Revisica
Sign in
ENGR5004 / Week 9
ENGR216 2022 Dynamics Q A2Past paperOld spec ENGR2162:125 marks30 min

ENGR216 Summer 2022 Dynamics Q A2[VALID]

Answer ALL parts (a) - (c).

Figure A2-1: pulley of radius R on a fixed pivot; rope from a spring k (anchored below) over the pulley to a hanging mass m.
Figure A2-1: pulley of radius R on a fixed pivot; rope from a spring k (anchored below) over the pulley to a hanging mass m.
Formulas you may need
  • Rotation about a fixed axis through G: ∑MG=IG α\sum M_G = I_G\,\alpha (learn this)
  • Angle-dependent integration: α=ω dωdθ\alpha = \omega\,\dfrac{d\omega}{d\theta}, so I ω dωdθ=T(ω)I\,\omega\,\dfrac{d\omega}{d\theta} = T(\omega) (learn this)
  • ∫ω dωa−bω2=−12bln⁡(a−bω2)\displaystyle\int \frac{\omega\,d\omega}{a - b\omega^2} = -\frac{1}{2b}\ln(a - b\omega^2); 1 rev =2π= 2\pi rad, rpm =ω⋅60/(2π)= \omega \cdot 60/(2\pi) (learn this)
  • Newton's second law for a particle: ∑F=ma\sum F = m a (learn this)
  • Rope over a pulley without slip: a=αRa = \alpha R; pulley with inertia: (T1−T2)R=IGα(T_1 - T_2)R = I_G\alpha, so meq=m+IG/R2m_{eq} = m + I_G/R^2 (learn this)
  • Work-energy: T1+∑U1→2=T2T_1 + \sum U_{1\to2} = T_2, spring work −12k(s22−s12)-\tfrac{1}{2}k(s_2^2 - s_1^2), gravity work mg Δsmg\,\Delta s (learn this)
  1. (a)
    Why is a 'moment of inertia' useful when determining the kinetics of a rotating planar rigid body?
    [4]Third
  2. (b(i))
    A rotating disc driven by a motor has a moment of inertia IG=50 kg m2I_G = 50\ \mathrm{kg\,m^2} and begins turning from rest at t=0t = 0. The torque TT applied to the disc by the drive motor is given by T=140−0.02 ω2T = 140 - 0.02\,\omega^2 where ω\omega is angular velocity measured in rad/s. What will be the angular velocity in rpm (revolutions per minute) of the disc when it has turned 500 revolutions?
    [5]
  3. (b(ii))
    What is the maximum angular velocity (in rpm) that the disc reaches?
    [3]2:2
  4. (c(i))
    Figure A2-1 shows a pulley-spring-mass system. The pulley has radius R=150R = 150 mm and moment of inertia IG=0.15 kg m2I_G = 0.15\ \mathrm{kg\,m^2} and the spring has spring constant k=120k = 120 N/m. The mass m=4m = 4 kg. The system is released from rest with the spring in the unstretched position. At the point when the mass has fallen 0.2 m, what is the angular acceleration of the pulley?
    [4]
  5. (c(ii))
    For the condition in (i), what will be the tension in the rope between the mass and the pulley?
    [4]2:2
  6. (c(iii))
    Determine the maximum distance the mass falls before rebounding.
    [5]2:2