Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Problem 40

A uniform chain with a mass of \(1.32 \mathrm{~kg}\) per meter of length is coiled on a table. One end is pulled upward at a constant rate of \(0.47 \mathrm{~m} / \mathrm{s}\). a) Calculate the net force acting on the chain. b) At the instant when \(0.15 \mathrm{~m}\) of the chain has been lifted off the table, how much force must be applied to the end being raised?

Short Answer

Expert verified
Answer: The force applied to lift the chain at the specific instant is approximately 1.94 N.

Step by step solution

01

Write down the given information

We are given the following values: - mass per meter of the chain: \(1.32\mathrm{~kg/m}\) - speed with which the chain is being pulled upward: \(0.47\mathrm{~m/s}\) - length of chain lifted off the table at a specific instant: \(0.15\mathrm{~m}\)
02

Calculate the net force acting on the chain

To find the net force acting on the chain, we'll use the equation: \(F_{net} = m_{lifted}\cdot a\) Here, \(m_{lifted}\) is the mass of the chain that has been lifted off the table, and \(a\) is the acceleration due to gravity (which is \(9.81\mathrm{~m/s^2}\)). To find \(m_{lifted}\), we multiply the mass per meter of the chain by the length of the chain lifted off the table: \(m_{lifted} = (1.32\mathrm{~kg/m}) \cdot (0.15\mathrm{~m}) = 0.198\mathrm{~kg}\) Now, we can calculate the net force: \(F_{net} = 0.198\mathrm{~kg} \cdot 9.81\mathrm{~m/s^2} = 1.94\mathrm{~N}\) So the net force acting on the chain is approximately \(1.94\mathrm{~N}\).
03

Calculate the force applied to lift the chain at the specific instant

Since the chain is being pulled upward at a constant rate, the force required to lift the chain is equal to the net force acting on the chain. Thus, at the instant when \(0.15\mathrm{~m}\) of the chain has been lifted off the table, the force applied to lift the chain is also approximately \(1.94\mathrm{~N}\).

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 350 -kg cannon, sliding freely on a frictionless horizontal plane at a speed of \(7.5 \mathrm{~m} / \mathrm{s}\), shoots a 15 -kg cannonball at an angle of \(55^{\circ}\) above the horizontal. The velocity of the ball relative to the cannon is such that when the shot occurs, the cannon stops cold. What is the velocity of the ball relative to the cannon?

A \(1000 .-\mathrm{kg}\) cannon shoots a \(30.0-\mathrm{kg}\) shell at an angle of \(25.0^{\circ}\) above the horizontal and a speed of \(500 . \mathrm{m} / \mathrm{s}\). What is the recoil velocity of the cannon?

A catapult on a level field tosses a 3 -kg stone a horizontal distance of \(100 \mathrm{~m}\). A second 3 -kg stone tossed in an identical fashion breaks apart in the air into 2 pieces, one with a mass of \(1 \mathrm{~kg}\) and one with a mass of \(2 \mathrm{~kg} .\) Both of the pieces hit the ground at the same time. If the 1 -kg piece lands a distance of \(180 \mathrm{~m}\) away from the catapult, how far away from the catapult does the 2 -kg piece land? Ignore air resistance. a) \(20 \mathrm{~m}\) c) \(100 \mathrm{~m}\) e) \(180 \mathrm{~m}\) b) \(60 \mathrm{~m}\) d) \(120 \mathrm{~m}\)

A toy car of mass \(2.0 \mathrm{~kg}\) is stationary, and a child rolls a toy truck of mass 3.5 kg straight toward it with a speed of \(4.0 \mathrm{~m} / \mathrm{s}\) a) What is the velocity of the center of mass of the system consisting of the two toys? b) What are the velocities of the truck and the car with respect to the center of mass of the system consisting of the two toys?

A circular pizza of radius \(R\) has a circular piece of radius \(R / 4\) removed from one side, as shown in the figure. Where is the center of mass of the pizza with the hole in it?
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Space Physics

Read Explanation

Astrophysics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Physical Quantities And Units

Read Explanation

Electricity and Magnetism

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