A block sliding on a frictionless surface is analyzed with equations of motion. Given mass (m) = 36.8000 slug; acceleration (a) = 31.2000 ft/s^2, determine the net force (F) in lbf.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for F:

   $$F = m a$$

3. Step 3

   $$List the givens: mass (m) = 36.8000 slug, acceleration (a) = 31.2000 ft/s^2$$

4. Step 4 — Substitute the given values:

   $$F = 36.8000 31.2000$$

5. Step 5 — Evaluate:

   $$F = 1148\ \text{lbf}$$

6. Step 6 — Check: returning F = 1,148 lbf to

   $$\sum F = m a$$

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

Why the other options are there

• 2,296 — kept a factor of two that cancels in the correct rearrangement.
• 574.1 — dropped that same factor in the other direction.
• 1,263 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

A cart towed by a cable is solved using the equations of motion. Given acceleration (a) = 7.5000 ft/s^2; net force (F) = 356.0 lbf, determine the mass (m) in slug.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for m:

   $$m = \dfrac{F}{a}$$

3. Step 3

   $$List the givens: acceleration (a) = 7.5000 ft/s^2, net force (F) = 356.0 lbf$$

4. Step 4 — Substitute the given values:

   $$m = \dfrac{356.0}{7.5000}$$

5. Step 5 — Evaluate:

   $$m = 47.4667\ \text{slug}$$

6. Step 6 — Check: returning m = 47.4667 slug to

   $$\sum F = m a$$

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

Why the other options are there

• 94.9333 — kept a factor of two that cancels in the correct rearrangement.
• 23.7333 — dropped that same factor in the other direction.
• 52.2133 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

An elevator cab's equations of motion determine cable tension during acceleration. Given mass (m) = 26.5000 slug; net force (F) = 727.0 lbf, determine the acceleration (a) in ft/s^2.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• Everything except a is given, so isolate a 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for a:

   $$a = \dfrac{F}{m}$$

3. Step 3

   $$List the givens: mass (m) = 26.5000 slug, net force (F) = 727.0 lbf$$

4. Step 4 — Substitute the given values:

   $$a = \dfrac{727.0}{26.5000}$$

5. Step 5 — Evaluate:

   a = 27.4340\ \text{ft/s^2}

6. Step 6 — Check: returning a = 27.4340 ft/s^2 to

   $$\sum F = m a$$

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

Why the other options are there

• 54.8679 — kept a factor of two that cancels in the correct rearrangement.
• 13.7170 — dropped that same factor in the other direction.
• 30.1774 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

A block sliding on a frictionless surface is analyzed with equations of motion. Given mass (m) = 36.5000 slug; acceleration (a) = 11.7000 ft/s^2, determine the net force (F) in lbf.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for F:

   $$F = m a$$

3. Step 3

   $$List the givens: mass (m) = 36.5000 slug, acceleration (a) = 11.7000 ft/s^2$$

4. Step 4 — Substitute the given values:

   $$F = 36.5000 11.7000$$

5. Step 5 — Evaluate:

   $$F = 427.0\ \text{lbf}$$

6. Step 6 — Check: returning F = 427.0 lbf to

   $$\sum F = m a$$

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

Why the other options are there

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

Reference: FE Handbook — Dynamics: Equations of Motion

A cart towed by a cable is solved using the equations of motion. Given acceleration (a) = 11.8000 ft/s^2; net force (F) = 811.0 lbf, determine the mass (m) in slug.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for m:

   $$m = \dfrac{F}{a}$$

3. Step 3

   $$List the givens: acceleration (a) = 11.8000 ft/s^2, net force (F) = 811.0 lbf$$

4. Step 4 — Substitute the given values:

   $$m = \dfrac{811.0}{11.8000}$$

5. Step 5 — Evaluate:

   $$m = 68.7288\ \text{slug}$$

6. Step 6 — Check: returning m = 68.7288 slug to

   $$\sum F = m a$$

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

Why the other options are there

• 137.5 — kept a factor of two that cancels in the correct rearrangement.
• 34.3644 — dropped that same factor in the other direction.
• 75.6017 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

An elevator cab's equations of motion determine cable tension during acceleration. Given mass (m) = 6.6000 slug; net force (F) = 886.0 lbf, determine the acceleration (a) in ft/s^2.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• Everything except a is given, so isolate a 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for a:

   $$a = \dfrac{F}{m}$$

3. Step 3

   $$List the givens: mass (m) = 6.6000 slug, net force (F) = 886.0 lbf$$

4. Step 4 — Substitute the given values:

   $$a = \dfrac{886.0}{6.6000}$$

5. Step 5 — Evaluate:

   a = 134.2\ \text{ft/s^2}

6. Step 6 — Check: returning a = 134.2 ft/s^2 to

   $$\sum F = m a$$

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

Why the other options are there

• 268.5 — kept a factor of two that cancels in the correct rearrangement.
• 67.1212 — dropped that same factor in the other direction.
• 147.7 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

A block sliding on a frictionless surface is analyzed with equations of motion. Given mass (m) = 25.9000 slug; acceleration (a) = 23.1000 ft/s^2, determine the net force (F) in lbf.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for F:

   $$F = m a$$

3. Step 3

   $$List the givens: mass (m) = 25.9000 slug, acceleration (a) = 23.1000 ft/s^2$$

4. Step 4 — Substitute the given values:

   $$F = 25.9000 23.1000$$

5. Step 5 — Evaluate:

   $$F = 598.3\ \text{lbf}$$

6. Step 6 — Check: returning F = 598.3 lbf to

   $$\sum F = m a$$

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

Why the other options are there

• 1,197 — kept a factor of two that cancels in the correct rearrangement.
• 299.1 — dropped that same factor in the other direction.
• 658.1 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

A cart towed by a cable is solved using the equations of motion. Given acceleration (a) = 1.4000 ft/s^2; net force (F) = 138.0 lbf, determine the mass (m) in slug.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for m:

   $$m = \dfrac{F}{a}$$

3. Step 3

   $$List the givens: acceleration (a) = 1.4000 ft/s^2, net force (F) = 138.0 lbf$$

4. Step 4 — Substitute the given values:

   $$m = \dfrac{138.0}{1.4000}$$

5. Step 5 — Evaluate:

   $$m = 98.5714\ \text{slug}$$

6. Step 6 — Check: returning m = 98.5714 slug to

   $$\sum F = m a$$

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

Why the other options are there

• 197.1 — kept a factor of two that cancels in the correct rearrangement.
• 49.2857 — dropped that same factor in the other direction.
• 108.4 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

An elevator cab's equations of motion determine cable tension during acceleration. Given mass (m) = 13.9000 slug; net force (F) = 441.0 lbf, determine the acceleration (a) in ft/s^2.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• Everything except a is given, so isolate a 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for a:

   $$a = \dfrac{F}{m}$$

3. Step 3

   $$List the givens: mass (m) = 13.9000 slug, net force (F) = 441.0 lbf$$

4. Step 4 — Substitute the given values:

   $$a = \dfrac{441.0}{13.9000}$$

5. Step 5 — Evaluate:

   a = 31.7266\ \text{ft/s^2}

6. Step 6 — Check: returning a = 31.7266 ft/s^2 to

   $$\sum F = m a$$

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

Why the other options are there

• 63.4532 — kept a factor of two that cancels in the correct rearrangement.
• 15.8633 — dropped that same factor in the other direction.
• 34.8993 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion

A block sliding on a frictionless surface is analyzed with equations of motion. Given mass (m) = 22.2000 slug; acceleration (a) = 8.9000 ft/s^2, determine the net force (F) in lbf.

Start with the thinking

• The governing relation printed in this handbook section is Equation of motion (Newton's second law).
• 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.
• The equations of motion apply Newton's second law to relate the net force on a body to its mass and acceleration.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$\sum F = m a$$

2. Step 2 — Rearrange symbolically for F:

   $$F = m a$$

3. Step 3

   $$List the givens: mass (m) = 22.2000 slug, acceleration (a) = 8.9000 ft/s^2$$

4. Step 4 — Substitute the given values:

   $$F = 22.2000 8.9000$$

5. Step 5 — Evaluate:

   $$F = 197.6\ \text{lbf}$$

6. Step 6 — Check: returning F = 197.6 lbf to

   $$\sum F = m a$$

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

Why the other options are there

• 395.2 — kept a factor of two that cancels in the correct rearrangement.
• 98.7900 — dropped that same factor in the other direction.
• 217.3 — rounded an intermediate value before the final step.

Reference: FE Handbook — Dynamics: Equations of Motion