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ENGR5004 / Week 4
ENGR216 2021 Dynamics Q A2Past paperOld spec ENGR2162:216 marks19 min

ENGR216 Summer 2021 Dynamics Q A2[VALID]

In a warehouse, crates of mass 100 kg move down a slope defined by the equation y=0.12x2y = 0.12x^2 (see Figure A2). At the instant x=7x = 7 m the crate in Figure A2 has a speed of 6 m/s. At this point, determine:

Figure A2: crate moving down the curve y = 0.12 x^2 at x = 7 m with speed 6 m/s.
Figure A2: crate moving down the curve y = 0.12 x^2 at x = 7 m with speed 6 m/s.
Formulas you may need
  • Normal-tangential kinetics: ∑Ft=mat\sum F_t = m a_t, ∑Fn=man\sum F_n = m a_n, at=v˙a_t = \dot v, an=v2ρa_n = \dfrac{v^2}{\rho} (learn this)
  • Radius of curvature of y(x)y(x): ρ=[1+(dy/dx)2]3/2∣d2y/dx2∣\rho = \dfrac{\left[1 + (dy/dx)^2\right]^{3/2}}{|d^2y/dx^2|} (learn this)
  • Slope angle: tan⁡θ=dy/dx\tan\theta = dy/dx; magnitude a=at2+an2a = \sqrt{a_t^2 + a_n^2} (learn this)
  1. (a)
    The rate of speed increase of the crate
    [4]
  2. (b)
    The force the slope exerts on the crate
    [4]
  3. (c)
    The magnitude and direction of the crate's acceleration
    [4]
  4. (d)
    State any assumptions that you have made, with full justification
    [4]Third