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Chapter 9: Problem 20

In a 'tug of war' two groups of men pull in opposite directions on either end of a rope. Each group applies \(2000 \mathrm{~N}\) of force. What is the tension in the rope? A. \(0 \mathrm{~N}\) B. \(1000 \mathrm{~N}\) C. \(2000 \mathrm{~N}\) D. \(4000 \mathrm{~N}\)

Short Answer

Expert verified
2000 N

Step by step solution

01

Understand the Problem

In a 'tug of war', two groups of men are pulling on opposite ends of a rope with equal forces of 2000 N each. The question asks for the tension in the rope.
02

Define Tension in the Rope

Tension is the force that is transmitted through a rope when it is pulled by forces acting from opposite ends. When two groups pull with equal forces on opposite ends of the rope, the tension is equal to the magnitude of the force applied by either group.
03

Calculate the Tension

Since each group applies 2000 N of force and they are pulling in opposite directions, the tension in the rope is equal to the force applied by one group, which is 2000 N.
04

Choose the Correct Answer

From the given options, the correct answer is C. 2000 N.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Tug of War
In a game of 'tug of war', two teams pull on opposite ends of a rope to see who can drag the other team across a certain line. This setup creates an interesting physics problem because it involves forces acting in direct opposition to one another. When two teams pull with an identical force, the rope remains stationary, but the tension within the rope reaches a certain value. This happens because each team鈥檚 pulling force counteracts the other.
Equal and Opposite Forces
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This principle is perfectly demonstrated in a 'tug of war'. When one team pulls the rope with a force of 2000 N and the opposing team also pulls with 2000 N, the forces balance each other out.

As a result, the net force acting on the rope is zero, which is why the rope doesn't move. Even though the net force is zero, the tension in the rope is not zero. The tension in the rope reflects the magnitude of the force that each team applies.
Calculating Tension
To calculate the tension in the rope during a 'tug of war', we need to understand that the tension is equivalent to the force exerted by one team. Since both teams pull with the same force (2000 N) in opposite directions, the tension within the rope is exactly 2000 N. This is because the rope has to withstand the force exerted by either team to stay taut.

We can summarize the calculation like this:

Assume team A pulls with force \(\text{F}_A = 2000 \text{N}\) and team B pulls with force \(\text{F}_B = 2000 \text{N}\). The tension \(\text{T}\) in the rope will be the force exerted by one team, as both forces are equal and opposite:

\[ T = F_A = 2000 \text{N} \]

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Most popular questions from this chapter

The passage comes from the imagination of a student. A real pendulum on the clock in orbit would: A. swing more slowly than it would if it were on the planet below. B. swing more swiftly than it would if it were on the planet below. C. swing at the same rate as it would if it were on the planet below. D. not swing on the orbiting spacecraft.

The earth spins on its axis flattening its spherical shape from pole to pole and bowing out at the equator. An object is placed on a scale at the equator. How does the centrifugal force and the distance from the center of gravity affect the weight (as measured by the scale) at the equator? A. Both the increased distance and the centrifugal force act to decrease the weight of the object. B. The increased distance tends to decrease the weight of the object while the centrifugal force tends to increase its weight. C. The increased distance tends to increase the weight of the object while the centrifugal force tends to decrease its weight. D. The increased distance tends to decrease the weight of the object and the centrifugal force does not affect the weight of the object.

The moon has no atmosphere, and has less gravity than earth. How will the path of a golf ball struck on the earth differ from one struck on the moon? A. Both the earth's atmosphere and gravity will act to lengthen the projectile path of the ball. B. Both the earth's atmosphere and gravity will act to shorten the projectile path of the ball. C. The earth's atmosphere will act to shorten the path of the ball but its gravity will act to lengthen the path. D. The earth's atmosphere will act to lengthen the path of the ball but its gravity will act to shorten the path.

If the bank angle \(\theta\) were increased to \(90^{\circ}\) and the vehicle did not fall, the frictional force on the vehicle would be: A. less than the weight of the vehicle. B. equal to the weight of the vehicle. C. greater than the weight of the vehicle. D. The laws of physics dictate that the vehicle must fall if the bank angle is increased to \(90^{\circ}\).

A ball is rolled down a \(1 \mathrm{~m}\) ramp placed at an angle of \(30^{\circ}\) to the horizontal. The same ball is rolled down a \(1 \mathrm{~m}\) ramp placed vertically. Which of the following statements is true? (Note: \(\sin 30^{\circ}=0.5, \cos 30^{\circ}=0.87\) ) A. The ball required the same amount of time for both trips. B. The ball had the same displacement at the end of both trips. C. The ball accelerated at the same rate for both trips. D. The ball reached approximately \(\mathbf{1 . 4}\) times the speed on the second trip as it did on the first trip.
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