VECTOR MECHANIC
VECTOR MECHANIC
12th Edition
ISBN: 9781264095032
Author: BEER
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 8, Problem 8.136RP

(a)

To determine

Find the magnitude of the force P requires to move the cabinet to the right if all casters are locked.

(a)

Expert Solution
Check Mark

Answer to Problem 8.136RP

The magnitude of the force P required is 36lb()_.

Explanation of Solution

Given information:

The weight of the cabinet is W=120lb.

The coefficient of static friction between the floor and the caster is μs=0.30.

The height at which the force P is acting from the bottom is h=32in..

Calculation:

Show the free-body diagram of the cabinet as in Figure 1.

VECTOR MECHANIC, Chapter 8, Problem 8.136RP

For tipping; NA=FA=0.

Find the tipping force P by taking moment about point B.

MB=0120(12)Ptip(32)=0Ptip=45lb

Find the friction force (FA)  at point A using the relation.

FA=μsNA

Find the friction force (FB) at point B using the relation.

FB=μsNB

Resolve the vertical component of forces.

Fy=0NA+NB120=0NA+NB=120

Resolve the horizontal component of forces.

Fx=0PFAFB=0PμsNAμsNB=0Pμs(NA+NB)=0

Substitute 0.30 for μs and 120 lb for (NA+NB).

P0.30×120=0P=36lb()

Here,

P=36lb<Ptip=45lb

Therefore, the magnitude of the force P required is 36lb()_.

(b)

To determine

Find the magnitude of the force P requires to move the cabinet to the right if the casters at B are locked and at A is free.

(b)

Expert Solution
Check Mark

Answer to Problem 8.136RP

The magnitude of the required force P is 30lb()_.

Explanation of Solution

Given information:

The weight of the cabinet is W=120lb.

The coefficient of static friction between the floor and the caster is μs=0.30.

The height at which the force P is acting from the bottom is h=32in..

Calculation:

Refer to Figure 1;

Find the friction force (FA)  at point A using the relation.

FA=0

Find the friction force (FB) at point B using the relation.

FB=μsNB

Resolve the horizontal component of forces.

Fx=0P0FB=0PμsNB=0NB=Pμs

Find the magnitude of the force P by taking moment about point A.

MA=0120(12)P(32)+NB(24)=01,44032P+24Pμs=0

Substitute 0.30 for μs.

1,44032P+24×P0.30=032P+80P=1,440P=30lb

Here,

P=30lb<Ptip=45lb

Therefore, the magnitude of the force P required is 30lb()_.

(c)

To determine

Find the magnitude of the force P requires to move the cabinet to the right if the casters at A are locked and at B is free.

(c)

Expert Solution
Check Mark

Answer to Problem 8.136RP

The magnitude of the force P required is 12.86lb()_.

Explanation of Solution

Given information:

The weight of the cabinet is W=120lb.

The coefficient of static friction between the floor and the caster is μs=0.30.

The height at which the force P is acting from the bottom is h=32in..

Calculation:

Refer to Figure 1;

Find the friction force (FA)  at point A using the relation.

FA=μsNA

Find the friction force (FB) at point B using the relation.

FB=0

Resolve the horizontal component of forces.

Fx=0P0FA=0PμsNA=0NA=Pμs

Find the magnitude of the force P by taking moment about point A.

MB=0120(12)P(32)NA(24)=01,44032P24Pμs=0

Substitute 0.30 for μs.

1,44032P24×P0.30=032P+80P=1,440P=12.86lb

Here,

P=12.86lb<Ptip=45lb

Therefore, the magnitude of the force P required is 12.86lb()_.

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Chapter 8 Solutions

VECTOR MECHANIC

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