/*! 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} 40P A can of sardines is made to mov... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A can of sardines is made to move along an x axis from x=0.25m tox=1.25m by a force with a magnitude given byF=exp(-4x2) with x in meters and Fin newtons. (Here exp is the exponential function.) How much work is done on the can by the force?

Short Answer

Expert verified

The work done on the can by the force is, 0.21 J.

Step by step solution

01

Given

  1. The motion of can starts fromxi=0.25m
  2. The final position of the can is,xf=1.25m
  3. The function of force is,F=e-4x2
  4. The scale for vertical axis is, Fs=10.0N
02

Concept of calculating force done by a variable force.

The problem deals with the concept of work done. It includes both forces exerted on the body and the total displacement of the body. We can use the equation of the work done by a variable force.

Formula:

W=∫xixfF(x)dx

03

Calculate the work done

The equation for work done is,

W=∫xixfFxdx

Substitute the value of F(x) in the above equation.

W=∫0.251.25e-4x2dx

By solving this integral, we get

W=0.21J

Therefore, work done by the force on the can is 0.21 J.

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 91Ó°ÊÓ!

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

Figure 21-14 shows two charged particles on an axis. The charges are free to move. However, a third charged particle can be placed at a certain point such that all three particles are then in equilibrium. (a) Is that point to the left of the first two particles, to their right, or between them? (b) Should the third particle be positively or negatively charged? (c) Is the equilibrium stable or unstable?

Question: Harvard Bridge, which connects MIT with its fraternities across the Charles River, has a length of 364.4 Smoots plus one ear. The unit of one Smoot is based on the length of Oliver Reed Smoot, Jr., class of 1962, who was carried or dragged length by length across the bridge so that other pledge members of the Lambda Chi Alpha fraternity could mark off (with paint) 1-Smoot lengths along the bridge. The marks have been repainted biannually by fraternity pledges since the initial measurement, usually during times of traffic congestion so that the police cannot easily interfere. (Presumably, the police were originally upset because the Smoot is not an SI base unit, but these days they seem to have accepted the unit.) Figure 1-4 shows three parallel paths, measured in Smoots (S), Willies (W), and Zeldas (Z). What is the length of 50.0 Smoots in (a) Willies and (b) Zeldas?

Figure 1-4Problem 8

Question: Figure shoes four isotropic point sources of sound that are uniformly spaced on an x axis. The sources emit sound at the same wavelength λand same amplitude smand they emit in phase. A point, is shown on the y axis. Assume that as the sound waves travel to, the decrease in their amplitude is negligible. What multiple of toP if distance din the figure is (a)λ4,(b)λ2,(c)λ

A certain capacitor is charged to a potential differenceV. If you wish to increase its stored energy by 10%, by what percentage should you increaseV?

Question:Earth has a mass of5.98×1024kg . The average mass of the atoms that make up Earth is 40 u. How many atoms are there in Earth?

See all solutions

Recommended explanations on Physics Textbooks

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.