The English Public School.
Sir Walter Scott.
The relations between Employers and Employed.
The responsibilities of a First-rate Power.
The Battle of Jutland.
A carriage with wheels of radius \(a\) is drawn along a level road with velocity \(v\). Particles of mud are thrown off continually from the rims of the wheels. Find the maximum height \(h\) of the particles after leaving the rim, and draw a graph showing the relation of \(h\) to \(v\), as \(v\) increases from zero.
A projectile of mass \(M\) lb., moving horizontally with a speed of \(v\) feet per second, strikes an inelastic pin of mass \(m\) lb. projecting horizontally from a block of mass \(M'\) lb., which is free to slide on a smooth plane. Prove that the pin is driven \[ x = \frac{MM'}{(M+M'+m)(M+m)}\frac{v^2}{gF} \] inches into the block, where \(F\) lb. weight is the mean resistance of the block to penetration by the pin.
A railway train is being accelerated at a certain rate when it reaches the foot of an incline. It ascends to a ridge and descends, at the same inclination, to the former level. The pull of the engine and the wheel resistance remain constant throughout. Determine the inclination of the water surface in the tank during ascent and descent, and prove that the difference between the two inclinations is twice the inclination of the slopes.
A square plate of side \(a\) and mass \(M\) is hinged about its highest edge, which is horizontal. When at rest it is struck horizontally, at a depth \(h\) below the hinge, by a particle of mass \(m\) travelling with velocity \(v\). The particle becomes embedded in the plate close to the surface. Determine the subsequent motion of the plate.
A vessel in the form of a regular tetrahedron of height \(h\) rests with one face on a horizontal table. The other faces are uniform heavy plates of weight \(w\), freely hinged about their lowest edge, and fitting closely when shut. Water is poured into the vessel through a small hole at the top, and the pressure on the sides raises the plates and opens the vessel when the height of water is \(mh\). Show that, if \(\rho w\) is the weight of water poured in, \[ 9\rho(2m^2-m^3)=2(m^2-3m+3). \]