(a) Consider the mechanical system (shown below in Figure Q4a) is released from rest when = 180, and the uncompressed spring of stiffness k = 1500 N.m at this instance is just touching the underside of the 7 kg collar. Using energy approach, calculate the angle corresponding to the maximum compression of the spring. The whole motion of the system is only in the vertical plane, all the pin joints and the sliding collar are frictionless, the mass of the links may be neglected and you can use g = 9.81 m.s. Hint: you can solve the following quadratic expression, (A sin 0 + B sin 0 + C = 0} using the quadratic formula, by assuming x = sin 0. [15%] 5 kg 5 kg 7 kg Figure Q4a (b) A 70 kg pole vaulter (shown below in Figure Q4b) carrying a 5.30 m, 5 kg pole reaches a velocity v on his approach to the jump and just barely clear the bar set at a record height of 6.16 m. Using energy approach, calculate the minimum value of v required for him to make the jump. You can assume as he clears the bar, his velocity and that of the pole are zero. Also on the approach, you can assume the pole is held horizontally at the same height as the centre of gravity of the vaulter, which as shown below is 950 mm above the ground and you can use g = 9.81 m.s. [10% ] 250 mm - 250 mm 400 mm L 6.16 m 5.30 m Figure Q4b. 950 mm