Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 67

If you pull the boom rope with constant speed, the angle the boom makes with the horizontal will a. increase at a constant rate. b. increase at an increasing rate. c. increase at a decreasing rate. d. decrease.

Short Answer

Expert verified
The answer is c. The angle will increase, but at a decreasing rate.

Step by step solution

01

Analyze the Situation

Pulling the boom rope at a constant speed means that the height of the boom is increasing constantly over time. Due to this, the base - height relationship of the right-angled triangle (made by boom, horizontal and the line of pull) changes. The base is constant but the height is increasing.
02

Consider the Triangle Trigonometry

In this right angle triangle, the angle between boom and horizontal is determined using trigonometry, specifically tangent rule. Tan of that angle equals to the height divided by base.
03

Interpret the Behavior of Angle

As the height increases, tan of the angle also increases. Tangent function is an increasing function meaning that when pulling the rope makes the boom lift (increasing the height), the angle the boom makes with the horizontal also increases.
04

Analyze the Rate of Increase

While we have established the angle is increasing, we need to determine how 'fast' it's increasing. It's key to understand that a constant increase in the height of a right angled triangle (due to pulling of rope) doesn't correspond to a constant rate of increase in the angle. As the angle approaches 90 degrees, the change for each incremental height boost gets smaller. This is inherent to the properties of the tangent function, which grows more slowly as it gets larger.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A 4.2 -m-long beam is supported by a cable at its center. A \(65-\mathrm{kg}\) steelworker stands at one end of the beam. Where should a \(190-\mathrm{kg}\) bucket of concrete be suspended for the beam to be in static equilibrium?

A cubical block rests on an inclined board with two sides parallel to the incline. The coefficient of static friction between block and board is \(0.95 .\) If the inclination angle of the board is increased, will the block first slide or first tip over?

A portion of a roller-coaster track is described by \(h=0.94 x-0.010 x^{2},\) where \(h\) and \(x\) are the height and horizontal position in meters. (a) Find a point where the roller-coaster car could be in static equilibrium on this track. (b) Is this equilibrium stable or unstable?

Pregnant women often assume a posture with their shoulders held far back from their normal position. Why?

A uniform, solid cube of mass \(m\) and side \(s\) is in stable equilibrium when sitting on a level tabletop. How much energy is required to bring it to an unstable equilibrium where it's resting on its corner?
See all solutions

Recommended explanations on Physics Textbooks

Oscillations

Read Explanation

Space Physics

Read Explanation

Nuclear Physics

Read Explanation

Medical Physics

Read Explanation

Fluids

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free