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ENGR5004 / Week 4
Dynamics L8 Worked example 1TutorialOld spec ENGR2162:212 min

ENGR216 Dynamics L8 worked example 1 (slides 10-11) official answers

A fairground ride consists of an arm BC of length 10 m pinned to the ground at C; a seat at the end B is pin connected to the arm so that it stays level. The arm swings upwards (anticlockwise), so the passenger at B moves on a circle of radius 10 m about C, towards A at the top. At the instant when the arm is at θ=45∘\theta = 45^\circ above the horizontal, the 75 kg passenger has a speed of 6 m/s, which is increasing at 0.5 m/s2^2. Neglect the passenger's size and the mass of the seat; take g=9.81g = 9.81 m/s2^2.

Find the horizontal and vertical components of the force of the seat on the passenger.

Arm CB of length 10 m pinned at C, inclined at theta to the horizontal; the passenger at B moves along the circular arc towards A.
Arm CB of length 10 m pinned at C, inclined at theta to the horizontal; the passenger at B moves along the circular arc towards A.
Formulas you may need
  • Equations of motion in n-t components: ∑Fn=mv2ρ\sum F_n = m\dfrac{v^2}{\rho}, ∑Ft=mv˙\sum F_t = m\dot v (learn this)