Explanation Given information: The density ρ b of bronze is 8 , 650 kg / m 3 . The density ρ p of fiber reinforced polycarbonate is 1 , 250 kg / m 3 . Calculation: Sketch the cross section of molded flat belt pulley as shown in figure 1. Express the mass ( m ) of cylindrical ring as shown below: m = ρ V (1) Here, ρ is density and V is volume of cylindrical ring. Substitute ρ t for ρ and π 4 ( d 2 2 − d 1 2 ) in Equation (1). m = [ ( ρ b t b ) π 4 ( d 2 2 − d 1 2 ) b + ( ρ p t p ) π 4 ( d 2 2 − d 1 2 ) p + t i ( d 2 2 − d 1 2 ) i + t 0 ( d 2 2 − d 1 2 ) o ] (2) Here, ( d 2 2 − d 1 2 ) b is diameter of bronze section, ( d 2 2 − d 1 2 ) b is diameter of fiber reinforced polycarbonate section, t p is thickness of fiber reinforced polycarbonate section, t b is thickness of bronze section, t ( d 2 2 − d 1 2 ) i is polycarbonate inner section, and t ( d 2 2 − d 1 2 ) o is polycarbonate outer section Refer to Figure 9.28, “Mass moment of inertia of common geometric shapes” in the textbook. Express the moment of inertia with respect to axis A A ′ as shown below: I A A ′ = 1 2 m 2 ( d 2 2 ) 2 − 1 2 m 1 ( d 1 2 ) 2 = 1 8 [ ( ρ t × π 4 d 2 2 ) d 2 2 − ( ρ t × π 4 d 1 2 ) d 1 2 ] = 1 8 [ ( ρ t × π 4 d 2 4 ) − ( ρ t × π 4 d 1 4 ) ] = 1 8 ( π 4 ρ t ) ( d 2 4 − d 1 4 ) = 1 8 ( π 4 ρ t ) ( d 2 2 − d 1 2 ) ( d 2 2 + d 1 2 ) I A A ′ = 1 8 m ( d 1 2 + d 2 2 ) Consider the roller as three concentric rings and working from the bronze outward. Substitute 8 , 650 kg / m 3 for ρ b , 1 , 250 kg / m 3 for ρ p , 17.5 mm for t b , 17.5 mm for t P , ( 11 − 5 ) mm for ( d 2 2 − d 1 2 ) b , ( 17 − 11 ) mm for ( d 2 2 − d 1 2 ) p , 2 mm for t i , 9.5 mm for t o , ( 22 − 17 ) mm for ( d 2 2 − d 1 2 ) b , and ( 28 − 22 ) mm for ( d 2 2 − d 1 2 ) p in Equation (2). Convert mm to m. 17.5 mm = 17.5 mm ( 1 m 1 , 000 mm ) = 0.0175 m Similarly convert the all values. m = π 4 { 8 , 650 × 0

11th Edition

ISBN: 9781259633133

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

Videos

Question

Chapter 9.5, Problem 9.128P

To determine

Find the mass moment of inertia and radius of gyration of molded flat-belt pulley with respect to axis AA′.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.5, Problem 9.127P

Chapter 9.5, Problem 9.129P

Students have asked these similar questions

The pickup truck weighs 3220 Ib and reaches a speed of 30 mi/hr from rest in a distance of 200 ft up the 10-percent incline with constant acceleration. Calculate the normal force under each pair of wheels and the friction force under the rear driving wheels. The effective coefficient of friction between the tires and the road is known to be at least 0.8.

1. The figure shows a car jack to support 400kg (W=400kg). In the drawing, the angle (0) varies between 15 and 70 °. The links are machined from AISI 1020 hot-rolled steel bars with a minimum yield strength of 380MPa. Each link consists of two bars, one on each side of the central bearings. The bars are 300mm in length (/) and 25 mm in width (w). The pinned ends have the buckling constant (C) of 1.4 for out of plane buckling. The design factor (nd) is 2.5. (1) Find the thickness (t) of the bars and the factor of safety (n). (2) Check if the bar is an Euler beam. D

(Read image)

Chapter 9 Solutions

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS

Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - Prob. 9.3P Ch. 9.1 - Prob. 9.4P Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.7P Ch. 9.1 - Prob. 9.8P Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P

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 mass moment of inertia and radius of gyration of molded flat-belt pulley with respect to axis A A ′ .

Solution Summary: The author calculates the mass moment of inertia and radius of gyration of the molded flat-belt pulley with respect to axis AAprime .

Concept explainers

Videos

Find the mass moment of inertia and radius of gyration of molded flat-belt pulley with respect to axis AA′.

Want to see the full answer?

Chapter 9 Solutions