OCR GCE AS Level Further Maths B (MEI) Mechanics a (optional - choose any two of Y411/Y412/Y413/Y414) June 2019 question paper Y411

A child is pulling a toy block in a straight line along a horizontal floor. The block is moving with a constant speed of 2 m s^-1 by means of a constant force of magnitude 20 N acting at an angle of θ ° above the horizontal.

The work done by the force in 10 s is 350 J.

Calculate the value of θ.

The surface tension of a liquid allows a metal needle to be at rest on the surface of the liquid. The greatest mass m of a needle of length l which can be supported in this way by a liquid of surface tension S is given by the formula

where g is the acceleration due to gravity.

A box weighing 130 N is on a rough plane inclined at 12° to the horizontal. The box is held at rest on the plane by the action of a force of magnitude 70 N acting up the plane in a direction parallel to a line of greatest slope of the plane. The box is on the point of slipping up the plane.

Find the coefficient of friction between the box and the plane.

The force of magnitude 70 N is removed.

Determine whether or not the box remains in equilibrium.

A shovel consists of a blade and handle, as shown in Fig. 4.1 and Fig. 4.2. The dimensions shown in the figures are in metres. The blade is modelled as a uniform rectangular lamina ABCD lying in the O xy plane, where O is the mid-point of AB. The handle is modelled as a thin uniform rod EF. The handle lies in the Oyz plane, and makes an angle α with Oy, where sin α = . The rod and lamina are rigidly attached at E, the mid-point of CD. The blade of the shovel has mass 1.25 kg and the handle of the shovel has mass 0.5 kg.

Find,

the y-coordinate of the centre of mass of the shovel,

the z-coordinate of the centre of mass of the shovel.

The shovel is freely suspended from O and hangs in equilibrium.

Calculate the angle that OE makes with the vertical.

A car of mass 4000 kg travels up a line of greatest slope of a straight road inclined at an angle of θ to the horizontal, where sin θ = 0.1. The power developed by the car’s engine is constant and the resistance to the motion of the car is constant and equal to 850 N. The car passes through a point A on the road with speed 18 m s^-1 and acceleration 0.75 m s^-2.

Calculate the power developed by the car.

The car later passes through a point B on the road with speed 25 m s^-1. The car takes 17.8 s to travel from A to B.

Find the distance AB.

Three particles, A, B and C are in a straight line on a smooth horizontal surface. The particles have masses 5 kg, 3 kg and 1 kg respectively. Particles B and C are at rest. Particle A is projected towards B with a speed of u m s^-1 and collides with B. The coefficient of restitution

Particle B subsequently collides with C. The coefficient of restitution between B and C is

Determine whether any further collisions occur.

Given that the loss of kinetic energy during the initial collision between A and B is 4.8 J, find

the value of u.

Fig. 7

Fig. 7 shows a uniform rod AB of length 4 a and mass m. The end A rests against a rough vertical wall. A light inextensible string is attached to the rod at B and to a point C on the wall vertically above A, where AC = 4 a. The plane ABC is perpendicular to the wall and the angle ABC is 30°.

The system is in limiting equilibrium.

Find the coefficient of friction between the wall and the rod.