A partial cross-section of an amusement park ride is shown. While the ride spins

Question

A partial cross-section of an amusement park ride is shown. While the ride spins up to the angular speed omega c , there is a small platform a t F on which the person P stands. Once the ride reaches the desired angular speed, the platform falls away and only friction keeps the person from sliding to the floor of the ride. The wall, against which the person lies, is inclined at the angle theta = 18degree with respect to the vertical. Model the person as a particle that is a distance d = 21 ft from the spin axis A B and let the coefficient of static friction between the person and the wall be mu s = 0.8. Determine the maximum value of omega c before the person slides up the wall and out of the ride.

Explanation / Answer

m=mass of person;N=normal contact force;

(momega^2_cd cos heta+mgsin heta = N) ...eq1

(mgcos heta =momega^2_cdsin heta +mu _sN) ...eq2

solving by substituting N from eq1 into eq2

(omega ^2_c=[g(cos heta-mu _sson heta)]/[d(mu _scos heta+sin heta)])

hence, taking g=9.8 m/s^2 ; d=3.9624 meter; u=0.1 cos14=0.97;sin14=0.242

(omegapprox2.62745 radians/second)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.