HW #04 - Third Homework Assignment PDF

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Third Homework Assignment...

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1/24/2019

Score:

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45/45

Points

100

%

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Problem 03.070 - A couple formed by two forces on a rectangular plate - DEPENDENT MULTI-PART PROBLEM ASSIGN ALL PARTS

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Two forces are applied as shown to the corners B and D of a rectangular plate. Given: P =80-N. 

  References Section Break

Problem 03.070 - A couple formed by two forces on a rectangular plate DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS

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1.

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Award: 4 out of 4.00 points

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Problem 03.070.a - Moment of the couple formed by two forces

Determine the moment of the couple formed by the two forces by resolving each force into horizontal and vertical components and adding the moments of the two resulting couples. (You must provide an answer before moving to the next part.)

M=

7.33

N•m (Counterclockwise)



Hints Hint #1

References Worksheet

Problem 03.070.a - Moment of the couple formed by two forces



Problem 03.070.a - Moment of the couple formed by two forces Determine the moment of the couple formed by the two forces by resolving each force into horizontal and vertical components and adding the moments of the two resulting couples. (You must provide an answer before moving to the next part.)

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M=

7.33 ± 2% N•m (Counterclockwise)

 Explanation:

Resolve the forces into components. S = P sin 50° T = P cos 50° M = T(0.5 m) – S(0.3 m) 

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Award: 3 out of 3.00 points

Problem 03.070.b - Perpendicular distance between the two forces that cause an equivalent couple

Use the result obtained to determine the perpendicular distance between lines BE and DF.

The perpendicular distance is

91.6

mm.



Hints Hint #1

References Worksheet

Problem 03.070.b Perpendicular distance between the two forces that cause an equivalent couple



Problem 03.070.b - Perpendicular distance between the two forces that cause an equivalent couple Use the result obtained to determine the perpendicular distance between lines BE and DF.

The perpendicular distance is

91.6 ± 2% mm.

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 Explanation:

M = Fd M = Pd



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Award: 3 out of 3.00 points

Problem 03.070.b - Perpendicular distance between the two forces that cause an equivalent couple

Use the result obtained to determine the perpendicular distance between lines BE and DF.

The perpendicular distance is

91.6

mm.



Hints Hint #1

References Worksheet

Problem 03.070.b Perpendicular distance between the two forces that cause an equivalent couple



Problem 03.070.b - Perpendicular distance between the two forces that cause an equivalent couple Use the result obtained to determine the perpendicular distance between lines BE and DF.

The perpendicular distance is

91.6 ± 2% mm.

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 Explanation:

M = Fd M = Pd



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Problem 03.072 - Couple and force-couple systems - DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A multiple-drilling machine is used to simultaneously drill six holes in the steel plate shown. Each drill exerts a clockwise couple of magnitude 38 lb·in. on the plate. 

  References Section Break

Problem 03.072 - Couple and force-couple systems DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS

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Award: 4 out of 4.00 points

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Problem 03.072.a - Equivalent force-couple

Determine an equivalent couple formed by the smallest possible forces acting at A and C. The smallest possible force acting at A and C is

19

lb.

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Hints Hint #1

References Worksheet

Problem 03.072.a Equivalent force-couple

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Problem 03.072.a - Equivalent force-couple Determine an equivalent couple formed by the smallest possible forces acting at A and C. The smallest possible force acting at A and C is

19 ± 2% lb.

 Explanation:

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Equivalent couple must have moment

The smallest forces at A and C are perpendicular to AC.

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Award: 3 out of 3.00 points

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Problem 03.072.b - Equivalent force-couple

Determine an equivalent couple formed by the smallest possible forces acting at A and D. The smallest possible force acting at A and D is

15.2

lb.

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Hints Hint #1

References Worksheet

Problem 03.072.b Equivalent force-couple



Problem 03.072.b - Equivalent force-couple Determine an equivalent couple formed by the smallest possible forces acting at A and D. The smallest possible force acting at A and D is

15.2 ± 2% lb.

 Explanation:

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Equivalent couple must have moment

The smallest force at A and D is perpendicular to AD.



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6.

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Award: 3 out of 3.00 points

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Problem 03.072.c - Equivalent force-couple

Determine an equivalent couple formed by the smallest possible forces acting on the plate. The smallest force acting on the plate is

11.4

lb.

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Hints Hint #1 Hint #2

References Worksheet

Problem 03.072.c Equivalent force-couple

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Problem 03.072.c - Equivalent force-couple Determine an equivalent couple formed by the smallest possible forces acting on the plate. The smallest force acting on the plate is

11.4 ± 2% lb.

 Explanation: http://ezto.mheducation.com/hm.tpx?todo=C15PrintView&wid=13252710666208115&role=student&sid=13252710676255489

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Equivalent couple must have moment

The smallest possible forces are applied at B and C, are perpendicular to BC, and are the farthest apart.

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Problem 03.081 - An equivalent force-couple system on a bent plate - DEPENDENT MULTI-PART PROBLEM ASSIGN ALL PARTS

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A 570-N force P is applied to a bent plate as shown.

References Section Break

Problem 03.081 - An equivalent force-couple system on a bent plate DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL PARTS

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7.

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Award: 5 out of 5.00 points

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Problem 03.081.a - An equivalent force-couple system

Determine an equivalent force-couple system at B. (You must provide an answer before moving to the next part.) The equivalent force-couple system at B is FB =

570

N⦪ 30°

MB =

98.2

N·m (Clockwise)



Hints Hint #1 Hint #2

References Worksheet

Problem 03.081.a - An equivalent force-couple system



Problem 03.081.a - An equivalent force-couple system http://ezto.mheducation.com/hm.tpx?todo=C15PrintView&wid=13252710666208115&role=student&sid=13252710676255489

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Determine an equivalent force-couple system at B. (You must provide an answer before moving to the next part.) The equivalent force-couple system at B is FB = MB =

570 ± 2% N⦪ 30° 98.2 ± 2% N·m (Clockwise)

 Explanation: MB = rB × F where F = (P sin 30°)i – (P cos 30°)j rB = 0.3i –0.175j The equivalent force-couple system at B is FB = 570 N⦪ 30° MB = −98.2k N·m = 98.2 N·m 

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Award: 5 out of 5.00 points

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Problem 03.081.b - An equivalent force-couple system

Determine an equivalent system formed by a vertical force at A and a force at B.

Force at A =

785.7

Force at B =

1310.7

N↑ N

77.4

°



Hints Hint #1 Hint #2

References Worksheet

Problem 03.081.b - An equivalent force-couple system

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Problem 03.081.b - An equivalent force-couple system Determine an equivalent system formed by a vertical force at A and a force at B. http://ezto.mheducation.com/hm.tpx?todo=C15PrintView&wid=13252710666208115&role=student&sid=13252710676255489

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Force at A =

785.7 ± 2% N ↑

Force at B =

1310.7 ± 2% N

77.4 ± 2% °

 Explanation: Equivalence requires

F = A + B or B = F − A



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9.

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Award: 10 out of 10.00 points

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Problem 03.087 - Replacement of a force system with multiple forces by an equivalent system with a single force

The shearing forces exerted on the cross section of a steel channel can be represented by a 900-N vertical force and two 276-N horizontal forces P as shown. Replace this force and couple with a single force F applied at point C, and determine the distance x from C to line BD. (Point C is defined as the shear center of the section.)

The magnitude of the force is The distance x from C to the line BD is

900

N↓. .0552

m.



Hints Hint #1

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Hint #2

References Worksheet

Problem 03.087 Replacement of a force system with multiple forces by an equivalent system with a single force



Problem 03.087 - Replacement of a force system with multiple forces by an equivalent system with a single force The shearing forces exerted on the cross section of a steel channel can be represented by a 900-N vertical force and two 276-N horizontal forces P as shown. Replace this force and couple with a single force F applied at point C, and determine the distance x from C to line BD. (Point C is defined as the shear center of the section.)

The magnitude of the force is

900 ± 2% N↓.

The distance x from C to the line BD is

0.055 ± 2% m.

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 Explanation:

MH = P(0.18 m) = F(x)



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Problem 03.090 - Multiple forces are applied to a plate

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A rectangular plate is acted upon by the force and couple shown. This system is to be replaced with a single equivalent force. The force acting at point B is FB = 48 N. 

References Section Break

Problem 03.090 - Multiple forces are applied to a plate

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10.

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Award: 5 out of 5.00 points

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Problem 03.090.a - Equivalent single-force system

For α = 40°, determine the magnitude and the location of the line of action of the equivalent force. The magnitude of the equivalent force is

48

N and the line of action F' intersects line AB at

.144

m to the left of B.



Hints Hint #1 Hint #2

References Worksheet

Problem 03.090.a Equivalent single-force system



Problem 03.090.a - Equivalent single-force system For α = 40°, determine the magnitude and the location of the line of action of the equivalent force. The magnitude of the equivalent force is

48 ± 2% N and the line of action F' intersects line AB at

0.144 ± 2% m to the left of B.

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Explanation:

The given force-couple system (F, M) at B is F = 48 N ↓ and M = ∑MB.

The single equivalent force F' is equal to F. Further to equivalence,

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