Vector Mechanics For Engineers
Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977305
Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.
Publisher: Mcgraw-hill Education,
bartleby

Videos

Textbook Question
Book Icon
Chapter 12.1, Problem 12.31P

A 10-Ib block B rests as shown on a 20-1b bracket A. The coefficients of friction are μ s = 0.30 and μ k = 0.25 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. (b) If the weight of block C is 10 percent larger than the answer found in a, determine the accelerations of A, B, and C.

  Chapter 12.1, Problem 12.31P, A 10-Ib block B rests as shown on a 20-1b bracket A. The coefficients of friction are s=0.30 and

Expert Solution
Check Mark
To determine

(a)

Maximum weight of block C if block B is not to slide on bracket A.

Answer to Problem 12.31P

Maximum weight of block C is WC=2.43lbs.

Explanation of Solution

Given:

Vector Mechanics For Engineers, Chapter 12.1, Problem 12.31P , additional homework tip  1

μs=0.30

μk=0.25

WA=20lb

WB=10lb

Concept used:

Kinematics :

Let xA and xB be the horizontal coordinates of A and B measured from a fixed vertical line to the left of A and B.

Let yC be the distance that block C is below the pulley.

Note that yC increases when C moves downward.

Vector Mechanics For Engineers, Chapter 12.1, Problem 12.31P , additional homework tip  2

The cable length is fixed.

L=(xBxA)+(xPxA)+yC+constant

Differentiating and noting that xP=0

vB2vA+vC=0

2aA+aB+aC=0 … (1)

Here. aA and aB are positive to the right and aC is positive downward.

Kinetics :

Let T be the tension in the cable and FAB be the friction force between blocks A and B.

The free body diagrams are shown here:

Bracket A:

Vector Mechanics For Engineers, Chapter 12.1, Problem 12.31P , additional homework tip  3

Block B:

Vector Mechanics For Engineers, Chapter 12.1, Problem 12.31P , additional homework tip  4

Block C:

Vector Mechanics For Engineers, Chapter 12.1, Problem 12.31P , additional homework tip  5

Bracket A:

+Fx=max :

2TFAB=WAgaA … (2)

Block B:

+Fx=max

FABT=WBgaB … (3)

+Fy=may :

NABWB=0

NAB=WB

Block C:

+Fy=may :

mCT=WCgaC … (4)

Adding Eqs. (2). (3) and (4) and transposing.

WAgaA+WBgaB+WCgaC=WC … (5)

Subtracting Eq. (4) from Eq. (3) and transposing.

WBgaBWCgaC=FABWC … (6)

No slip between A and B.

aB=aA

From Eq. (1).

aA=aB=aC=a

From Eq. (5).

a=WCgWA+WB+WC

For impeding slip.

FAB=μsNAB=μsWB

Substituting into Eq. (6).

(WBWC)WA+WB+WC=μsWBWC

Solving for WC.

WC=μsWB(WA+WB)WA+2WBμsWB

WC=(0.30)(10)(20+10)20+2(10)(0.30)(10)

WC=2.43lb

Expert Solution
Check Mark
To determine

(b)

Accelerations of A, B, and C, if the weight of block C is 10 percent larger than the result of part a.

Answer to Problem 12.31P

Accelerations of A. B and C:

aA=3.14ft/s2

aB=0.881ft/s2

aC=5.41ft/s2

Explanation of Solution

Given:

WC increased by 10%.

WB=2.6757lb (increased by 10%)

Since slip is occurring.

FAB=μkNAB=μkWB

Eq. (6) becomes.

WBgaBWCgaC=FABWC

Or:

10aB2.6757aC=[(0.25)(10)2.6757](32.2) … (7)

With given data. Eq. (5) becomes

20aC+10aB+2.6757aC=(2.6757)(32.2) … (8)

Solving Eqs. (1). (7). and (8) gives

aA=3.144ft/s2,aB=0.881ft/s2,aC=5.407ft/s2

So,

aA=3.14ft/s2

And,

aB=0.881ft/s2

And

aC=5.41ft/s2

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
SITUATION 2: A packing crate of mass 40 kg is pulled by a rope as shown. Knowing that the coefficient of static friction between the crate and the floor is 0.35, answer the following questions: 4. If α = 40°, determine the magnitude of the force P required to move the crate, in N. (ANSWER: 139) 5. If the crate must be moved to the left along the floor without tipping, determine the largest allowable value of α in degrees. (ANSWER: 58)
Blocks A and B have masses of 10 kg and 20 kg respectively. The coefficient of static friction between A and B is 0.20, between B and C is 0.10 and at D, 0.15. Block B impends to slide up the 30°- incline plane. (A) Draw the FBD of block A (B) Draw the FBD of block B (C) What is the weight of the hanging block that will maintain static equilibrium? Note: Use T, and T, for tension on the tight side and slack side of the cord respectively. A 20' w/
Blocks A and B have masses of 10 kg and 20 kg respectively. The coefficient of static friction between A and B is 0.20, between B and C is 0.10 and at D, 0.15. Block B impends to slide up the 30°- incline plane. (A) Draw the FBD of block A (B) Draw the FBD of block B (C) What is the weight of the hanging block that will maintain static equilibrium? Note: Use T, and T, for tension on the tight side and slack side of the cord respectively. 20

Chapter 12 Solutions

Vector Mechanics For Engineers

Ch. 12.1 - A pilot of mass m flies a jet in a half-vertical...Ch. 12.1 - Wires AC and BC are attached to a sphere that...Ch. 12.1 - A collar of mass m is attached to a spring and...Ch. 12.1 - Four pins slide in four separate slots cut in a...Ch. 12.1 - At the instant shown, the length of the boom AB is...Ch. 12.1 - Prob. 12.F11PCh. 12.1 - Pin B has a mass m and slides along the slot in...Ch. 12.1 - Prob. 12.1PCh. 12.1 - Prob. 12.2PCh. 12.1 - Prob. 12.3PCh. 12.1 - A spring scale A and a lever scale B having equal...Ch. 12.1 - A loading car is at rest on a track forming an...Ch. 12.1 - A 0.5-oz model rocket is launched vertically from...Ch. 12.1 - Determine the maximum theoretical speed that may...Ch. 12.1 - A tugboat pulls a small barge through a harbor....Ch. 12.1 - If an automobile's braking distance from 108 km/h...Ch. 12.1 - A 4-kg package is released from rest at point A...Ch. 12.1 - The coefficients of friction the load and the...Ch. 12.1 - A light train made up of two cars is traveling at...Ch. 12.1 - The two blocks shown are originally at rest....Ch. 12.1 - The two blocks shown are originally at rest....Ch. 12.1 - Each of the systems shown is initially at rest....Ch. 12.1 - Boxes A and B are at rest on a conveyor belt that...Ch. 12.1 - A 5000-1b truck is being used to lift a 1000-1b...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - Block A has a mass of 40 kg, and block B has a...Ch. 12.1 - Prob. 12.20PCh. 12.1 - Prob. 12.21PCh. 12.1 - To unload a bound stack of plywood from a truck;...Ch. 12.1 - To transport a series of bundles of shingles A to...Ch. 12.1 - Prob. 12.24PCh. 12.1 - Determine the maximum theoretical speed that a...Ch. 12.1 - Prob. 12.26PCh. 12.1 - A spring AB of constant k is attached to a support...Ch. 12.1 - Prob. 12.28PCh. 12.1 - Prob. 12.29PCh. 12.1 - An athlete pulls handle A to the left with a...Ch. 12.1 - A 10-Ib block B rests as shown on a 20-1b bracket...Ch. 12.1 - Prob. 12.32PCh. 12.1 - Knowing that k=0.30 , determine the acceleration...Ch. 12.1 - The 30-Ib block B is supported by the 55-Ib block...Ch. 12.1 - Block B of mass 10 kg rests as shown on the upper...Ch. 12.1 - Knowing that the swings of an amusement park ride...Ch. 12.1 - During a hammer thrower's practice swings, the...Ch. 12.1 - Prob. 12.38PCh. 12.1 - A single wire ACB passes through a ring at C...Ch. 12.1 - Two wires AC and BC are tied at C to a sphere that...Ch. 12.1 - Prob. 12.41PCh. 12.1 - Prob. 12.42PCh. 12.1 - As part of an outdoor display, a 5-kg model C of...Ch. 12.1 - A 130-ib wrecking ball B is attached to a...Ch. 12.1 - During a high-speed chase, a 2400-Ib sports car...Ch. 12.1 - An airline pilot climbs to a new flight level...Ch. 12.1 - The roller-coaster track shown is contained in a...Ch. 12.1 - A spherical-cap governor is fixed to a vertical...Ch. 12.1 - A series of small packages, each with a mass of...Ch. 12.1 - A 55-kg pilot flies a jet trainer in a half...Ch. 12.1 - A carnival ride is designed to allow the general...Ch. 12.1 - Prob. 12.52PCh. 12.1 - Prob. 12.53PCh. 12.1 - Prob. 12.54PCh. 12.1 - A 3-kg block is at rest relative to a parabolic...Ch. 12.1 - A polisher is started so that the fleece along the...Ch. 12.1 - Prob. 12.57PCh. 12.1 - The carnival ride from Prob. 12.51 is modified so...Ch. 12.1 - Prob. 12.59PCh. 12.1 - Prob. 12.60PCh. 12.1 - Prob. 12.61PCh. 12.1 - Prob. 12.62PCh. 12.1 - Prob. 12.63PCh. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - A small 250-g collar C can slide on a semicircular...Ch. 12.1 - An advanced spatial disorientation trainer allows...Ch. 12.1 - Prob. 12.67PCh. 12.1 - The 3-kg collar B slides on the frictionless arm...Ch. 12.1 - A 0.5-kg block B slides without friction inside a...Ch. 12.1 - Pin B weighs 4 oz and is free to slide in a...Ch. 12.1 - The parasailing system shown uses a winch to let...Ch. 12.1 - A 700-kg horse A lifts a 50-kg hay bale B as...Ch. 12.1 - Slider C has a weight of 0.5 Ib and may move in a...Ch. 12.2 - A particle of mass m is projected from point A...Ch. 12.2 - For the particle of Prob. 12.74, show (a) that the...Ch. 12.2 - Prob. 12.76PCh. 12.2 - For the particle of Prob. 12.76, determine the...Ch. 12.2 - Determine the mass of the earth knowing that the...Ch. 12.2 - Prob. 12.79PCh. 12.2 - Prob. 12.80PCh. 12.2 - Prob. 12.81PCh. 12.2 - The orbit of the planet Venus is nearly circular...Ch. 12.2 - A satellite is placed into a circular orbit about...Ch. 12.2 - The periodic time (see Prob. 12.83) of an earth...Ch. 12.2 - Prob. 12.85PCh. 12.2 - Prob. 12.86PCh. 12.2 - Prob. 12.87PCh. 12.2 - Prob. 12.88PCh. 12.2 - Prob. 12.89PCh. 12.2 - A 1 -kg collar can slide on a horizontal rod that...Ch. 12.2 - A 1-Ib ball A and a 2-Ib ball B are mounted on a...Ch. 12.2 - Two 2.6-Ib collars A and B can slide without...Ch. 12.2 - A small ball swings in a horizontal circle at the...Ch. 12.3 - A uniform crate C with mass m is being transported...Ch. 12.3 - A uniform crate C with mass m is being transported...Ch. 12.3 - A particle of mass m is projected from point A...Ch. 12.3 - A particle of mass m describes the logarithmic...Ch. 12.3 - Prob. 12.96PCh. 12.3 - Prob. 12.97PCh. 12.3 - Prob. 12.98PCh. 12.3 - It was observed that during the Galileo...Ch. 12.3 - Prob. 12.100PCh. 12.3 - Prob. 12.101PCh. 12.3 - Prob. 12.102PCh. 12.3 - Prob. 12.103PCh. 12.3 - A satellite describes a circular orbit at an...Ch. 12.3 - A space probe is to be placed in a circular orbit...Ch. 12.3 - Prob. 12.106PCh. 12.3 - Prob. 12.107PCh. 12.3 - Prob. 12.108PCh. 12.3 - Prob. 12.109PCh. 12.3 - Prob. 12.110PCh. 12.3 - Prob. 12.111PCh. 12.3 - Prob. 12.112PCh. 12.3 - Prob. 12.113PCh. 12.3 - Prob. 12.114PCh. 12.3 - Prob. 12.115PCh. 12.3 - Prob. 12.116PCh. 12.3 - Prob. 12.117PCh. 12.3 - A satellite describes an elliptic orbit about a...Ch. 12.3 - Prob. 12.119PCh. 12.3 - Prob. 12.120PCh. 12.3 - Show that the angular momentum per unit mass h of...Ch. 12 - In the braking test of a sports car, its velocity...Ch. 12 - A bucket is attached to a rope of length L=1.2 m...Ch. 12 - Block A has a weight of 40 Ib, and block B has a...Ch. 12 - Prob. 12.125RPCh. 12 - Prob. 12.126RPCh. 12 - The parasailing system shown uses a winch to pull...Ch. 12 - A robot arm moves in the vertical plane so that...Ch. 12 - Telemetry technology is used to quantify kinematic...Ch. 12 - Prob. 12.130RPCh. 12 - Prob. 12.131RPCh. 12 - Prob. 12.132RPCh. 12 - Disk A rotates in a horizontal plane about a...
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
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
How to balance a see saw using moments example problem; Author: Engineer4Free;https://www.youtube.com/watch?v=d7tX37j-iHU;License: Standard Youtube License