/*! 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 211 An electric motor \(M\) is used ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 211

An electric motor \(M\) is used to reel in cable and hoist a bicycle into the ceiling space of a garage. Pulleys are fastened to the bicycle frame with hooks at locations \(A\) and \(B\), and the motor can reel in cable at a steady rate of 12 in./sec. At this rate, how long will it take to hoist the bicycle 5 feet into the air? Assume that the bicycle remains level.

Short Answer

Expert verified
The bicycle will be hoisted in 5 seconds.

Step by step solution

01

Convert Units

First, convert the distance the bicycle needs to be hoisted from feet to inches. There are 12 inches in a foot, so:\(5 \text{ ft} = 5 \times 12 \text{ in} = 60 \text{ in}\).
02

Calculate Time

The motor reels in cable at a rate of 12 inches per second. To find the time it will take to hoist the bicycle 60 inches, use the formula:\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]Substituting the known values:\[ \text{Time} = \frac{60 \text{ in}}{12 \text{ in/sec}} = 5 \text{ seconds} \].

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Cable Systems
Cable systems in engineering mechanics are used to transmit force or motion.
They are common in lifting mechanisms and similar applications where cables pull or hold loads.
These systems rely on the tensile strength of the cable and the configuration of pulleys to move or lift objects.
  • Components: A typical cable system comprises a cable, pulleys, and sometimes a motor.
  • Pulleys: They redirect the cable direction and can multiply force, making it easier to lift heavy objects.
  • Motor: In powered systems, a motor is used to apply continuous force to reel in or release the cable.
Understanding how these systems work helps in designing efficient lifting and holding mechanisms, like the garage hoist for a bicycle.
Pulley Mechanics
Pulley mechanics simplify the lifting of heavy loads by changing the direction of the applied force.
When multiple pulleys are used together, they form a "block and tackle" system that can reduce the amount of force needed.
  • Single Pulley: Only changes force direction without force multiplication.
  • Multiple Pulleys: Reduces the needed input force by distributing the load across multiple lines.
  • Friction: Ideally minimal in pulley systems to maintain mechanical advantage.
In the example with the bicycle, pulleys could be attached at different points to balance and evenly lift the load while ensuring it remains level.
Unit Conversion
Unit conversion is critical in engineering to ensure consistency and accuracy in calculations.
Converting units helps in understanding and solving real-life engineering problems more easily.
  • Standard Units: Common units in mechanics include feet, inches, meters, and centimeters.
  • Conversion Factor: Use known equivalencies, like 12 inches = 1 foot, for conversions.
  • Application: Converting units of rate and distance ensures calculations are straightforward, like converting the lifting distance from feet to inches.
Efficient use of unit conversion simplifies processes, reducing errors in engineering tasks.
Motion Analysis
Motion analysis involves evaluating the movement of objects to predict how they will behave under different conditions.
In engineering mechanics, this is vital for designing systems that support moving loads, like hoists or elevators.
  • Constant Speed: Involves analyzing systems like motors working at a steady rate, as with the reeling in of cable.
  • Time Calculation: Use formulas such as \( \text{Time} = \frac{\text{Distance}}{\text{Rate}} \) to find durations for tasks.
  • Balanced Loads: Ensures the weight distribution is even to maintain stability during movement.
By understanding motion analysis, engineers can design more effective systems, ensuring safety and functionality in lifting operations.

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

Ball 1 is launched with an initial vertical velocity \(v_{1}=160 \mathrm{ft} / \mathrm{sec} .\) Three seconds later, ball 2 is launched with an initial vertical velocity \(v_{2}\). Determine \(v_{2}\) if the balls are to collide at an altitude of \(300 \mathrm{ft} .\) At the instant of collision, is ball 1 ascending or descending?

A minivan starts from rest on the road whose constant radius of curvature is \(40 \mathrm{m}\) and whose bank angle is \(10^{\circ} .\) The motion occurs in a horizontal plane. If the constant forward acceleration of the minivan is \(1.8 \mathrm{m} / \mathrm{s}^{2},\) determine the magnitude \(a\) of its total acceleration 5 seconds after starting.

A ship capable of making a speed of 16 knots through still water is to maintain a true course due west while encountering a 3 -knot current running from north to south. What should be the heading of the ship (measured clockwise from the north to the nearest degree)? How long does it take the ship to proceed 24 nautical miles due west?

A toy helicopter is flying in a straight line at a constant speed of \(4.5 \mathrm{m} / \mathrm{s}\). If a projectile is launched vertically with an initial speed of \(v_{0}=28 \mathrm{m} / \mathrm{s}\), what horizontal distance \(d\) should the helicopter be from the launch site \(S\) if the projectile is to be traveling downward when it strikes the helicopter? Assume that the projectile travels only in the vertical direction.

A helicopter approaches a rescue scene. A victim \(P\) is drifting along with the river current of speed \(v_{C}=2 \mathrm{m} / \mathrm{s} .\) The wind is blowing at a speed \(v_{W}=\) \(3 \mathrm{m} / \mathrm{s}\) as indicated. Determine the velocity relative to the wind which the helicopter must acquire so that it maintains a steady overhead position relative to the victim.
See all solutions

Recommended explanations on Physics Textbooks

Solid State Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Modern Physics

Read Explanation

Magnetism

Read Explanation

Space Physics

Read Explanation

Mechanics and Materials

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.