/*! 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 67 Two identical objects with the s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 67

Two identical objects with the same initial speed collide and stick together. If the composite object moves with half the initial speed of either object, what was the angle between the initial velocities?

Short Answer

Expert verified
The angle between the initial velocities is \(\theta = \cos^{-1}(1/2)\), which is approximately 60 degrees.

Step by step solution

01

Understand the conservation of momentum

The conservation of momentum implies that the total momentum before the collision is equal to the total momentum after the collision. In this case, since the objects have the same mass and speed before collision, their total momentum is \(2Mv\), where \(v\) is the initial speed and \(M\) is the mass.
02

Calculate the total momentum after collision

After the collision, the objects stick together and move with half the initial speed, therefore, their total speed is \(Mv/2\), and since they are moving together their mass is now \(2M\), hence the total momentum after collision is \(2M * (v/2) = Mv\).
03

Equate the momentum before and after collision

To find the angle of collision, equate the momentum before and after collision. This gives us the following equation: \(2Mv = 2Mv \cos(\theta)\), where \(\theta\) is the angle between the vectors of initial velocities.
04

Find the angle

Solving for \(\theta\), we get \(\theta = \cos^{-1}(1/2)\).

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

Model rocket motors are specified by giving the impulse they "provide, in \(\mathrm{N} \cdot \mathrm{s}\), over the entire time the rocket is firing. The table below shows the results of rocket-motor tests with different motors used to launch rockets of different masses. Determine two data-based quantities that, when plotted against each other, should give a straight line and whose slope should allow you to determine \(g .\) Plot the data, establish a best-fit line, and determine \(g\). Assume that the maximum height is much greater than the distance over which the rocket motor is firing, so you can neglect the latter. You're also neglecting air resistance- -but explain how that affects your experimentally determined value for \(g\). $$\begin{array}{|l|r|r|r|r|r|} \hline \text { Impulse, } J(\mathrm{N} \cdot \mathrm{s}) & 4.5 & 7.8 & 4.5 & 7.8 & 11 \\ \hline \begin{array}{l}\text { Rocket mass }(\mathrm{g}) \\ \text { (including motor) }\end{array} & 180 & 485 & 234 & 234 & 485 \\ \hline \begin{array}{l}\text { Maximum height } \\\\\text { achieved (m) }\end{array} & 22 & 13 & 19 & 51 & 23 \\\\\hline\end{array}$$

Wildlife biologists fire \(20-\mathrm{g}\) rubber bullets to stop a rhinoceros charging at \(0.81 \mathrm{m} / \mathrm{s} .\) The bullets strike the rhino and drop vertically to the ground. The biologists' gun fires 15 bullets each second, at \(73 \mathrm{m} / \mathrm{s}\), and it takes \(34 \mathrm{s}\) to stop the rhino. (a) What impulse does each bullet deliver? (b) What's the rhino's mass? Neglect forces between rhino and ground.

Two identical trucks have mass \(5500 \mathrm{kg}\) when empty, and the maximum permissible load for each is 8000 kg. The first truck, carrying \(3800 \mathrm{kg},\) is at rest. The second truck plows into it at 65 \(\mathrm{km} / \mathrm{h},\) and the pair moves away at \(27 \mathrm{km} / \mathrm{h} .\) As an expert witness, you're asked to determine whether the second truck was overloaded. What do you report?

Explain why a high jumper's center of mass need not clear the bar.

A car moving at speed \(v\) undergoes a one-dimensional collision with an identical car initially at rest. The collision is neither elastic nor fully inelastic; \(5 / 18\) of the initial kinetic energy is lost. Find the velocities of the two cars after the collision.
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Wave Optics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Electrostatics

Read Explanation

Electromagnetism

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.