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ENGR5004 / Week 8
ENGR216 2019 Q B3Past paperOld spec ENGR2162:225 marks30 min

ENGR216 Summer 2019 Q B3[VALID]

The uniform steel plate shown in Figure B3 rotates about point C in the xx-yy plane due to the combined effects of gravity and the vertical force, P. At the instant shown in Figure B3, the plate has an angular velocity, ω=20\omega = 20 rad/s and an angular acceleration, α=15 rad/s2\alpha = 15\ \mathrm{rad/s^2} both in the counter-clockwise direction. The plate has a mass of m=10m = 10 kg, and dimensions b=0.5b = 0.5 m and h=0.24h = 0.24 m.

Figure B3: rectangular plate b x h pinned at C (0.10 m from the left edge, 0.12 m above the bottom edge); vertical force P upward at the top right corner; alpha and omega counter-clockwise.
Figure B3: rectangular plate b x h pinned at C (0.10 m from the left edge, 0.12 m above the bottom edge); vertical force P upward at the top right corner; alpha and omega counter-clockwise.
Formulas you may need
  • Plate about its centroid: IG=m12(b2+h2)I_G = \dfrac{m}{12}(b^2 + h^2) (given in the question)
  • Moment of inertia definition IO=∫mr2 dmI_O = \int_m r^2\,dm and radius of gyration kO=IO/mk_O = \sqrt{I_O/m} (given in the 2019 Section B appendix; learn this)
  • Parallel-axis theorem: IC=IG+md2I_C = I_G + m d^2 (learn this)
  • Fixed-axis rotation of G: an=ω2rG/Ca_n = \omega^2 r_{G/C} (towards C), at=αrG/Ca_t = \alpha r_{G/C} (learn this)
  • Equations of motion: ∑F=maG\sum\mathbf{F} = m\mathbf{a}_G, ∑MC=ICα\sum M_C = I_C\alpha (or ∑MG=IGα\sum M_G = I_G\alpha) (given in the 2019 Section B appendix; not on the 2026 sheet, so learn this)
  1. (a)
    For the plate shown in Figure B3, the moment of inertia for rotation in the xx-yy plane about an axis located at the centroid is given by IG=m12(b2+h2)I_G = \frac{m}{12}(b^2 + h^2) Explain what a moment of inertia is, and calculate IGI_G for the plate.
    [4]Third
  2. (b)
    In your answer book, sketch a free body diagram of the plate showing the location and direction of external forces acting on the plate, and sketch the corresponding kinetic diagram showing the couple moments that are produced by the dynamic forces.
    [6]
  3. (c)
    Calculate the normal and transverse components of acceleration acting on the plate's centre of mass (centroid).
    [6]
  4. (d)
    Determine the magnitude of force P.
    [4]
  5. (e)
    Determine the reactions in the x direction, CxC_x and the y direction, CyC_y that are produced at point C.
    [5]