Barge Pulled by Tugboats

Contents

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 $θ_{2} =$ 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 $θ_{1} =$ 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.