Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Q38P (page 215)

Jack & Jill are maneuvering a 3000Kgboat near a dock. Initially the boat’s position is 2,0,3and its speed is 1.3m/s . As the boat moves to position (4,0,2). Jack exerts a force (-400, 0, 200) N and Jill exert a force and Jill exert a force (150,0,300)N . (a) How much work does jack do? (b) How much work does Jill do? (c) Without doing any calculations, say what is the angle between the (vector) force that Jill exert, and the (vector) velocity of the boat. Explain briefly how you know this (d) Assuming that we can neglect the work done by the water on the boat, what is the final speed of the boat?

Short Answer

Expert verified

a. Jack does -1000J work.

Step by step solution

01

Given data

  • Mass of the boat, m = 3000 kg.
  • The initial position of the boat, xi,yi,zi=2,0,3m.
  • The initial speed of the boat,vi=1.3m/s.
  • Final location of the boat, xf,yf,zf=4,0,2m.
  • Force exerted by Jack, FJack→=-400,0,200N.
  • Force exerted by Jill, FJill→=(150,0,300)N.
02

Introduction

A vector quantity means the physical quantity which has same directionsas well as magnitude.

03

Solution

The work done by a constant forceF→:

Acting through a displacement △r→ is given by

W=F→.△r→

The displacement vector of the boat is given by

△r→=xf,yfzf-xi,yi,zi△r→=-400,0,200N2,0,-1△r→=-800+0-200J△r→=-1000J

It is negative because the boat’s position is opposite.

Hence, Jack does -1000J work.

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

n electron is travelling at a speed of 0.95cin an electron accelerator. An electric force of 1.6×10-13Nis applied in the direction of motion while the electron travels a distance of 2m. What is the new speed of the electron?

An object that is originally at locationmoves to locationas shown in Figure 6.80. While it is moving it is acted on by a constant force of.

(a) How much work is done on the object by this force? (b) Does the kinetic energy of the object increase or decrease?

(c) A different object moves from locationto location , as shown in Figure 6.81. While it is moving it is acted on by a constant force of . How much work is done on the second object by this force? (d) Does the kinetic energy of the object increase or decrease?

An automobile traveling on a highway has an average kinetic energy of . Its mass is . What is its average speed? Convert your answer to miles per hour to see whether it makes sense. If you could use all of themc2rest energy of some amount of fuel to provide the car with its kinetic energy of , What mass of fuel would you need?

A spacecraft is coasting toward Mars. The mass of Mars is 6.4×103kg and its radius is 3400km(3.4×106m). When the spacecraft is 7000km(7×106m) from the center of Mars, the spacecraft's speed is 3000m/s . Later, when the spacecraft is (4000km4×106m from the center of Mars, what is its speed? Assume that the effects of Mar's two tiny moons, the other planets, and the Sun are negligible. Precision is required to land on Mars, so make an accurate calculation, not a rough, approximate calculation.

A proton(H1)and a deuteron ((H2), “heavy” hydrogen) start out far apart. An experimental apparatus shoots them toward each other (with equal and opposite momenta). If they get close enough to make actual contact with each other, they can react to form a helium-3nucleus and a gamma ray (a high-energy photon, which has kinetic energy but zero rest energy):H1+2H→3He+y

This is one of the thermonuclear or fusion reactions that takes place inside a star such as our Sun.

The mass of the proton is 1.0073 u(unified atomic mass unit,1.7×10-27kg), the mass of the deuteron is 2.0136 u, the mass of the helium-3nucleus is 3.0155 u, and the gamma ray is massless. Although in most problems you solve in this course it is adequate to use values of constants rounded to two or three significant figures, in this problem you must keep at least six significant figures throughout your calculation. Problems involving mass changes require many significant figures because the changes in mass are small compared to the total mass. (a) The strong interaction has a very short range and is essentially a contact interaction. For this fusion reaction to take place, the proton and deuteron have to come close enough together to touch. The approximate radius of a proton or neutron is about1×10-15m. What is the approximate initial total kinetic energy of the proton and deuteron required for the fusion reaction to proceed, in joules and electron volts (1eV=1.6×10-19J)? (b) Given the initial conditions found in part (a), what is the kinetic energy of theHe3plus the energy of the gamma ray, in joules and in electron volts? (c) The net energy released is the kinetic energy of theHe3plus the energy of the gamma ray found in part (b), minus the energy input that you calculated in part (a). What is the net energy release, in joules and in electron volts? Note that you do get back the energy investment made in part (a). (d) Kinetic energy can be used to drive motors and do other useful things. If a mole of hydrogen and a mole of deuterium underwent this fusion reaction, how much kinetic energy would be generated? (For comparison, aroundare obtained from burning a mole of gasoline.) (e) Which of the following potential energy curvesin Figure 6.87 is a reasonable representation of the interaction in this fusion reaction? Why?

As we will study later, the average kinetic energy of a gas molecule is32kbT, whereis the “Boltzmann constant,”1.4×10-23J/K, andis the absolute or Kelvin temperature, measured from absolute zero (so that the freezing point of water is273K). The approximate temperature required for the fusion reaction to proceed is very high. This high temperature, required because of the electric repulsion barrier to the reaction, is the main reason why it has been so difficult to make progress toward thermonuclear power generation. Sufficiently high temperatures are found in the interior of the Sun, where fusion reactions take place.
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Particle Model of Matter

Read Explanation

Electrostatics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Rotational Dynamics

Read Explanation

Torque and Rotational Motion

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