Explanation Given: The mass of the passengers is 80 kg . The chair exerts on 50 kg . The angle θ is 30 ° Write the equation of normal acceleration a n = υ 2 r (I). Here, centripetal acceleration is a , the velocity is υ and the radius is r . Draw the free body diagram 80 kg passenger shown in Figure (1). Refer Figure (1) and calculate the radius of curvature. r = ( 4 + 6 sin θ ) m Refer Figure (1) and write the equation of motion along normal direction to calculate the normal force. ∑ F n = m a n (II). Here, acts in the positive normal direction is ∑ F y mass is m and acceleration in the normal direction is a n . Refer Figure (1) calculate the , in the normal direction. ∑ F n = T sin 30 ° (III). Refer Figure (1) and write the equation of motion in b direction. ∑ F b = 0 Here, component of force in b direction is ∑ F b . Refer Figure (1) resolve the forces in b direction. ∑ F b = T cos 30 ° − m ( 9.81 m/s 2 ) (IV). Draw the free body diagram 50 kg passenger shown in Figure (2). Refer Figure (2) and write the equation of motion along normal direction to calculate the normal force. ∑ F n = m a n (V). Here, acts in the positive normal direction is ∑ F y mass is m and acceleration in the normal direction is a n . Refer Figure (2) calculate the normal force in the normal direction. ∑ F n = F n (VI). Refer Figure (2) and write the equation of motion in b direction. ∑ F b = 0 Here, component of force in b direction is ∑ F b . Refer Figure (2) resolve the forces in b direction. ∑ F b = F b − m ( 9.81 m/s 2 ) (VII). Refer Figure (2) and write the equation of motion along tangential direction to calculate the tangential acceleration. ∑ F t = 0 Here, acts in the direction of motion or tangential direction is ∑ F t mass is m and acceleration in the tangential direction is a t . Refer Figure (2) resolve the forces in the tangential direction. ∑ F t = F t (VIII). Conclusion: Substitute ( 4 + 6 sin 30 ° ) m for r in Equation (I). a n = υ 2 r = υ 2 ( 4 + 6 sin 30 ° ) Substitute υ 2 ( 4 + 6 sin 30 ° ) for a n and 80 kg for m in Equation (II). ∑ F n = m a n = 80 ( υ 2 ( 4 + 6 sin 30 ° ) ) Substitute 80 ( υ 2 ( 4 + 6 sin 30 ° ) ) for ∑ F n in Equation (III)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 13.5, Problem 65P

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The constant speed of the passengers and components of force in the n , t and b directions during the motion of the system.

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Chapter 13.5, Problem 64P

Chapter 13.5, Problem 66P

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The constant speed of the passengers and components of force in the n , t and b directions during the motion of the system.

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The constant speed of the passengers and components of force in the n , t and b directions during the motion of the system.

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