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  • Revision Tutorial

    1.   During a manufacturing process, a machine moves in a path such that its displacement is described by the equation:

    s=3t3-12t2+5t=16 (cm)
    i)    Calculate the displacement after 2s.[1]
    ii)    Produce a table and plot a velocity-time graph for 0-5s time span.[5]
    iii)     Calculate the acceleration of the machine after 2.5s.[2]
    iv)     At what time is the acceleration equal to 12 cm/s2[2]


    2.   A reciprocating machine of mass 500 kg is supported by paired springs which are arranged such that each pair has a
    spring of stiffness 30 kN/m and a spring of stiffness 50 kN/m in series, with 6 of these pairs arranged in parallel.
    Determine:
    i)    the total stiffness of the spring system in N/m;[5]
    ii)    the natural frequency of free vibration of the machine in Hz;[2]
    iii)    the time elapsed after 3 cycles of free vibration, and show this on an amplitude-time graph.[3]

    3.   A mass of 7g is required to balance a motorcar wheel. If the mass is attached to the 0.33m diameter wheel rim,
    calculate the centripetal force acting on the rim of the wheel when the speed of rotation is 471 rev/min    		           [5]