Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 72

For a system of three particles moving along a line, an observer in a laboratory measures the following masses and velocities. What is the velocity of the \(\mathrm{CM}\) of the system? $$\begin{array}{cc}\hline \text { Mass }(\mathrm{kg}) & v_{x}(\mathrm{m} / \mathrm{s}) \\\\\hline 3.0 & +290 \\\5.0 & -120 \\\2.0 & +52 \\\\\hline\end{array}$$

Short Answer

Expert verified
Answer: The velocity of the center of mass for the system of three particles is 37.4 m/s.

Step by step solution

01

Calculate the total mass of the system

We need to calculate the total mass of the system: \(M = \sum_{i=1}^{3} m_i\). Using the given values, we have: $$M = 3.0\,\text{kg} + 5.0\,\text{kg} + 2.0\,\text{kg} = 10.0\,\text{kg}$$
02

Calculate the total momentum of the system

Now, we need to calculate the total momentum of the system: \(p_{total} = \sum_{i=1}^{3} m_iv_i\). Using the given values, we have: $$p_{total} = (3.0\,\text{kg}\cdot 290\,\text{m/s}) + (5.0\,\text{kg}\cdot -120\,\text{m/s}) + (2.0\,\text{kg}\cdot 52\,\text{m/s}) = 870\,\text{kg·m/s} - 600\,\text{kg·m/s} + 104\,\text{kg·m/s} = 374\,\text{kg·m/s}$$
03

Calculate the velocity of the center of mass

Finally, we can use the formula \(v_{CM} = \frac{p_{total}}{M}\) to calculate the velocity of the center of mass. $$v_{CM} = \frac{374\,\text{kg·m/s}}{10.0\,\text{kg}} = 37.4\,\text{m/s}$$ The velocity of the center of mass of the system is \(37.4\,\text{m/s}\).

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 3.0-kg body is initially moving northward at \(15 \mathrm{m} / \mathrm{s}\) Then a force of \(15 \mathrm{N},\) toward the east, acts on it for 4.0 s. (a) At the end of the 4.0 s, what is the body's final velocity? (b) What is the change in momentum during the \(4.0 \mathrm{s} ?\)
Two pendulum bobs have equal masses and lengths \((5.1 \mathrm{m}) .\) Bob \(\mathrm{A}\) is initially held horizontally while bob \(\mathrm{B}\) hangs vertically at rest. Bob A is released and collides elastically with bob B. How fast is bob B moving immediately after the collision?
A \(58-\) kg astronaut is in space, far from any objects that would exert a significant gravitational force on him. He would like to move toward his spaceship, but his jet pack is not functioning. He throws a 720 -g socket wrench with a velocity of \(5.0 \mathrm{m} / \mathrm{s}\) in a direction away from the ship. After \(0.50 \mathrm{s}\), he throws a 800 -g spanner in the same direction with a speed of \(8.0 \mathrm{m} / \mathrm{s} .\) After another $9.90 \mathrm{s}\(, he throws a mallet with a speed of \)6.0 \mathrm{m} / \mathrm{s}$ in the same direction. The mallet has a mass of \(1200 \mathrm{g}\) How fast is the astronaut moving after he throws the mallet?
In a nuclear reactor, a neutron moving at speed \(v_{\mathrm{i}}\) in the positive \(x\)-direction strikes a deuteron, which is at rest. The neutron is deflected by \(90.0^{\circ}\) and moves off with speed $v_{\mathrm{i}} / \sqrt{3}\( in the positive \)y\(-direction. Find the \)x\(- and \)y$-components of the deuteron's velocity after the collision. (The mass of the deuteron is twice the mass of the neutron.)
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 \(1.0 \mathrm{m} / \mathrm{s} ?\)
See all solutions

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Read Explanation

Classical Mechanics

Read Explanation

Waves Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Engineering Physics

Read Explanation

Modern 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