Explanation Given information: The coefficient of static friction ( μ s ) between the wall and the platform is 0.2. The mass of the rider ( m ) is 80 kg. Calculation: Write the general equation of normal acceleration in the curved motion: a = v 2 ρ (1) Here, v is the velocity and ρ is the radius. Sketch the geometry of carnival and rider as shown in Figure (1). Refer Figure (1). Find the equation of radius ( ρ ) . ρ = 5 + 1.5 cos 70 ° = 5.513 m Minimum and Maximum speeds occur if slipping is impending. Sketch the free body diagram and kinetic diagram of the rider moves down as shown in Figure (2). Refer Figure (2): Write the general equation of ( f ) . f = μ s N Find the equation of normal force ( N ) on the rider. Apply Newton’s law of equation along y -axis. Σ F y = 0 N cos 70 ° + f sin 70 ° − m g = 0 Substitute μ s N for N . N cos 70 ° + μ s N sin 70 ° − m g = 0 N ( μ s sin 70 ° + cos 70 ° ) = m g N = m g μ s sin 70 ° + cos 70 ° Here, m is the mass of the rider and g is the acceleration due to gravity. Substitute 80 kg for m , 9.81 m/s 2 for g , and 0.2 for μ s . N = ( 80 ) ( 9.81 ) ( 0.2 ) sin 70 ° + cos 70 ° = 1 , 480.9 N Finding the minimum speed so that rider does not slide down the wall Apply Newton’s law of equation along n -axis. Σ F n = m a n N sin 70 ° − f cos 70 ° = m a n Substitute μ s N for f and v min 2 ρ for a n . N sin 70 ° − μ s N cos 70 ° = m ( v min 2 ρ ) v min 2 = N ρ ( sin 70 ° − μ s cos 70 ° ) m Substitute 1 , 480.9 N for N , 5.513 m for ρ , 0.2 for μ s and 80 kg for m . v min 2 = ( 1 , 480.9 ) ( 5.513 ) ( sin 70 ° − 0

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Clutches, Brakes, Couplings, and Flywheels

The clutch is described as a machine element used to connect or disconnect two shafts together to transmit torque or power. The clutch works on the principles of friction. The clutch is commonly used in automobiles to transfer power from the driving shaf…

Videos

Question

Chapter 12.1, Problem 12.59P

To determine

Find the range of values of the constant speed v0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.1, Problem 12.58P

Chapter 12.1, Problem 12.60P

Students have asked these similar questions

A 40-kg packing crate is pulled by a rope as shown. The coefficient of static friction between the crate and the floor is 0.35. If α =40°,determine (a) the magnitude of the force P required to move the crate, (b) whether the crate will slide or tip.

A 12° wedge is used to spread a split ring. The coefficient of static friction between the wedge and the ring is 0.30. Knowing that a force P with a magnitude of 120 N was required to insert the wedge, determine the magnitude of the forces exerted on the ring by the wedge after insertion.

2. A 10-1b block B rests as shown on a 20-1b bracket A. The coefficients of friction are µg= 0.30 between block B and bracket A, and there is no friction in the pulley or between the bracket and the horizontal surface. (a) Determine the maximum weight of block C if block B is not to slide on bracket A. A B. C

Chapter 12 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 12.1 - A 1000-lb boulder B is resting on a 200-lb...Ch. 12.1 - Marble A is placed in a hollow tube, and the tube...Ch. 12.1 - The two systems shown start from rest. On the...Ch. 12.1 - Blocks A and B are released from rest in the...Ch. 12.1 - People sit on a Ferris wheel at points A, B, C,...Ch. 12.1 - Crate A is gently placed with zero initial...Ch. 12.1 - Two blocks weighing WA and WB are at rest on a...Ch. 12.1 - Objects A, B, and C have masses mA, mB, and mC,...Ch. 12.1 - Prob. 12.4FBP Ch. 12.1 - Blocks A and B have masses mA and mB,...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find the range of values of the constant speed v 0 .

Solution Summary: The author calculates the range of values of the constant speed v_0 and the equation of normal acceleration in the curved motion.

Concept explainers

Videos

Find the range of values of the constant speed v0.

Want to see the full answer?

Chapter 12 Solutions