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Phys011 / Fall 2006
Mid-term Examination (24 Oct 2005)
Answer ALL questions.
Full mark: 250
1. (60 marks)
(a) Two blocks connected by a rope of negligible mass are being pulled by a horizontal force F = 68.0 N. m1 = 12.0 kg, m2 = 18.0 kg, and the coefficient of kinetic friction between each block and the surface is 0.100. (i) Draw a free-body diagram for each block. (ii) Determine the tension T and the magnitude of the acceleration of the system.
(b) A small ball A is attached to one end of a rigid massless rod, while an identical ball B is attached to the center of the rod. Each ball has a mass of m = 0.50 kg and the length of the rod is L = 0.80 m. This arrangement is held by the empty end C and set into circular motion in a horizontal plane. Ball A travels at a constant speed of vA = 5.00 m/s. Draw a free-body diagram for each ball. Find the tension in each of half of the rod.
2. (50 marks) A block of mass 1.6 kg is attached to a horizontal spring that has a force constant of 1.0x103 N/m, as shown below. The spring is stretched 2.0 cm and is then released from rest.
(a) Calculate the speed of the block as it passes through the equilibrium position x = 0 if the surface is frictionless.
(b) Calculate the speed of the block as it passes through the equilibrium position if a constant friction force of 4.0 N resists its motion from the moment it is released.
(c) At what position x of the block is its speed a maximum?
(d) If the friction force is increased to 10.0 N, at what position of the block does its maximum speed occur?
3. (40 marks) The figure above below the potential energy of a 0.5 kg particle as it moves along the x-axis. suppose the particles mechanical energy is 12 J.
(a) What is the particles speed when it is at x = 2. 0 m?
(b) What is the particles maximum speed ? At what position(s) does this occur?
(c) As the particle moves from the left turning point to the right turning point, how does the force acting on the particle change?
(d) Describe the motion in terms of speed and acceleration as the particle moves to the right.
4. (50 marks)
(a) A small bob of mass m is suspended on a light rigid rod of length L and negligible mass. What is the minimum speed vb must the bob be given at the bottom so that the pendulum bob will barely swing through a complete vertical circle?
(b) If the rigid rod is replaced by an inextensible string, what is the minimum speed vb at the bottom must the bob be given to maintain circular motion in a vertical circle?
(c) If the bob and string system is given the speed at the bottom vb in (a), find the angle at which circular motion fails and the speed of the bob at this angular position.
(d) Describe qualitatively the motion of the bob when it breaks away from circular motion.