/*! 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 5 You want to raise a piano a give... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 5

You want to raise a piano a given height using a ramp. With a fixed, nonzero coefficient of friction, will you have to do more work if the ramp is steeper or more gradual? Explain.

Short Answer

Expert verified
The total work done to raise the piano to a given height remains consistent whether the ramp is steeper or more gradual. This is due to the inverse relationship between the ramp's steepness and the distance over which the work is done, both of which are factors in the work equation (W=F*d). But it's worth to consider that in a real-world scenario, factors like increased friction on longer distances could affect this ideal situation.

Step by step solution

01

Understanding Concepts

The key principle guiding this is the physics concept of work, defined as the force exerted on an object times the distance the object is moved (W=F*d). The force required to move the piano up the ramp is determined by the weight of the piano and the angle of the ramp, due to friction. The angle of the ramp determines both the distance over which the force needs to be exerted and the magnitude of the force.
02

Discussing the Steeper Ramp

If the ramp is steeper, the distance the piano needs to be moved is shorter. However, the force required to move the piano up the ramp will be larger due to the increased angle. This will result in a larger vertical component of the force tightening the gravitational pull.
03

Discussing the More Gradual Ramp

If the ramp is more gradual, then it will be longer, and therefore the distance the piano has to travel increases. However, the necessary force to move the piano up the ramp decreases due to a reduced angle. This equates to having a smaller vertical component of the force opposing the gravitational pull.
04

Determining Total Work Done

The total work done in both scenarios remains the same. This is because the work formula (W = F*d) accounts for both the force applied and the distance travelled, which adjust inversely with steepness in this scenario (more force, less distance in a steeper ramp and vice versa in a more gradual ramp). So, the product of the two remains the same, in an ideal world, without considering other real-world factors like variable friction.

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!

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

You do \(2.2 \mathrm{kJ}\) of work pushing a \(78-\mathrm{kg}\) trunk at constant speed \(3.1 \mathrm{m}\) along a ramp inclined upward at \(22^{\circ} .\) What's the frictional coefficient between trunk and ramp?

A force given by \(F=b / \sqrt{x}\) acts in the \(x\) -direction, where \(b\) is a constant with the units \(\mathrm{N} \cdot \mathrm{m}^{1 / 2} .\) Show that even though the force becomes arbitrarily large as \(x\) approaches zero, the work done in moving from \(x_{1}\) to \(x_{2}\) remains finite even as \(x_{1}\) approaches zero. Find an expression for that work in the limit \(x_{1} \rightarrow 0\).

A horse plows a 200 -m-long furrow in 5.0 min, exerting a \(750-\mathrm{N}\) force. Find its power output, measured in watts and in horsepower.

A meteorite plunges to Earth, embedding itself \(75 \mathrm{cm}\) in the ground. If it does 140 MJ of work in the process, what average force does the meteorite exert on the ground?

(a) Find the work done in lifting 1 L of blood (mass 1 kg) from the foot to the head of a 1.7 -m-tall person. (b) If blood circulates through the body at the rate of \(5.0 \mathrm{L} / \mathrm{min}\), estimate the heart's power output. (Your answer underestimates the power by a factor of about 5 because it neglects fluid friction and other factors.)
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Translational Dynamics

Read Explanation

Electrostatics

Read Explanation

Physics of Motion

Read Explanation

Magnetism

Read Explanation

Fundamentals of Physics

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.