Explanation Given information: The diameter of the cable is 0.4 in. The weight of the elevator is 800 lb. The length of the elevator is 150 ft = 1 , 800 in . below the drum. The elevator is descending at the constant rate of 2 ft/sec = 24 in ./sec when the drum suddenly stops. Young’s modulus or modulus of elasticity of the steel cable is E s t = 29 ( 10 3 ) ksi = 29 ( 10 6 ) psi . The permissible stress in the bar is σ Y = 50 ksi = 50,000 psi . The acceleration due to gravity is g = 32.2 ft/sec 2 = ( 32.2 × 12 ) in ./sec 2 . Explanation: Area of the bar: Determine the area of the cable ( A ) using the formula. A = π d 2 4 (1) Here, d is diameter of the cable. Stiffness: Determine the stiffness of the spring when the load is applied on top of the post using the equation. k = A E L (2) Here, E is Young’s modulus of the steel cable and L is the length of the cable. Conservation of energy: Express the equation for conservation of energy as follows: U e = U i 1 2 m v 2 + W Δ max = 1 2 k Δ max 2 (3) Here, m is mass of the elevator, v is constant rate, W is the weight of the elevator, and Δ max is the maximum displacement. Maximum dynamic force developed in the cable ( P max ) : Determine the maximum dynamic force developed in the cable using the equation. P max = k Δ max (4) Maximum stress in the cable ( σ max ) : Determine the maximum stress developed in the cable using the formula. σ max = P max A (5) Mass of the cable: Determine the mass of the cable ( m ) using the relation. m = W g (6) Show the calculation of values as follows: Conclusion: Substitute 0.4 in. for d in Equation (1). A = π × 0.4 2 4 = 0

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Pressure Vessels

The term pressure vessel refers to a closed container that contains gas or liquid at a different pressure than environment pressure. The pressure vessels have a wide scale of applications in our day-to-day lives and other industrial places. Some common e…

Videos

Question

Chapter 14.4, Problem 14.47P

To determine

The maximum stress developed in the cable.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 14.46P

Chapter 14.4, Problem 14.48P

Students have asked these similar questions

This course 7E Hide blocks The pipe assembly shown is subjected to a force F = 5000 N. The pipe has an inner diameter of 20 mm and an outer diameter of 30 mm. It is made of steel with Sy = 250 MPa. Determine the safety factor at point A using the maximum shear stress theory. 200 mm 150 mm 100 mm 200 mm 116 B/s A ENG I6 B/s

The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 kW of power to the shaft while it is turning at 50 rev/s. If gears A, B, and C remove 3 kW, 4 kW, and 5 kW, respectively, determine the absolute maximum shear stress in the shaft. 5 kW 25 mm 12 kW 3 kW 4 kW A B D ΕF. ווו(

The load D has a mass of 220 kg and is being hoisted by the motor M with constant velocity. Determine the resultant normal force acting on the cross section at point E in the beam. Determine the resultant shear force acting on the cross section at point E in the beam. (Express answer to three significant figures and include appropriate units.)

Chapter 14 Solutions

Mechanics of Materials (10th Edition)

Ch. 14.2 - A material is subjected to a general state of...Ch. 14.2 - The strain-energy density for plane stress must be...Ch. 14.2 - The A-36 steel bar consists of two segments, one...Ch. 14.2 - Determine the torsional strain energy in the A992...Ch. 14.2 - Using bolts of the same material and...Ch. 14.2 - If P = 60 kN, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - Determine the torsional strain energy in the A992...Ch. 14.2 - Determine the torsional strain energy in the A-36...Ch. 14.2 - The shaft assembly is fixed at C. The hollow...

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.

The maximum stress developed in the cable.

Solution Summary: The author determines the maximum stress developed in the cable using the formula.

Concept explainers

Videos

The maximum stress developed in the cable.

Want to see the full answer?

Chapter 14 Solutions