Mathematics > QUESTION PAPER & MARK SCHEME > Further Mathematics Advanced Subsidiary Further Mathematics options 25: Further Mechanics 1 (Part of (All)

Further Mathematics Advanced Subsidiary Further Mathematics options 25: Further Mechanics 1 (Part of options C, E, H and J)

Document Content and Description Below

A small book of mass m is held on a rough straight desk lid which is inclined at an angle α to the horizontal, where tanα = 3 4 . The book is released from rest at a distance of 0.5m from the ed ... ge of the desk lid, as shown in Figure 1. The book slides down the desk lid and then hits the floor that is 0.8m below the edge of the desk lid. The coefficient of friction between the book and the desk lid is 0.4 The book is modelled as a particle which, after leaving the desk lid, is assumed to move freely under gravity. (a) Find, in terms of m and g, the magnitude of the normal reaction on the book as it slides down the desk lid. (2) (b) Use the work-energy principle to find the speed of the book as it hits the floor. A particle of mass em is at rest on a smooth horizontal plane between two smooth fixed parallel vertical walls, as shown in the plan view in Figure 2. The particle is projected along the plane with speed u towards one of the walls and strikes the wall at right angles. The coefficient of restitution between the particle and each wall is e and air resistance is modelled as being negligible. Using the model, (a) find, in terms of m, u and e, an expression for the total loss in the kinetic energy of the particle as a result of the first two impacts. (3) Given that e can vary such that 0 < e < 1 and using the model, (b) find the value of e for which the total loss in the kinetic energy of the particle as a result of the first two impacts is a maximum, (4) (c) describe the subsequent motion of the particle. (2 [Show More]

Last updated: 3 years ago

Preview 1 out of 28 pages

Buy Now

Instant download

We Accept: