Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Q43_P (page 381)

A string is wrapped around a uniform disk of mass M and radius R. Attached to the disk are four low-mass rods of radius b, each with a small mass m at the end (Figure 9.63).

The apparatus is initially at rest on a nearly frictionless surface. Then you pull the string with a constant force F. At the instant when the center of the disk has moved a distance d, an additional length w of string has unwound off the disk. (a) At this instant, what is the speed of the center of the apparatus? Explain your approach. (b) At this instant, what is the angular speed of the apparatus? Explain your approach.

Short Answer

Expert verified

Data given

Step by step solution

01

Step 1

This is step 1m

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 box contains machinery that can rotate. The total mass of the box plus the machinery is7kg. A string wound around the machinery comes out through a small hole in the top of the box. Initially the box sits on the ground, and the machinery inside is not rotating (left side of Figure 9.61). Then you pull upward on the string with a force of constant magnitude . At an instant when you have pulled 0.6mof string out of the box (indicated on the right side of Figure 9.61), the box has risen a distance of 0.2 mand the machinery inside is rotating.


POINT PARTICLE SYSTEM (a) List all the forms of energy that change for the point particle system during this process. (b) What is theycomponent of the displacement of the point particle system during this process? (c) What is the ycomponent of the net force acting on the point particle system during this process? (d) What is the distance through which the net force acts on the point particle system? (e) How much work is done on the point particle system during this process? (f) What is the speed of the box at the instant shown in the right side of Figure 9.61? (g) Why is it not possible to find the rotational kinetic energy of the machinery inside the box by considering only the point particle system?

EXTENDED SYSTEM (h) the extended system consists of the box, the machinery inside the box, and the string. List all the forms of energy that change for the extended system during this process. (i) What is the translational kinetic energy of the extended system, at the instant shown in the right side of Figure 9.61? (j) What is the distance through which the gravitational force acts on the extended system? (k) How much work is done on the system by the gravitational force? (I) what is the distance through which your hand moves? (m) How much work do you do on the extended system? (n) At the instant shown in the right side of Figure 9.61, what is the total kinetic energy of the extended system? (o) what is the rotational kinetic energy of the machinery inside the box?

You hold up an object that consists of two blocks at rest, each of massM=5kg, connected by a low-mass spring. Then you suddenly start applying a larger upward force of constant magnitudeF=167N(which is greater than2Mg). Figure9.60shows the situation some time later, when the blocks have moved upward, and the spring stretch has increased.

The heights of the centers of the two blocks are as follows:

Initial and final positions of block 1:y1i=0.3m,y1f=0.5m

Initial and final positions of block 2:y2i=0.7m,y2f=1.2m

It helps to show these heights on a diagram. Note that the initial center of mass of the two blocks isy1i+y1i/2, and the final center of mass of the two blocks isrole="math" localid="1656911769231" y1f+y1f/2. (a) Consider the point particle system corresponding to the two blocks and the spring. Calculate the increase in the total translational kinetic energy of the two blocks. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts. (b) Consider the extended system corresponding to the two blocks and the spring. Calculate the increase of(Kvib+Us), the vibrational kinetic energy of the two blocks (their kinetic energy relative to the center of mass) plus the potential energy of the spring. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts.

It is sometimes claimed that friction forces always slow an object down, but this is not true. If you place a box of mass Mon a moving horizontal conveyor belt, the friction force of the belt acting on the bottom of the box speeds up the box. At first there is some slipping, until the speed of the box catches up to the speed vof the belt. The coefficient of friction between box and belt isμ. (a) What is the distance d(relative to the floor) that the box moves before reaching the final speed v? Use energy arguments, and explain your reasoning carefully. (b) How much time does it take for the box to reach its final speed? (c) The belt and box of course get hot. Is the effective distance through which the friction force acts on the box greater than or less than d? Give as quantitative an argument as possible. You can assume that the process is quick enough that you can neglect transfer of energyQ due to a temperature difference between the belt and the box. Do not attempt to use the results of the friction analysis in this chapter; rather, apply the methods of that analysis to this different situation. (d) Explain the result of part (c) qualitatively from a microscopic point of view, including physics diagrams.E

A man whose mass is 80kg and a woman whose mass is 50kgsit at opposite ends of a canoe 5m long, whose mass is 30kg. (a) Relative to the man, where is the mass of the system consisting of man-woman, and canoe? (Hint: Choose a specific coordinate system with a specific origin.) (b) Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water? Explain your work and your assumptions.

Under what conditions does the energy equation for the point particle system differ from the energy equation for the extended system? Give two examples of such a situation. Give one example of a situation where the two equations look exactly alike.
See all solutions

Recommended explanations on Physics Textbooks

Engineering Physics

Read Explanation

Fields in Physics

Read Explanation

Solid State Physics

Read Explanation

Fluids

Read Explanation

Force

Read Explanation

Nuclear 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.

Sign-up for free