COLM-07-PROBLEMS

PROBLEMS 1.. A car P is moving with a uniform speed of 5 (3½) m/s to- C wards a carriage of mass 9 kg at rest kept on the rails at a point B as shown in fig. The height AC is 120 m. Cannon P balls of kg are fired from the car with an initial velocity 100 A m/s at an angle 300 with the horizontal. The first cannon B ball hits the stationary carriage after a time t0 and sticks to it. Determine t0. AT t0 , the second connon ball is fired. Assume that the resistive force between the rails and the carriage is constant and ignore the vertical motion of the carriage throughout. If the second ball also hits and sticks to the carriage, what will be the horizontal velocity of the carriage just after the second impact? 2. One a frictionless horizontal surface, assumed to be the x-y plane, y as small trolley A is moving along a straight lien parallel to the y- A axis (see figure) with a constant velocity of  1 m/s. At a particular instant, when the line OA makes an angle of 45º with the x-axis, a ball is thrown along the surface from the origin O. Its velocity makes an angle  with the x-axis and it hits the trolley. (a) The motion of the ball is observed from the frame of the trol- ley. Calculate the angle  made by the velocity vector of the ball with the x-axis in this frame. (b) Find the speed of the ball with respect to the surface, if   4/ 3 . 45º O 3. Two blocks of mass 2kg and M are rest on an inclined plane and are separated by a distance of 6.0 m as shown. The coefficient of friction between each of the blocks and the inclined plane is 0.25. The 2kg block is given a velocity of 10.0 m/s up the inclined plane. It collides with M, comes back and has a velocity of 1.0 m/s when it reaches its initial position. The other block M after the collision moves 0.5m up and comes to rest. Calculate the coefficient of restitu- tion between the blocks and the mass of the block M. [Take sinθ  sin θ  0.05 and g  10m / s 2 ]. 4. A block of mass 2m is placed on another block B of mass 4m which in turn is placed on a fixed table. The two blocks have the same length 4d and they are placed as in fig. The coefficient of friction (both static and kinetic) between the block and the table is μ . There is no friction between the two blocks. A small object of mass m moving horizontally along a line passing through the centre of mass of the block B and perpendicular to its face with a speed v collides elastically with the block B at a height d above the table. (a) What is the minimum value of v (call it v0) required to make the block A topple (b) if v = 2v0 find the distance (from the point P) at which the mass m falls on the table after collision. m 4d