/*! 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} Problem 84 A 60.0 -kg woman stands at one e... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 84

A 60.0 -kg woman stands at one end of a \(120-\) kg raft that is $6.0 \mathrm{m}\( long. The other end of the raft is \)0.50 \mathrm{m}$ from a pier. (a) The woman walks toward the pier until she gets to the other end of the raft and stops there. Now what is the distance between the raft and the pier? (b) In (a), how far did the woman walk (relative to the pier)?

Short Answer

Expert verified
Solution: (a) The distance between the raft and the pier after the woman walks to the other end of the raft is 3.50 m. (b) The woman has moved 3 m relative to the pier.

Step by step solution

01

1. List Given Information

- Mass of the woman, \(m_w = 60 \thinspace kg\) - Mass of the raft, \(m_r = 120 \thinspace kg\) - Length of the raft, \(L = 6.0 m\) - Initial distance between the raft and the pier, \(d_i = 0.50 m\)
02

2. Applying Conservation of Momentum

Since no external force acts on the woman-raft system, the momentum of the system is conserved. Initially, both the woman and the raft are at rest, so the initial momentum of the system is zero. As the woman walks towards the pier, both the woman and the raft will experience equal and opposite changes in their positions due to momentum conservation. Let the woman's final position be \(x_w\) m from her initial position, and the raft's final position be \(x_r\) m from its initial position. The total momentum before and after the woman walks should be equal: \(m_w * x_w = m_r * x_r\)
03

3. Finding the Woman's Final Position

The woman walks to the other end of the raft, so her final position is \(x_w = 6.0m\) from her initial position.
04

4. Finding the Raft's Final Position

Now, substitute the values of \(m_w\), \(m_r\), and \(x_w\) in the momentum conservation equation: \(60 * 6 = 120 * x_r\) Solve for \(x_r\): \(x_r = \frac{60 * 6}{120} = 3 m\) The raft has moved 3 m away from its initial position.
05

5. Calculate the Final Distance Between the Raft and the Pier

The initial distance between the raft and the pier is \(0.50m\). The raft moves away from the pier by \(3m\). So, the final distance between the raft and the pier is: \(d_f = d_i + x_r = 0.50 + 3 = 3.50m\) So the final distance between the raft and the pier is \(3.50m\). Answer to part (a): The distance between the raft and the pier after the woman.walks to the other end of the raft is 3.50 m.
06

6. Calculate the Woman's Distance Relative to the Pier

Since the woman moves \(6.0 m\) to the other end of the raft, and the raft moves away from the pier by \(3m\), the woman moves a total of: \(distance = 6 - 3 = 3m\) Answer to part (b): The woman has moved 3 m relative to the pier.

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 91影视!

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

In the railroad freight yard, an empty freight car of mass \(m\) rolls along a straight level track at \(1.0 \mathrm{m} / \mathrm{s}\) and collides with an initially stationary, fully loaded boxcar of mass 4.0m. The two cars couple together on collision. (a) What is the speed of the two cars after the collision? (b) Suppose instead that the two cars are at rest after the collision. With what speed was the loaded boxcar moving before the collision if the empty one was moving at \(1.0 \mathrm{m} / \mathrm{s} ?\)
In a circus trapeze act, two acrobats actually fly through the air and grab on to one another, then together grab a swinging bar. One acrobat, with a mass of \(60 \mathrm{kg},\) is moving at \(3.0 \mathrm{m} / \mathrm{s}\) at an angle of \(10^{\circ}\) above the horizontal and the other, with a mass of $80 \mathrm{kg},\( is approaching her with a speed of \)2.0 \mathrm{m} / \mathrm{s}$ at an angle of \(20^{\circ}\) above the horizontal. What is the direction and speed of the acrobats right after they grab on to each other? Let the positive \(x\) -axis be in the horizontal direction and assume the first acrobat has positive velocity components in the positive \(x\)- and \(y\)-directions.
A sled of mass \(5.0 \mathrm{kg}\) is coasting along on a frictionless ice- covered lake at a constant speed of \(1.0 \mathrm{m} / \mathrm{s} .\) A \(1.0-\mathrm{kg}\) book is dropped vertically onto the sled. At what speed does the sled move once the book is on it?
A cannon on a railroad car is facing in a direction parallel to the tracks. It fires a \(98-\mathrm{kg}\) shell at a speed of \(105 \mathrm{m} / \mathrm{s}\) (relative to the ground) at an angle of \(60.0^{\circ}\) above the horizontal. If the cannon plus car have a mass of \(5.0 \times 10^{4} \mathrm{kg},\) what is the recoil speed of the car if it was at rest before the cannon was fired? [Hint: A component of a system's momentum along an axis is conserved if the net external force acting on the system has no component along that axis.]
A 1500-kg car moving east at \(17 \mathrm{m} / \mathrm{s}\) collides with a 1800-\(\mathrm{kg}\) car moving south at \(15 \mathrm{m} / \mathrm{s}\) and the two cars stick together. (a) What is the velocity of the cars right after the collision? (b) How much kinetic energy was converted to another form during the collision?
See all solutions

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Read Explanation

Fluids

Read Explanation

Thermodynamics

Read Explanation

Dynamics

Read Explanation

Radiation

Read Explanation

Geometrical and Physical Optics

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.