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ENGR5004 / Week 5
ENGR216 2019 Q B1Past paperOld spec ENGR2162:225 marks30 min

ENGR216 Summer 2019 Q B1[VALID]

Figure B1 shows a farm loader with an extendable boom. The boom is intended to be operated with the vehicle stationary. A service engineer has taken measurements of the loader in use and determined that the polar coordinates of point A on the bucket are functions of time (in seconds) given by r=2+0.1t2r = 2 + 0.1t^2 (m) and θ=0.03t2\theta = 0.03t^2 (rad).

Figure B1: farm loader; boom pivots at the cab, point A on the bucket at radius r and angle theta from the horizontal x axis (y up).
Figure B1: farm loader; boom pivots at the cab, point A on the bucket at radius r and angle theta from the horizontal x axis (y up).
Formulas you may need
  • Polar velocity: vr=r˙v_r = \dot r, vθ=rθ˙v_\theta = r\dot\theta, v=vr2+vθ2v = \sqrt{v_r^2 + v_\theta^2} (given in the 2019 Section B appendix; not on the 2026 sheet, so learn this)
  • Polar acceleration: ar=r¨−rθ˙2a_r = \ddot r - r\dot\theta^2, aθ=rθ¨+2r˙θ˙a_\theta = r\ddot\theta + 2\dot r\dot\theta, a=ar2+aθ2a = \sqrt{a_r^2 + a_\theta^2} (given in the 2019 Section B appendix; not on the 2026 sheet, so learn this)
  • Angular velocity: ω=θ˙\omega = \dot\theta (given in the 2019 Section B appendix; learn this)
  • Newton's second law in polar components: ∑Fr=mar\sum F_r = m a_r, ∑Fθ=maθ\sum F_\theta = m a_\theta (learn this; the 2019 appendix only gives ∑FG=maG\sum \mathbf{F}_G = m\mathbf{a}_G)
  • Weight resolved along ur\mathbf{u}_r, uθ\mathbf{u}_\theta: Wr=−mgsin⁡θW_r = -mg\sin\theta, Wθ=−mgcos⁡θW_\theta = -mg\cos\theta (learn this)
  1. (a)
    For the time t=3t = 3 s, determine the velocity of point A in terms of radial and transverse components.
    [6]
  2. (b)
    For the time t=3t = 3 s, determine the angular velocity of point A.
    [3]
  3. (c)
    For the time t=3t = 3 s, determine the acceleration of point A in terms of radial and transverse components.
    [8]
  4. (d)
    If the load bucket weighs 120 kg and has a centre of mass located at point A, determine the radial and transverse components of force that act on the bucket from its supports for the time t=3t = 3 s.
    [8]2:1