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ENGR5004 / Week 4
Dynamics L8 Worked example 3TutorialOld spec ENGR2162:210 min

ENGR216 Dynamics L8 worked example 3 (slides 14-15) official answers

A car of mass 1700 kg travels on a circular track of radius of curvature 100 m that is banked at θ=20∘\theta = 20^\circ (the track rises away from the centre of curvature). The coefficient of static friction between tyres and road is μs=0.2\mu_s = 0.2. Treating the car as a particle, find the maximum constant speed at which it can travel without slipping up the slope. Take g=9.81g = 9.81 m/s2^2.

Cross-section of the banked track: the road surface is inclined at theta to the horizontal, rising away from the centre of curvature at distance rho.
Cross-section of the banked track: the road surface is inclined at theta to the horizontal, rising away from the centre of curvature at distance rho.
Formulas you may need
  • n-t equations of motion: ∑Fn=mv2ρ\sum F_n = m\dfrac{v^2}{\rho}, ∑Fb=0\sum F_b = 0 (learn this)
  • Friction at impending slip: F=μsNF = \mu_s N, opposing the impending motion (learn this)