VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
12th Edition
ISBN: 9781260265521
Author: BEER
Publisher: MCG
bartleby

Videos

Question
Book Icon
Chapter 16, Problem 16.161RP
To determine

(a)

The force in the patellar tendon.

Expert Solution
Check Mark

Explanation of Solution

Given information:

Cylinder weight with hole = 16 lb

Cylinder weight without hole = 15 lb

Angular velocity = 5 rad/s

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS, Chapter 16, Problem 16.161RP , additional homework tip  1

Schematic of cylinder 1

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS, Chapter 16, Problem 16.161RP , additional homework tip  2

Figure A

Unit vectors along X and Y directions be i and j and along angular direction k

Angular acceleration of cylinder be α In vector form it is α=αk

Let mass centre of the cylinder be G at a distance b from centre A.

Let point P coordinates with point C be (x,y). So, its position vector will become rP/C=xi+yj

Let point G coordinates with point C be (0,(rb)). So, its position vector will become rG/C=(rb)j

Let point A coordinates with point C be (0,r). So, its position vector will become rA/C=rj

Point C acceleration,

aC=(aC)x+(aC)y

Here, (aC)x = Point C acceleration in horizontal direction

(aC)y = Point C acceleration in vertical direction

Here, (aC)x = 0 since cylinder rolls on surface that is curved.

Hence,

aC=0+(aC)y

aC=(aC)y

At any location on the cylinder, acceleration is

aP=aC+(α×rP/C)ω2rP/C

aP=(aC)y+(αk×(xi+yj))ω2(xi+yj)

aP=(aC)y+αx(k×i)+αy(k×j)ω2xiω2yj

aP=(aC)y+αx(j)+αy(i)+ω2x+ω2y

aP=(aC)y+αx+αy+ω2x+ω2y

Point G acceleration,

aG=aC+(rG/C×α)ω2rG/C

aG=(aC)y+((rb)j×αk)ω2(rb)j

=(aC)y+((rb)α)(j×k)ω2(rb)j

=(aC)y+((rb)α)(i)ω2(rb)j

aG=(aC)y+(rb)α+(rb)ω2 .............(Equation A)

Point A acceleration,

aA=aC+(rA/C×α)ω2rA/C

aA=(aC)y+((r)j×αk)ω2(r)j

=(aC)y+((r)α)(j×k)ω2(r)j

=(aC)y+(rα)(i)ω2(r)j

aA=(aC)y+rα+rω2

Substitute (aC)y=aArαrω2 in equation A

aG=aArαrω2+(rb)α+(rb)ω2

=aArαrω2+rαbα+rω2bω2 ....(Equation B)

=aA+bα+bω2

Point A acceleration,

aA=(aA)x+(aA)y

aA=rα+(aA)y

Substitute the above in equation B,

aG=rα+(aA)y+bα+bω2

=(rb)α+(aA)y+bω2 ......(Equation C)

Point A velocity,

vA=(rω)

Point A acceleration vertical component,

(aA)y=(vA2R+r)

(aA)y=((rω)2R+r)

(aA)y=(r2ω2R+r)

Substitute the above in equation C,

aG=(rb)α+(aA)y+bω2

=(rb)α+(r2ω2R+r)+bω2

=(rb)α+ω2(r2R+rb)

Effective force,

maG=m[(rb)α+ω2(r2R+rb)]

=m(rb)α+mω2(r2R+rb)

Cylinder free body diagram

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS, Chapter 16, Problem 16.161RP , additional homework tip  3

Figure B

Moment at point C from above figure,

0=[mω2(r2R+rb)][0]+Iα+[(rb)][m(rb)α]

Iα+[m(rb)2α]=0 .... (Equation D)

(I+m(rb)2)α=0

From equation D, angular acceleration is zero.

Conclusion:

The cylinder angular acceleration is zero.

To determine

(b)

Components of the reaction force between the cylinder and the ground.

Expert Solution
Check Mark

Explanation of Solution

Given information:

Cylinder weight with hole = 16 lb

Cylinder weight without hole = 15 lb

Angular velocity = 5 rad/s

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS, Chapter 16, Problem 16.161RP , additional homework tip  4

Forces horizontal component from figure B,

Cx=m(rb)α

Here, α=0

Hence, Cx=m(rb)0

Cx=0

Forces vertical component from figure B,

Cy=WWg(r2R+rb)ω2 ...........(Equation E)

Cylinder as combination of hole and solid is shown below

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS, Chapter 16, Problem 16.161RP , additional homework tip  5

Solid cylinder area,

A1=Πr2

Solid centre of gravity in vertical direction,

y1¯=0

Hole area,

A2=Πr216

Hole centre of gravity in vertical direction,

y2¯=23r

Equilibrium equation,

bA=Ay1¯

b(A1+A2)=A1y1¯+A2y2¯

b(Πr2Πr216)=(Πr2)0+(Πr216)(23r)

b(15Πr216)=Πr324

b=245r

Substituting in equation E we get,

Cy={15lb15lb32.2ft/s2((12in.)2(36in.)+(12in.)245(12in.))(1ft12in.)(5rad/s)2}

Cy=12.61lb

Conclusion:

The horizontal component reaction is zero and vertical reaction is Cy=12.61lb.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Continuity equation A y x dx D T معادلة الاستمرارية Ly X Q/Prove that ди хе + ♥+ ㅇ? he me ze ོ༞“༠ ?
Q Derive (continuity equation)? I want to derive clear mathematics.
motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine: a) the minimum permissible diameter for aluminum shafts (1) and (2) b) the minimum permissible diameter for steel shaft (3). c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).

Chapter 16 Solutions

VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS

Ch. 16.1 - Prob. 16.4PCh. 16.1 - A uniform rod BC of mass 4 kg is connected to a...Ch. 16.1 - A 2000-kg truck is being used to lift a 400-kg...Ch. 16.1 - The support bracket shown is used to transport a...Ch. 16.1 - Prob. 16.8PCh. 16.1 - A 20-kg cabinet is mounted on casters that allow...Ch. 16.1 - Prob. 16.10PCh. 16.1 - A completely filled barrel and its contents have a...Ch. 16.1 - A 40-kg vase has a 200-mm-diameter base and is...Ch. 16.1 - Prob. 16.13PCh. 16.1 - Bars AB and BE, each with a mass of 4 kg, are...Ch. 16.1 - At the instant shown, the tensions in the vertical...Ch. 16.1 - Three bars, each of mass 3 kg, are welded together...Ch. 16.1 - Prob. 16.17PCh. 16.1 - Prob. 16.18PCh. 16.1 - Prob. 16.19PCh. 16.1 - The coefficients of friction between the 30-lb...Ch. 16.1 - Prob. 16.21PCh. 16.1 - Prob. 16.22PCh. 16.1 - Prob. 16.23PCh. 16.1 - Prob. 16.24PCh. 16.1 - Prob. 16.25PCh. 16.1 - Prob. 16.26PCh. 16.1 - Prob. 16.27PCh. 16.1 - Solve Prob. 16.27, assuming that the initial...Ch. 16.1 - The 100-mm-radius brake drum is attached to a...Ch. 16.1 - The 180-mm-radius disk is at rest when it is...Ch. 16.1 - Solve Prob. 16.30, assuming that the direction of...Ch. 16.1 - In order to determine the mass moment of inertia...Ch. 16.1 - Prob. 16.33PCh. 16.1 - Each of the double pulleys shown has a mass moment...Ch. 16.1 - Prob. 16.35PCh. 16.1 - Solve Prob. 16.35, assuming that the couple M is...Ch. 16.1 - Gear A weighs 1 lb and has a radius of gyration of...Ch. 16.1 - The 25-lb double pulley shown is at rest and in...Ch. 16.1 - A belt of negligible mass passes between cylinders...Ch. 16.1 - Solve Prob. 16.39 for P=2.00lb .Ch. 16.1 - Disk A has a mass of 6 kg and an initial angular...Ch. 16.1 - Prob. 16.42PCh. 16.1 - Prob. 16.43PCh. 16.1 - Disk B is at rest when it is brought into contact...Ch. 16.1 - Cylinder A has an initial angular velocity of 720...Ch. 16.1 - Prob. 16.46PCh. 16.1 - Prob. 16.47PCh. 16.1 - Prob. 16.48PCh. 16.1 - (a) In Prob. 16.48, determine the point of the rod...Ch. 16.1 - A force P with a magnitude of 3 N is applied to a...Ch. 16.1 - Prob. 16.51PCh. 16.1 - A 250-lb satellite has a radius of gyration of 24...Ch. 16.1 - Prob. 16.53PCh. 16.1 - A uniform semicircular plate with a mass of 6 kg...Ch. 16.1 - Prob. 16.55PCh. 16.1 - Prob. 16.56PCh. 16.1 - The 12-lb uniform disk shown has a radius of r=3.2...Ch. 16.1 - Prob. 16.58PCh. 16.1 - Prob. 16.59PCh. 16.1 - Prob. 16.60PCh. 16.1 - The 400-lb crate shown is lowered by means of two...Ch. 16.1 - Prob. 16.62PCh. 16.1 - Prob. 16.63PCh. 16.1 - A beam AB with a mass m and of uniform...Ch. 16.1 - Prob. 16.65PCh. 16.1 - Prob. 16.66PCh. 16.1 - Prob. 16.67PCh. 16.1 - Prob. 16.68PCh. 16.1 - Prob. 16.69PCh. 16.1 - Solve Prob. 16.69, assuming that the sphere is...Ch. 16.1 - A bowler projects an 8-in.-diameter ball weighing...Ch. 16.1 - Solve Prob. 16.71, assuming that the bowler...Ch. 16.1 - A uniform sphere of radius r and mass m is placed...Ch. 16.1 - A sphere of radius r and mass m has a linear...Ch. 16.2 - A cord is attached to a spool when a force P is...Ch. 16.2 - A cord is attached to a spool when a force P is...Ch. 16.2 - A front-wheel-drive car starts from rest and...Ch. 16.2 - A front-wheel-drive car starts from rest and...Ch. 16.2 - Prob. 16.F5PCh. 16.2 - Prob. 16.F6PCh. 16.2 - Prob. 16.F7PCh. 16.2 - Prob. 16.F8PCh. 16.2 - Show that the couple I of Fig. 16.15 can be...Ch. 16.2 - Prob. 16.76PCh. 16.2 - Prob. 16.77PCh. 16.2 - A uniform slender rod of length L=36 in. and...Ch. 16.2 - Prob. 16.79PCh. 16.2 - Prob. 16.80PCh. 16.2 - Prob. 16.81PCh. 16.2 - Prob. 16.82PCh. 16.2 - Prob. 16.83PCh. 16.2 - A uniform rod of length L and mass m is supported...Ch. 16.2 - Prob. 16.85PCh. 16.2 - Prob. 16.86PCh. 16.2 - Prob. 16.87PCh. 16.2 - Two identical 4-lb slender rods AB and BC are...Ch. 16.2 - Prob. 16.89PCh. 16.2 - Prob. 16.90PCh. 16.2 - Prob. 16.91PCh. 16.2 - Prob. 16.92PCh. 16.2 - Prob. 16.93PCh. 16.2 - Prob. 16.94PCh. 16.2 - A homogeneous sphere S, a uniform cylinder C, and...Ch. 16.2 - Prob. 16.96PCh. 16.2 - Prob. 16.97PCh. 16.2 - Prob. 16.98PCh. 16.2 - Prob. 16.99PCh. 16.2 - A drum of 80-mm radius is attached to a disk of...Ch. 16.2 - Prob. 16.101PCh. 16.2 - Prob. 16.102PCh. 16.2 - Prob. 16.103PCh. 16.2 - Prob. 16.104PCh. 16.2 - Prob. 16.105PCh. 16.2 - A 12-in.-radius cylinder of weight 16 lb rests on...Ch. 16.2 - A 12-in.-radius cylinder of weight 16 lb rests on...Ch. 16.2 - Gear C has a mass of 5 kg and a centroidal radius...Ch. 16.2 - Two uniform disks A and B, each with a mass of 2...Ch. 16.2 - Prob. 16.110PCh. 16.2 - Prob. 16.111PCh. 16.2 - Prob. 16.112PCh. 16.2 - Prob. 16.113PCh. 16.2 - A small clamp of mass mBis attached at B to a hoop...Ch. 16.2 - Prob. 16.115PCh. 16.2 - A 4-lb bar is attached to a 10-lb uniform cylinder...Ch. 16.2 - The uniform rod AB with a mass m and a length of...Ch. 16.2 - Prob. 16.118PCh. 16.2 - A 40-lb ladder rests against a wall when the...Ch. 16.2 - A beam AB of length L and mass m is supported by...Ch. 16.2 - End A of the 6-kg uniform rod AB rests on the...Ch. 16.2 - Prob. 16.122PCh. 16.2 - Prob. 16.123PCh. 16.2 - The 4-kg uniform rod ABD is attached to the crank...Ch. 16.2 - The 3-lb uniform rod BD is connected to crank AB...Ch. 16.2 - Prob. 16.126PCh. 16.2 - Prob. 16.127PCh. 16.2 - Prob. 16.128PCh. 16.2 - Prob. 16.129PCh. 16.2 - Prob. 16.130PCh. 16.2 - Prob. 16.131PCh. 16.2 - Prob. 16.132PCh. 16.2 - Prob. 16.133PCh. 16.2 - Prob. 16.134PCh. 16.2 - Prob. 16.135PCh. 16.2 - The 6-kg rod BC connects a 10-kg disk centered at...Ch. 16.2 - In the engine system shown, l=250 mm and b=100 mm....Ch. 16.2 - Solve Prob. 16.137 when =90 .Ch. 16.2 - The 4-lb uniform slender rod AB, the 8-lb uniform...Ch. 16.2 - Prob. 16.140PCh. 16.2 - Two rotating rods in the vertical plane are...Ch. 16.2 - Prob. 16.142PCh. 16.2 - Prob. 16.143PCh. 16.2 - Prob. 16.144PCh. 16.2 - Prob. 16.145PCh. 16.2 - Prob. 16.146PCh. 16.2 - Prob. 16.147PCh. 16.2 - Prob. 16.148PCh. 16.2 - Prob. 16.149PCh. 16.2 - Prob. 16.150PCh. 16.2 - (a) Determine the magnitude and the location of...Ch. 16.2 - Draw the shear and bending-moment diagrams for the...Ch. 16 - A cyclist is riding a bicycle at a speed of 20 mph...Ch. 16 - Prob. 16.154RPCh. 16 - The total mass of the Baja car and driver,...Ch. 16 - Prob. 16.156RPCh. 16 - Prob. 16.157RPCh. 16 - Prob. 16.158RPCh. 16 - A bar of mass m=5 kg is held as shown between four...Ch. 16 - A uniform plate of mass m is suspended in each of...Ch. 16 - Prob. 16.161RPCh. 16 - Two 3-kg uniform bars are connected to form the...Ch. 16 - Prob. 16.163RPCh. 16 - Prob. 16.164RP
Knowledge Booster
Background pattern image
Mechanical Engineering
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
BEARINGS BASICS and Bearing Life for Mechanical Design in 10 Minutes!; Author: Less Boring Lectures;https://www.youtube.com/watch?v=aU4CVZo3wgk;License: Standard Youtube License