SECTION ONE

(a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass as shown below:

Derive the expression for the magnitude of acceleration and Tension T on the rope

(b) A traffic light weighing 130N hangs from a cable tied to two other cables fastened to a support , the upper cable makes angles of 33° and 53° with the horizontal. These upper cables are not as strong as the vertical cables, so it will break if the tension exceeds 90N. does the traffic light remain hanged in this situation or will one of the cables break?

(c) A pirate ship located 560m from a port defending the harbor entrance of an island. A defence at sea level located at the entrance of the island fires shells at initial speed 82m/s. at what angle from the horizontal must the shell be fired to hit the ship?

(d) A stone is thrown up from the top of a platform with an initial velocity of Um/s. if the platform is taken to be the ground level, write the expression for (i) the maximum height reached by the stone (ii) velocity just before reaching the ground level

SECTION TWO

a. Derive the expression for the volume of liquid passing per seconds, V, through a pipe when the flow is steady. Assuming that v is proportional to (i) the coefficient of viscosity n of the liquid (ii) the radius r of the pipe and (iii) the pressure gradient, (pill, causing the flow, where p is the pressure difference between the ends of the pipe and I its length.

b. A hockey puck having a mass of 0.40kg slides on the frictionless horizontal surface of an ice rink. Two hockey slicks strike the puck simultaneously exerting the forces F^→₁ = 6N at 5O° and F_z^→ = 8N at 220° on the pluck. Taking +x-axls as the frame of reference, Determine the magnitude and direction of the acceleration?

c. The force F experienced by a charge q L- 2C moving with velocity V in a magnetic field B is given by F = qV x D. Given that F = 4i^{^}- 20j^{^} + 12k^ and V = 2i + 4j^{^} + 6k^{^}. Find B if B_x = B_y