Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 27

Two cranes are lifting identical steel beams at the same time. One crane is putting out twice as much power as the other. Assuming friction is negligible, what can you conclude is happening to explain this difference?

Short Answer

Expert verified
Answer: The difference in power output is due to the difference in time taken to lift the beam. The crane with the higher power output lifts the steel beam twice as fast as the one with the lower power output, given that friction is negligible, and the force applied and the distance traveled are the same for both cranes.

Step by step solution

01

Understand the concept of power

Power is the rate at which work is done or energy is transferred. The formula for power (P) is given as P = W/t = F * d / t, where W is the work done, F is the force applied, d is the distance traveled, and t is the time taken.
02

Identify the factors affecting power

Since we are given that friction is negligible, we can focus on the factors affecting power in this scenario. There are three factors to consider - the force applied (F), the distance traveled (d), and the time taken (t).
03

Analyze the force applied by the cranes

Let's first consider F. Since both cranes are lifting identical steel beams and friction is negligible, the force applied by each crane should be equal to the weight of the steel beam. Thus, the force applied by both cranes should be the same.
04

Analyze the distance traveled by the cranes

Next, let's consider the distance traveled (d). Again, since both cranes are lifting identical steel beams at the same time, it's reasonable to assume that the distance traveled by both cranes should be the same.
05

Analyze the time taken by the cranes

Finally, we need to consider the time taken (t). If one crane exerts twice the power of the other, it's likely that the time it takes for the crane with the higher power output to lift the beam is shorter than the time taken for the crane with the lower power output. Mathematically, if the first crane (1) has power P1 and the second crane (2) has power P2, P1 = 2 * P2, so P1 = 2 * F * d / t2 => t1 = t2 / 2.
06

Conclude the reason for the difference in power output

From our analysis, we can conclude that the difference in power output between the two cranes is due to the difference in time taken to lift the beam. The crane with the higher power output lifts the steel beam twice as fast as the one with the lower power output, given that friction is negligible, and the force applied and the distance traveled are the same for both cranes.

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 ball is thrown straight upward from the surface of the Moon. Is the maximum height it reaches less than, equal to, or greater than the maximum height reached by a ball thrown upward on Earth with the same initial speed? (Ignore air resistance in both cases.) Explain.

A person runs up several flights of stairs and is exhausted at the top. Later, the same person walks up the same stairs and does not feel as tired. Why is this? Ignoring air resistance, does it take more work or energy to run up the stairs than to walk up?

During a head-on collision between two automobiles, the occupants are decelerated rapidly. Use the idea of work to explain why an air bag that quickly inflates in front of an occupant reduces the likelihood of injury.

Identify as many different ways as you can for giving energy to a basketball.

Solar-powered spotlights have batteries that are charged by solar cells during the day and then operate lights at night. Describe the energy conversions in this entire process, starting with the Sun's nuclear energy and ending with the light from the spotlight being absorbed by the surroundings. Name all of the forms of energy that are involved.
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Electricity and Magnetism

Read Explanation

Rotational Dynamics

Read Explanation

Space Physics

Read Explanation

Work Energy and Power

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