Physics Answers

A uniform ladder AB of wieght W and length 2l rests with the end A against a smooth vertical wall and the end B on a rough horizontal ground. A man of weight equal to that of the ladder stands at the point C on the ladder, where BC = 5l/3 . The coefficient of friction between the ladder and the ground is 1/3. Given that the ladder is in limiting equilibrium when it makes an angle s to the horizontal;
(a) Show that tans = 2
(b) Find the magnitude of the reaction force at the wall and on the ground.

A car mass 1400kg moves with a steady speed of 20 m/s on a straight rough road with its engine working at a constant rate of 36KW.
(a) Calculate the resistance R to the motion of the car if the road is horizontal.
Given that R is proportional to the square of the speed of the car,
(b) Show that R = 9v^2 /2 .

One end of an inextensible string of length 3m is fastened to a fixed point O, 2m above horizontal ground. A small particle is attached to the other end of the string. The particle describes a horizontal circle 1m below O. Find in terms of g, the tension in the string and the angular velocity of the particle.

A particle P of mass 2m lies on a rough horizontal table. P is connected by a light inextensible string passing over a smooth pulley fixed at the edge of the table to another particle Q of mass 5m, hanging freely. The system is released from rest with the string taught and the hanging part vertical. If the acceleration of the system is of magnitude 4g/7, find
(a) the tension in the string
(b) the coefficient of friction between the first particle and the table.

A particle starts from rest and moves in a straight line on a smooth horizontal surface. Its acceleration at time t seconds is k(4v + 1)m/s^2 , where k is a positive constant and v m/s is the speed of the particle. Given that v = (e^2 - 1)/4 when t = 1, show that v = 1/4(e^(2t) - 1)

A smooth sphere A of mass 3m moving on a smooth horizontal table with speed 4u, impiges directly on another smooth sphere B of mass 2m, moving with speed u in the opposite direction to A. The coefficient of restitution between A and B is e.
(a) Find the impulse exerted on A by the impact.
At the moment of the impact, the line of centres of the spheres is perpendicular to a vertical wall which is at a distance x from the point of collision and nearer to B than to A, and B subsequently collides with the wall.
(b) Find in terms of x, the distance of A from the wall at the instant B hits the wall.

A smooth sphere A of mass 3m moving on a smooth horizontal table with speed 4u, impiges directly on another smooth sphere B of mass 2m, moving with speed u in the opposite direction to A. The coefficient of restitution between A and B is e.
(a) Find in terms of e and u, the speed of B after the impact.
(b) Show that e = 1/3
(c) Find the impulse exerted on A by the impact.

A uniform ladder of weight W abd length 2a rests in limiting equilibrium with one end on a rough horizontal ground and the other end on a rough vertical wall. The coefficients of friction between the ladder and the ground and between the ladder and the wall are u and t respectively.
(a) Show that 5u + 6tu - 6 = 0
(b) Find the values of u and t, given that ut = 1/2
(c) Show by integration that tge centroid of a uniform semi-circular lamina of radius a from the centre is 4a/(3*pie).

In an experiment to determine the specific charge (e/m) of an electron, electrons where accelerated by an electric field strength of 10N/C and the magnetic field strength of 0.1H is used to deflect them. Find the speed of the accelerated electrons. What is the radius of the path described by the electron?

Briefly describe and experiment to determine the specific charge (e/m) of an electron using the combination of electric and magnetic fields.