of mass \(m\) slides down the face of a smooth inclined plane of mass \(M\) and inclination \(\alpha\) which is free to slide on a smooth horizontal plane. Prove that the acceleration of \(M\) is \(mg\sin\alpha\cos\alpha/(M+m\sin^2\alpha)\). Also find the pressure between the particle and the inclined plane.
Prove that \(v^2/r\) is the acceleration towards the centre of a particle moving in a circle with velocity \(v\). A heavy particle is placed inside a smooth circular tube fixed in a vertical plane. The particle is slightly displaced from rest at the highest point of the tube, prove that in the subsequent motion the pressures between it and the tube as it passes the extremity of the horizontal diameter and the lowest point of the tube are as 2:5.
The future of Aerial Navigation.
Roman Britain.
"A Liberal Education."
Opera.
Small Holdings.
The English Public School.
Sir Walter Scott.
The relations between Employers and Employed.