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 2. B.  1. C. A. 07B1Eng. HOME EXAM B1. PROBLEM 1. (a). (b). (c).

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  1. 2 B 1 C A 07B1Eng HOME EXAM B1 PROBLEM 1 (a) (b) (c) You have a spring whose natural length is L0 = 10 cm -figure (a)-. When a mass M = 250 g is hung on the spring, its length increases by L = 40 cm –figure (b)-. Finally, the hanging mass oscillates after the spring is stretched A = 10 cm and then released –figure (c)-. Answer the following questions: a) What is the constant of the spring? 0.5 p b) Find the period of the oscillation 0.5 p c) Find the position of the mass 6.98 s after the oscillations start. 1.0 p d) Find the period of the oscillation if you had hung the same mass M from two identical springs like this one disposed in a paralell way. 2.0 p PROBLEM 2 The mechanism depicted in the figure is composed by two rigid rods, each of lenght L. Rod AB girates around toggle A, whereas rod BC has a joint in point B and its end C slides on the floor. You know the lenght L, the angular velocity of rod AB, AB, and the angles 1 and 2. Find: a) The velocity of point B, vB, and the angle formed by vB with the horizontal. 2.0 p b) The angular velocity of rod BC, BC, and the velocity of point C, vC. 4.0 p

  2. 07B1_Eng HOME EXAM B1 PROBLEM 1 (a) (b) (c) You have a spring whose natural length is L0 = 10 cm -figure (a)-. When a mass M = 250 g is hung on the spring, its length increases by L = 40 cm –figure (b)-. Finally, the hanging mass oscillates after the spring is stretched A = 10 cm and then released –figure (c)-. Answer the following questions: a) What is the constant of the spring? 0.5 p b) Find the period of the oscillation 0.5 p c) Find the position of the mass 6.98 s after the oscillations start. 1.0 p d) Find the period of the oscillation if you had hung the same mass M from two identical springs like this one disposed in a paralell way. 2.0 p a) From Hooke’s law: From Newton’s 2nd law: c) b) We choose t = 0 when y = A That implies  = 0

  3. where PROBLEM 1 (SOLUTION CONTINUED) From Newton’s 2nd law: (The springs are identical) d) From Hooke’s law: Equation of the oscillation driven by two identical springs: Let us write the equation as The solution of this equation is The period is The set of two identical springs disposed in a parallel way (each constant = k) behaves as a single spring of constant 2 k.

  4. 2 1 PROBLEM 2 The mechanism depicted in the figure is composed by two rigid rods, each of lenght L. Rod AB girates around toggle A, whereas rod BC has a joint in point B and its end C slides on the floor. You know the lenght L, the angular velocity of rod AB, AB, and the angles 1 and 2. Find: B a) The velocity of point B, vB, and the angle formed by vB with the horizontal. 2.0 p b) The angular velocity of rod BC, BC, and the velocity of point C, vC. 4.0 p B C A

  5. See that B 1 A PROBLEM 2 (solution continued) a) Find: The velocity of point B, vB, and the angle formed by vB with the horizontal. From dot product definition: Rod AB

  6. 2 Vector B Let’s call 1 C A b) Find: The angular velocity of rod BC, BC, and the velocity of point C, vC. We know: This vectorial equation can be splitted into two equations, one for each component: Although we don’t know their values, we can write for angular velocity and velocity of point C: BC and vC are the quantities to find. C end slides on the floor

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