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ENGR5004 / Week 2
Dynamics Session 3 Worked example 2TutorialCurrent spec2:212 min

ENGR5004 Dynamics Session 3 worked example 2 (slides 18-21) official answers

A roller coaster travels along a vertical parabolic path y=0.01x2y = 0.01x^2 (xx, yy in m, origin at the bottom of the dip). At point B, where x=30x = 30 m, it is moving down the track towards the origin with a speed of 25 m/s, which is increasing at the rate of 3 m/s2^2.

Find the magnitude and direction of the roller coaster's acceleration at B.

Roller coaster track y = x^2/100; the car is at B, 30 m from the y axis, moving down towards the origin; the sketch shows a_t along the track (downhill) and a_n towards the centre of curvature.
Roller coaster track y = x^2/100; the car is at B, 30 m from the y axis, moving down towards the origin; the sketch shows a_t along the track (downhill) and a_n towards the centre of curvature.
Formulas you may need
  • Normal-tangential components: at=v˙a_t = \dot v, an=v2ρa_n = \dfrac{v^2}{\rho}, a=at2+an2a = \sqrt{a_t^2 + a_n^2} (learn this)
  • Radius of curvature of y=f(x)y = f(x): ρ=[1+(dy/dx)2]3/2∣d2y/dx2∣\rho = \dfrac{\left[1 + (dy/dx)^2\right]^{3/2}}{\left|d^2y/dx^2\right|} (learn this)