/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 121 Two canal workers pull a barge a... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 121

Two canal workers pull a barge along the narrow waterway at a constant speed. One worker pulls with a force of \(105 \mathrm{N}\) at an angle of \(28^{\circ}\) with respect to the forward motion of the barge and the other worker, on the opposite tow path, pulls at an angle of \(38^{\circ}\) relative to the barge motion. Both ropes are parallel to the ground. (a) With what magnitude force should the second worker pull to make the sum of the two forces be in the forward direction? (b) What is the magnitude of the force on the barge from the two tow ropes?

Short Answer

Expert verified
Answer: (a) The second worker should pull with a force of approximately \(72.63 \mathrm{N}\), and (b) the total magnitude of the force on the barge from the two tow ropes is approximately \(148.39 \mathrm{N}\).

Step by step solution

01

Understand the problem and draw a diagram

To begin, it's always good to visualize the problem by drawing a diagram. Here, we can represent the two workers, the barge, and the forces exerted by them on the barge, along with the respective angles.
02

Analyze the forces acting on the barge

Next, we need to analyze the forces acting on the barge and separate them into their horizontal and vertical components. Let F be the force exerted by the second worker. In order for the total force to remain in the forward direction, the vertical components of the forces by the first and second workers must be equal, canceling out each other's effects.
03

Separate the forces into their components

Now, we will separate the forces into their horizontal and vertical components. For the first worker, who pulls with a force of \(105 \mathrm{N}\) at an angle of \(28^{\circ}\), the horizontal and vertical components are: Horizontal component: \(105 \cos(28^{\circ})\) Vertical component: \(105 \sin(28^{\circ})\) For the second worker, with a force of \(F\) and an angle of \(38^{\circ}\): Horizontal component: \(F \cos(38^{\circ})\) Vertical component: \(F \sin(38^{\circ})\)
04

Equate the vertical components to find the magnitude of F

In order for the forces to sum in the forward direction, the vertical components must be equal, which means: \(105 \sin(28^{\circ}) = F \sin(38^{\circ})\) To find F, we can divide both sides by \(\sin(38^{\circ})\): \(F = \frac{105 \sin(28^{\circ})}{\sin(38^{\circ})} \approx 72.63 \mathrm{N}\)
05

Find the total horizontal force

Now we need to find the total horizontal force on the barge from the two tow ropes. The horizontal components of both forces acting on the barge sum together: Total horizontal force = \(105 \cos(28^{\circ}) + F \cos(38^{\circ}) \approx 105 \cos(28^{\circ}) + 72.63 \cos(38^{\circ}) \approx 148.39 \mathrm{N}\) So, (a) the second worker should pull with a force of approximately \(72.63 \mathrm{N}\) and (b) the total magnitude of the force on the barge from the two tow ropes is approximately \(148.39 \mathrm{N}\).

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Most popular questions from this chapter

An \(80.0-\mathrm{N}\) crate of apples sits at rest on a ramp that runs from the ground to the bed of a truck. The ramp is inclined at \(20.0^{\circ}\) to the ground. (a) What is the normal force exerted on the crate by the ramp? (b) The interaction partner of this normal force has what magnitude and direction? It is exerted by what object on what object? Is it a contact or a long-range force? (c) What is the static frictional force exerted on the crate by the ramp? (d) What is the minimum possible value of the coefficient of static friction? (e) The normal and frictional forces are perpendicular components of the contact force exerted on the crate by the ramp. Find the magnitude and direction of the contact force.
A truck driving on a level highway is acted on by the following forces: a downward gravitational force of \(52 \mathrm{kN}\) (kilonewtons); an upward contact force due to the road of \(52 \mathrm{kN} ;\) another contact force due to the road of \(7 \mathrm{kN},\) directed east; and a drag force due to air resistance of \(5 \mathrm{kN}\), directed west. What is the net force acting on the truck?
Four separate blocks are placed side by side in a left-toright row on a table. A horizontal force, acting toward the right, is applied to the block on the far left end of the row. Draw FBDs for (a) the second block on the left and for (b) the system of four blocks.
You want to push a \(65-\mathrm{kg}\) box up a \(25^{\circ}\) ramp. The coefficient of kinetic friction between the ramp and the box is \(0.30 .\) With what magnitude force parallel to the ramp should you push on the box so that it moves up the ramp at a constant speed?
You grab a book and give it a quick push across the top of a horizontal table. After a short push, the book slides across the table, and because of friction, comes to a stop. (a) Draw an FBD of the book while you are pushing it. (b) Draw an FBD of the book after you have stopped pushing it, while it is sliding across the table. (c) Draw an FBD of the book after it has stopped sliding. (d) In which of the preceding cases is the net force on the book not equal to zero? (e) If the book has a mass of \(0.50 \mathrm{kg}\) and the coefficient of friction between the book and the table is \(0.40,\) what is the net force acting on the book in part (b)? (f) If there were no friction between the table and the book, what would the free-body diagram for part (b) look like? Would the book slow down in this case? Why or why not?
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