Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 3

A \(10 \mathrm{~kg}\) box is lifted \(2 \mathrm{~m}\) off the floor and placed on a frictionless horizontal conveyor to take it \(30 \mathrm{~m}\) across a warehouse. At the end of the conveyor, it is lowered \(1 \mathrm{~m}\) where it ends up on a shelf. How much net gravitational potential energy was given to the box from the start to the end of the process?

Short Answer

Expert verified
Answer: The net gravitational potential energy given to the box throughout the process is -98.1 J.

Step by step solution

01

Determine the initial and final heights

Initially, the box is lifted 2 meters off the floor, so the initial height (h1) is 2 meters. After moving horizontally and lowered 1 meter, the final height (h2) of the box would be 1 meter (since it was lowered from the 2 meters initial height).
02

Calculate the change in gravitational potential energy

The change in gravitational potential energy (ΔPE) can be calculated using the formula: ΔPE = m * g * (h2 - h1) where m is the mass of the object (10 kg), g is the acceleration due to gravity (9.81 m/s²), h1 is the initial height (2 m), and h2 is the final height (1 m).
03

Solve for the net gravitational potential energy

Plugging the values into the formula, we get: ΔPE = 10 kg * 9.81 m/s² * (1 m - 2 m) ΔPE = 10 kg * 9.81 m/s² * (-1 m) ΔPE = -98.1 J The net gravitational potential energy given to the box is -98.1 J, which indicates a loss of potential energy as it is lowered to a final height of 1 meter.

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 gallon of gasoline contains about \(130 \mathrm{MJ}\) of chemical energy at a mass of around \(3 \mathrm{~kg}\). How high would you have to lift the gallon of gasoline to get the same amount of gravitational potential energy? Compare the result to the radius of the earth.

A typical American household uses approximately \(30 \mathrm{kWh}\) per day of electricity. Convert this to Joules and then imagine building a water tank \(10.8 \mathrm{~m}\) above the house \(^{37}\) to supply one day's worth of electricity. \(^{38}\) How much mass of water is this, in kg? At a density of \(1,000 \mathrm{~kg} / \mathrm{m}^{3}\), what is the volume in cubic meters, and what is the side length of a cube \(^{39}\) having this volume? Take a moment to visualize (or sketch) this arrangement.

If a 70 kg person climbs 10 flights of stairs, each flight \(3 \mathrm{~m}\) high, how much potential energy have they gained?

A hydroelectric facility is built to deliver a peak power of \(1 \mathrm{GW}\), which it manages to do for three months of the year during the spring snow- melt. But for three months in summer, it drops to \(700 \mathrm{MW}\), then \(500 \mathrm{MW}\) for three months in fall. In winter, it drops way down to \(200 \mathrm{MW}\) for three months. Using the concept of the capacity factor (Definition 11.2.1), what is the annual average capacity factor for this facility?

A dam 50 meters high is constructed on a river and is delivering \(180 \mathrm{MW}\) at some moment in time. What is the flow rate of water, in cubic meters per second, if the facility converts gravitational potential energy into electricity at \(90 \%\) efficiency?
See all solutions

Recommended explanations on Environmental Science Textbooks

Biological Resources

Read Explanation

Sustainability

Read Explanation

Environmental Policy

Read Explanation

Physical Environment

Read Explanation

Ecological Conservation

Read Explanation

Energy Resources

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