VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS
11th Edition
ISBN: 9781259633133
Author: BEER
Publisher: MCG
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Textbook Question
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Chapter 8.1, Problem 8.37P

A 1.2-m plank with a mass of 3 kg rests on two joists. Knowing that the coefficient of static friction between the plank and the joists is 0.30, determine the magnitude of the horizontal force required to move the plank when (a) a = 750 mm, (b) a = 900 mm.

Chapter 8.1, Problem 8.37P, A 1.2-m plank with a mass of 3 kg rests on two joists. Knowing that the coefficient of static

Fig. P8.37

(a)

Expert Solution
Check Mark
To determine

Find the magnitude of the horizontal force required to move the plank.

Answer to Problem 8.37P

The magnitude of the horizontal force required to move the plank is 2.94N_.

Explanation of Solution

Given information:

The length of the plank is L=1.2m.

The mass of each plank is m=3kg.

The coefficient of static friction between the plank and the joists is μs=0.30.

The distance between the points A and C in the plank is a=750mm.

Calculation:

Find the friction force (F) using the relation.

F=μsN

Show the free-body diagram of the member AB is vertical plane as in Figure 1.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 8.1, Problem 8.37P , additional homework tip  1

Take moment about point A.

MA=0NC(a)W(L2)=0NC=WL2a (1)

Resolve the vertical component of forces.

Fy=0NA+NCW=0NA+WL2aW=0NA=W2a(2aL) (2)

Show the free-body diagram of the member AB is horizontal plane as in Figure 2.

VECTOR MECH...,STAT.+DYNA.(LL)-W/ACCESS, Chapter 8.1, Problem 8.37P , additional homework tip  2

Take moment about point A.

MA=0FC(a)P(L)=0FC=PLa (3)

Resolve the vertical component of forces.

Fz=0FAP+FC=0FAP+PLa=0FA=Pa(La) (4)

Find the weight of the plank (W) using the relation.

W=mg

Here, the acceleration due to gravity is g.

Consider the acceleration due to gravity is g=9.81m/s2.

Substitute 3 kg for m and 9.81m/s2 for g.

W=3×9.81=29.43N

Substitute 29.43 N for W, 1.2 m for L, and 750 mm for a in Equation (1).

NC=29.43×1.22×750mm×1m1,000mm=23.544N

Substitute 29.43 N for W, 1.2 m for L, and 750 mm for a in Equation (2).

NA=29.432×750mm×1m1,000mm(2×750mm×1m1,000mm1.2)=5.886N

Substitute 1.2 m for L, and 750 mm for a in Equation (3).

FC=P×1.2750mm×1m1,000mm=1.6P

Substitute 1.2 m for L, and 750 mm for a in Equation (4).

FA=P750mm×1m1,000mm(1.2750mm×1m1,000mm)=0.6P

At point A, the plank to slip;

Find the horizontal force P using the relation.

FA=μsNA

Substitute 0.6P for FA, 0.30 for μs, and 5.886 N for NA.

0.6P=0.30×5.886P=2.94N

At point C, the plank to slip;

Find the horizontal force P using the relation.

FC=μsNC

Substitute 1.6P for FC, 0.30 for μs, and 23.544 N for NC.

1.6P=0.30×23.544P=4.41N

The smallest value of P will slip the plank. The plank will slip at A.

Therefore, the magnitude of the horizontal force required is 2.94N_.

(b)

Expert Solution
Check Mark
To determine

Find the magnitude of the horizontal force required to move the plank.

Answer to Problem 8.37P

The magnitude of the horizontal force required is 4.41N_.

Explanation of Solution

Given information:

The length of the plank is L=1.2m.

The mass of each plank is m=3kg.

The coefficient of static friction between the plank and the joists is μs=0.30.

The distance between the points A and C in the plank is a=900mm.

Calculation:

Refer part (a) for calculation.

Substitute 29.43 N for W, 1.2 m for L, and 900 mm for a in Equation (1).

NC=29.43×1.22×900mm×1m1,000mm=19.62N

Substitute 29.43 N for W, 1.2 m for L, and 900 mm for a in Equation (2).

NA=29.432×900mm×1m1,000mm(2×900mm×1m1,000mm1.2)=9.81N

Substitute 1.2 m for L, and 900 mm for a in Equation (3).

FC=P×1.2900mm×1m1,000mm=1.3333P

Substitute 1.2 m for L, and 900 mm for a in Equation (4).

FA=P900mm×1m1,000mm(1.2900mm×1m1,000mm)=0.3333P

At point A, the plank to slip;

Find the horizontal force P using the relation.

FA=μsNA

Substitute 0.3333P for FA, 0.30 for μs, and 9.81 N for NA.

0.3333P=0.30×9.81P=8.83N

At point C, the plank to slip;

Find the horizontal force P using the relation.

FC=μsNC

Substitute 1.3333P for FC, 0.30 for μs, and 19.62 N for NC.

1.3333P=0.30×19.62P=4.41N

The smallest value of P will slip the plank. The plank will slip at C.

Therefore, the magnitude of the horizontal force required is 4.41N_.

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Chapter 8 Solutions

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

Ch. 8.1 - The 10-kg block is attached to link AB and rests...Ch. 8.1 - Considering only values of less than 90,...Ch. 8.1 - Prob. 8.9PCh. 8.1 - Prob. 8.10PCh. 8.1 - The 50-lb block A and the 25-lb block B are...Ch. 8.1 - The 50-lb block A and the 25-lb block B are...Ch. 8.1 - Three 4-kg packages A, B, and C are placed on a...Ch. 8.1 - Prob. 8.14PCh. 8.1 - A uniform crate with a mass of 30 kg must be moved...Ch. 8.1 - A worker slowly moves a 50-kg crate to the left...Ch. 8.1 - Prob. 8.17PCh. 8.1 - Prob. 8.18PCh. 8.1 - Prob. 8.19PCh. 8.1 - Prob. 8.20PCh. 8.1 - Prob. 8.21PCh. 8.1 - Prob. 8.22PCh. 8.1 - Prob. 8.23PCh. 8.1 - Prob. 8.24PCh. 8.1 - Prob. 8.25PCh. 8.1 - Prob. 8.26PCh. 8.1 - The press shown is used to emboss a small seal at...Ch. 8.1 - The machine base shown has a mass of 75 kg and is...Ch. 8.1 - Prob. 8.29PCh. 8.1 - Prob. 8.30PCh. 8.1 - Prob. 8.31PCh. 8.1 - Prob. 8.32PCh. 8.1 - Prob. 8.33PCh. 8.1 - Prob. 8.34PCh. 8.1 - Prob. 8.35PCh. 8.1 - Prob. 8.36PCh. 8.1 - A 1.2-m plank with a mass of 3 kg rests on two...Ch. 8.1 - Two identical uniform boards, each with a weight...Ch. 8.1 - Prob. 8.39PCh. 8.1 - Prob. 8.40PCh. 8.1 - A 10-ft beam, weighing 1200 lb, is to be moved to...Ch. 8.1 - (a) Show that the beam of Prob. 8.41 cannot be...Ch. 8.1 - Two 8-kg blocks A and B resting on shelves are...Ch. 8.1 - Prob. 8.44PCh. 8.1 - Prob. 8.45PCh. 8.1 - Two slender rods of negligible weight are...Ch. 8.1 - Two slender rods of negligible weight are...Ch. 8.2 - The machine part ABC is supported by a...Ch. 8.2 - Prob. 8.49PCh. 8.2 - Prob. 8.50PCh. 8.2 - Prob. 8.51PCh. 8.2 - Prob. 8.52PCh. 8.2 - Solve Prob. 8.52 assuming that the end of the beam...Ch. 8.2 - Prob. 8.54PCh. 8.2 - Prob. 8.55PCh. 8.2 - Block A supports a pipe column and rests as shown...Ch. 8.2 - Prob. 8.57PCh. 8.2 - Prob. 8.58PCh. 8.2 - Prob. 8.59PCh. 8.2 - Prob. 8.60PCh. 8.2 - Prob. 8.61PCh. 8.2 - Prob. 8.62PCh. 8.2 - Prob. 8.63PCh. 8.2 - A 15 wedge is forced under a 50-kg pipe as shown....Ch. 8.2 - A 15 wedge is forced under a 50-kg pipe as shown....Ch. 8.2 - Prob. 8.66PCh. 8.2 - Prob. 8.67PCh. 8.2 - Prob. 8.68PCh. 8.2 - Prob. 8.69PCh. 8.2 - Prob. 8.70PCh. 8.2 - Prob. 8.71PCh. 8.2 - The position of the automobile jack shown is...Ch. 8.2 - Prob. 8.73PCh. 8.2 - Prob. 8.74PCh. 8.2 - Prob. 8.75PCh. 8.2 - Prob. 8.76PCh. 8.3 - A lever of negligible weight is loosely fitted...Ch. 8.3 - Prob. 8.78PCh. 8.3 - 8.79 and 8.80 The double pulley shown is attached...Ch. 8.3 - Prob. 8.80PCh. 8.3 - 8.81 and 8.82 The double pulley shown is attached...Ch. 8.3 - Prob. 8.82PCh. 8.3 - Prob. 8.83PCh. 8.3 - The block and tackle shown are used to lower a...Ch. 8.3 - Prob. 8.85PCh. 8.3 - Prob. 8.86PCh. 8.3 - Prob. 8.87PCh. 8.3 - 8.87 and 8.88 A lever AB of negligible weight is...Ch. 8.3 - Prob. 8.89PCh. 8.3 - Prob. 8.90PCh. 8.3 - Prob. 8.91PCh. 8.3 - 8.92 Knowing that a couple of magnitude 30 N·m is...Ch. 8.3 - Prob. 8.93PCh. 8.3 - Prob. 8.94PCh. 8.3 - Prob. 8.95PCh. 8.3 - Prob. 8.96PCh. 8.3 - Solve Prob. 8.93 assuming that the normal force...Ch. 8.3 - Prob. 8.98PCh. 8.3 - Prob. 8.99PCh. 8.3 - A 900-kg machine base is rolled along a concrete...Ch. 8.3 - Prob. 8.101PCh. 8.3 - Prob. 8.102PCh. 8.4 - A rope having a weight per unit length of 0.4...Ch. 8.4 - Prob. 8.104PCh. 8.4 - Two cylinders are connected by a rope that passes...Ch. 8.4 - Prob. 8.106PCh. 8.4 - Prob. 8.107PCh. 8.4 - Prob. 8.108PCh. 8.4 - A band belt is used to control the speed of a...Ch. 8.4 - Prob. 8.110PCh. 8.4 - The setup shown is used to measure the output of a...Ch. 8.4 - A flat belt is used to transmit a couple from drum...Ch. 8.4 - Prob. 8.113PCh. 8.4 - 8.114 Solve Prob. 8.113 assuming that the belt is...Ch. 8.4 - The speed of the brake drum shown is controlled by...Ch. 8.4 - The speed of the brake drum shown is controlled by...Ch. 8.4 - Prob. 8.117PCh. 8.4 - Bucket A and block C are connected by a cable that...Ch. 8.4 - Prob. 8.119PCh. 8.4 - Prob. 8.120PCh. 8.4 - 8.121 and 8.123 A cable is placed around three...Ch. 8.4 - Prob. 8.122PCh. 8.4 - Prob. 8.123PCh. 8.4 - Prob. 8.124PCh. 8.4 - Prob. 8.125PCh. 8.4 - Prob. 8.126PCh. 8.4 - Prob. 8.127PCh. 8.4 - The 10-lb bar AE is suspended by a cable that...Ch. 8.4 - Prob. 8.129PCh. 8.4 - Prove that Eqs. (8.13) and (8.14) are valid for...Ch. 8.4 - Complete the derivation of Eq. (8.15), which...Ch. 8.4 - Prob. 8.132PCh. 8.4 - Solve Prob. 8.113 assuming that the flat belt and...Ch. 8 - 8.134 and 8.135 The coefficients of friction are S...Ch. 8 - Prob. 8.135RPCh. 8 - Prob. 8.136RPCh. 8 - A slender rod with a length of L is lodged between...Ch. 8 - The hydraulic cylinder shown exerts a force of 3...Ch. 8 - Prob. 8.139RPCh. 8 - Bar AB is attached to collars that can slide on...Ch. 8 - Two 10 wedges of negligible weight are used to...Ch. 8 - A 10 wedge is used to split a section of a log....Ch. 8 - Prob. 8.143RPCh. 8 - A lever of negligible weight is loosely fitted...Ch. 8 - In the pivoted motor mount shown, the weight W of...
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