Barge Pulled by Tugboats

Barge Pulled by Tugboats#

A barge is pulled by the two tugboats shown in the following figure. One tugboat pulls on the barge with a force of magnitude \(F_2 = \) 5230 units of force at \(\theta_2 = \) 23\(^{\circ}\) above the line AB and the other tugboat pulls on the barge with a force of magnitude \(F_1 = \) 3512 units of force at \(\theta_1 = \) 13\(^{\circ}\) below the line AB.

Assume \(+y\) is straight ahead, and \(+x\) is to the right.

Figure of a barge pulled by two tugboats.
Figure of a barge pulled by two tugboats.
A straight line AB is drawn through the center of the barge. One tugboat pulls the barge to the left with a force of magnitude $F_1$ at an angle $\theta_1$ relative to AB. The other tugboat pulls to the right with a force $F_2$ at angle $\theta_2$ relative to AB.

Part 1#

Resolve the pulling forces to their components. What is the \(x\)-component of the right-force (i.e. \(F_2\))? Remember to consider the sign convention.

Answer Section#

Please enter in a numeric value in ‘units of force’.

Part 2#

Resolve the pulling forces to their components. What is the \(y\)-component of the right-force (i.e. \(F_2\))? Remember to consider the sign convention.

Answer Section#

Please enter in a numeric value in ‘units of force’.

Part 3#

Resolve the pulling forces to their components. What is the \(x\)-component of the left-force (i.e. \(F_1\))? Remember to consider the sign convention.

Answer Section#

Please enter in a numeric value in ‘units of force’.

Part 4#

Resolve the pulling forces to their components. What is the \(y\)-component of the left-force (i.e. \(F_1\))? Remember to consider the sign convention.

Answer Section#

Please enter in a numeric value in ‘units of force’.

Part 5#

What is the magnitude of the resultant pull?

Answer Section#

Please enter in a numeric value in ‘units of force’.

Part 6#

What is the direction of the resultant vector relative to the line AB?

Answer Section#

  • 8.65\(^{\circ}\) to the right of AB.

  • 8.65\(^{\circ}\) to the left of AB.

  • 81.3\(^{\circ}\) to the right of AB.

  • 81.3\(^{\circ}\) to the left of AB.

  • 86.5\(^{\circ}\) to the right of AB.

  • 86.5\(^{\circ}\) to the left of AB.

Attribution#

Problem is from the OpenStax University Physics Volume 1 textbook, licensed under the CC-BY 4.0 license.
Image representing the Creative Commons 4.0 BY license.