A statics problem uses Moment of a force. Given force (F) = 659.0 lb; moment arm (d) = 11.8000 ft, determine the moment (M) in lb·ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except M is given, so isolate M symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F \times d$$

2. Step 2 — Rearrange the relation so that M stands alone on the left-hand side.

3. Step 3

   $$List the givens: force (F) = 659.0 lb, moment arm (d) = 11.8000 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$M = 7776\ \text{lb·ft}$$

6. Step 6 — Check: returning M = 7,776 lb·ft to

   $$M = F \times d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 15,552 — kept a factor of two that cancels in the correct rearrangement.
• 3,888 — dropped that same factor in the other direction.
• 8,554 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Moments (Couples)

a cantilevered sign arm Given force (F) = 3,153 N; perpendicular distance (d) = 3.9000 m, determine the moment (M) in N\cdot m.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force about a point.
• Everything except M is given, so isolate M symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• A force acting at a perpendicular distance d produces a moment.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for M:

   $$M = M = F d$$

3. Step 3

   $$List the givens: force (F) = 3,153 N, perpendicular distance (d) = 3.9000 m$$

4. Step 4 — Substitute the given values:

   $$M = M = 3153 3.9000$$

5. Step 5 — Evaluate:

   $$M = 12295\ \text{N\cdot m}$$

6. Step 6 — Check: returning M = 12,295 N\cdot m to

   $$M = F d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 24,590 — kept a factor of two that cancels in the correct rearrangement.
• 6,147 — dropped that same factor in the other direction.
• 13,524 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics (Moments)

Two tugboat lines apply a couple to rotate a barge. Given couple force (F) = 242.0 lbf; perpendicular distance (d) = 2.0000 ft, determine the couple moment (M) in lbf-ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a couple.
• Everything except M is given, so isolate M symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• A couple made of two equal, opposite, parallel forces produces a pure moment used to analyze moments (couples) on rigid bodies.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for M:

   $$M = F d$$

3. Step 3

   $$List the givens: couple force (F) = 242.0 lbf, perpendicular distance (d) = 2.0000 ft$$

4. Step 4 — Substitute the given values:

   $$M = 242.0 2.0000$$

5. Step 5 — Evaluate:

   $$M = 484.0\ \text{lbf-ft}$$

6. Step 6 — Check: returning M = 484.0 lbf-ft to

   $$M = F d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 968.0 — kept a factor of two that cancels in the correct rearrangement.
• 242.0 — dropped that same factor in the other direction.
• 532.4 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics: Moments (Couples)

A statics problem uses Moment of a force. Given moment arm (d) = 9.9000 ft; moment (M) = 2,481 lb·ft, determine the force (F) in lb.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except F is given, so isolate F symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F \times d$$

2. Step 2 — Rearrange the relation so that F stands alone on the left-hand side.

3. Step 3 — List the givens: moment arm (d) = 9.9000 ft, moment (M) = 2,481 lb·ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$F = 250.6\ \text{lb}$$

6. Step 6 — Check: returning F = 250.6 lb to

   $$M = F \times d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 501.2 — kept a factor of two that cancels in the correct rearrangement.
• 125.3 — dropped that same factor in the other direction.
• 275.7 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Moments (Couples)

a wrench applied to an anchor nut Given moment (M) = 3,106 N\cdot m; perpendicular distance (d) = 3.2000 m, determine the force (F) in N.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force about a point.
• Everything except F is given, so isolate F symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• A force acting at a perpendicular distance d produces a moment.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for F:

   $$F = F = \dfrac{M}{d}$$

3. Step 3

   $$List the givens: moment (M) = 3,106 N\cdot m, perpendicular distance (d) = 3.2000 m$$

4. Step 4 — Substitute the given values:

   $$F = F = \dfrac{3106}{3.2000}$$

5. Step 5 — Evaluate:

   $$F = 970.7\ \text{N}$$

6. Step 6 — Check: returning F = 970.7 N to

   $$M = F d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,941 — kept a factor of two that cancels in the correct rearrangement.
• 485.4 — dropped that same factor in the other direction.
• 1,068 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics (Moments)

A steering wheel resists a couple applied by the driver's hands. Given perpendicular distance (d) = 3.3000 ft; couple moment (M) = 928.5 lbf-ft, determine the couple force (F) in lbf.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a couple.
• Everything except F is given, so isolate F symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• A couple made of two equal, opposite, parallel forces produces a pure moment used to analyze moments (couples) on rigid bodies.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for F:

   $$F = \dfrac{M}{d}$$

3. Step 3

   $$List the givens: perpendicular distance (d) = 3.3000 ft, couple moment (M) = 928.5 lbf-ft$$

4. Step 4 — Substitute the given values:

   $$F = \dfrac{928.5}{3.3000}$$

5. Step 5 — Evaluate:

   $$F = 281.4\ \text{lbf}$$

6. Step 6 — Check: returning F = 281.4 lbf to

   $$M = F d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 562.7 — kept a factor of two that cancels in the correct rearrangement.
• 140.7 — dropped that same factor in the other direction.
• 309.5 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics: Moments (Couples)

A statics problem uses Moment of a force. Given force (F) = 760.0 lb; moment (M) = 6,179 lb·ft, determine the moment arm (d) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except d is given, so isolate d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F \times d$$

2. Step 2 — Rearrange the relation so that d stands alone on the left-hand side.

3. Step 3 — List the givens: force (F) = 760.0 lb, moment (M) = 6,179 lb·ft.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$d = 8.1303\ \text{ft}$$

6. Step 6 — Check: returning d = 8.1303 ft to

   $$M = F \times d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 16.2605 — kept a factor of two that cancels in the correct rearrangement.
• 4.0651 — dropped that same factor in the other direction.
• 8.9433 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Moments (Couples)

a bracket bolted to a column flange Given moment (M) = 795.1 N\cdot m; force (F) = 1,909 N, determine the perpendicular distance (d) in m.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force about a point.
• Everything except d is given, so isolate d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• A force acting at a perpendicular distance d produces a moment.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for d:

   $$d = d = \dfrac{M}{F}$$

3. Step 3

   $$List the givens: moment (M) = 795.1 N\cdot m, force (F) = 1,909 N$$

4. Step 4 — Substitute the given values:

   $$d = d = \dfrac{795.1}{1909}$$

5. Step 5 — Evaluate:

   $$d = 0.4166\ \text{m}$$

6. Step 6 — Check: returning d = 0.4166 m to

   $$M = F d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 0.8332 — kept a factor of two that cancels in the correct rearrangement.
• 0.2083 — dropped that same factor in the other direction.
• 0.4583 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics (Moments)

A wrench applies a couple to loosen a rusted bolt. Given couple force (F) = 246.0 lbf; couple moment (M) = 2,477 lbf-ft, determine the perpendicular distance (d) in ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a couple.
• Everything except d is given, so isolate d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• A couple made of two equal, opposite, parallel forces produces a pure moment used to analyze moments (couples) on rigid bodies.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F d$$

2. Step 2 — Rearrange symbolically for d:

   $$d = \dfrac{M}{F}$$

3. Step 3

   $$List the givens: couple force (F) = 246.0 lbf, couple moment (M) = 2,477 lbf-ft$$

4. Step 4 — Substitute the given values:

   $$d = \dfrac{2477}{246.0}$$

5. Step 5 — Evaluate:

   $$d = 10.0671\ \text{ft}$$

6. Step 6 — Check: returning d = 10.0671 ft to

   $$M = F d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 20.1341 — kept a factor of two that cancels in the correct rearrangement.
• 5.0335 — dropped that same factor in the other direction.
• 11.0738 — rounded an intermediate value before the final step.

Reference: FE Handbook — Statics: Moments (Couples)

A statics problem uses Moment of a force. Given force (F) = 1,480 lb; moment arm (d) = 14.5000 ft, determine the moment (M) in lb·ft.

Start with the thinking

• The governing relation printed in this handbook section is Moment of a force.
• Everything except M is given, so isolate M symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Statics items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$M = F \times d$$

2. Step 2 — Rearrange the relation so that M stands alone on the left-hand side.

3. Step 3

   $$List the givens: force (F) = 1,480 lb, moment arm (d) = 14.5000 ft$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$M = 21460\ \text{lb·ft}$$

6. Step 6 — Check: returning M = 21,460 lb·ft to

   $$M = F \times d$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 42,920 — kept a factor of two that cancels in the correct rearrangement.
• 10,730 — dropped that same factor in the other direction.
• 23,606 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Statics → Moments (Couples)