/*! 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 92 A ball moving with velocity of \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 92

A ball moving with velocity of \(9 \mathrm{~m} / \mathrm{s}\) collides with another similar stationary ball. After the collision both the balls move in directions making an angle of \(30^{\circ}\) with the initial direction. After the collision their speed will be (a) \(2.6 \mathrm{~m} / \mathrm{s}\) (b) \(5.2 \mathrm{~m} / \mathrm{s}\) (c) \(0.52 \mathrm{~m} / \mathrm{s}\) (d) \(52 \mathrm{~m} / \mathrm{s}\)

Short Answer

Expert verified
The speed of each ball after the collision would be approximately \(5.2 \mathrm{~m/s}\), thus the correct answer is (b).

Step by step solution

01

Identify the Initial Condition

Before the collision, the moving ball has a velocity of \(9 \mathrm{~m} / \mathrm{s}\), while the stationary ball has a velocity of \(0 \mathrm{~m} / \mathrm{s}\). This gives an initial momentum of \(9m\), where \(m\) is the mass of the balls.
02

Set Up the Conservation of Momentum

The principle of conservation of momentum states that the total momentum before and after the collision should be the same. Thus, we set up the equation \(m \cdot (9 \mathrm{~m/s}) = 2m \cdot v \cdot \cos(30^{\circ})\), where \(v\) is the velocity of the balls after collision.
03

Solve the Equation

Solving the equation for \(v\) gives us \(v = \frac{9}{2\cos(30^{\circ})} \approx 5.2 \mathrm{~m} / \mathrm{s}\).
04

Match with the Correct Option

Option (b) matches our calculated velocity, thus (b) is the correct answer.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Collision
In physics, a collision is an event where two or more bodies exert forces on each other over a very short period of time. There are different types of collisions, but the main ones are elastic and inelastic. In an elastic collision, both momentum and kinetic energy are conserved. Meanwhile, in an inelastic collision, only momentum is conserved, meaning some kinetic energy is turned into other forms of energy, such as heat or sound.

**Types of Collisions:**
  • **Elastic Collision:** Both momentum and kinetic energy are conserved.
  • **Inelastic Collision:** Only momentum is conserved. Kinetic energy is not.
  • **Perfectly Inelastic Collision:** The objects stick together post-collision, losing more kinetic energy.
In the exercise you encountered, the collision is between two balls where momentum is conserved. The balls move away from each other at an angle after colliding, showing a typical collision scenario.
Velocity
Velocity is a vector quantity that describes the speed of an object in a particular direction. In the exercise, the ball had an initial velocity of \(9 \mathrm{~m/s}\) before it collided with the stationary ball. After the collision, the new velocities of both balls were calculated.

**Key Points About Velocity:**
  • **Direction Matters:** Unlike speed, velocity includes direction.
  • **Initial versus Final Velocity:** The initial velocity is what an object starts with, and final velocity is what it ends up with after an event like a collision.
  • **Conservation Impacts:** After a collision, stable systems will often show conserved total velocities adjusted by direction and other factors.
The calculated velocities of \(5.2 \mathrm{~m/s}\) post-collision for each ball show how energy is distributed equally in both directions.
Angle of Motion
The angle of motion in a physics problem is crucial to understand because it helps determine the final direction of objects after events like collisions. In this exercise, both balls moved at an angle of \(30^\circ\) relative to the original movement path of the first ball.

**Understanding Angles in Motion:**
  • **Direction Change:** Angles signify how much an object鈥檚 path changes post-event.
  • **Influences Calculation:** Angles are used in conservation laws to calculate exact velocities and momenta.
  • **Representation of Forces:** The angle shows how forces are distributed across different axes.
In calculations, it is crucial to convert angles into radians as needed for using trigonometric functions. Here, the cosine of \(30^\circ\) is used to find the post-collision velocity, demonstrating how angles directly influence the physics calculations.
Physics Problem Solving
Physics problem solving involves a structured approach to tackle complex scenarios with logical and mathematical techniques. The process requires understanding the given information and applying relevant physics laws, such as the conservation of momentum.

**Effective Problem-Solving Approach:**
  • **Identify Known and Unknown Variables:** Always start by listing what is already known and what needs to be found.
  • **Apply Relevant Principles:** Choose the right physics laws鈥攃onservation laws, in this case.
  • **Construct Equations From Principles:** Use the principles to build equations that relate known and unknown variables.
  • **Solve Systematically:** Break down the big problem into manageable parts to simplify the mathematical process.
By setting up and solving the equation \(m \cdot (9 \mathrm{~m/s}) = 2m \cdot v \cdot \cos(30^{\circ})\), you can effectively find the desired velocities, confirming that problem-solving requires detailed analysis and calculation.

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 uniform chain of length \(\overline{L \text { and mass } M \text { is lying on a smooth table and one third of its length is }}\) hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on to the table is (a) \(M g L\) (b) \(\frac{M g L}{3}\) (c) \(\frac{M g L}{9}\) (d) \(\frac{M g L}{18}\)

The mass of a bucket containing water is \(10 \mathrm{~kg}\). What is the work done in pulling up the bucket from a well of depth \(10 \mathrm{~m}\) if water is pouring out at a uniform rate from a hole in it and there is loss of \(2 k g\) of water from it while it reaches the top \(\left(g=10 \mathrm{~m} / \mathrm{sec}^{2}\right)\) (a) \(1000 J\) (b) \(800 J\) (c) \(900 J\) (d) \(500 J\)

Three particles \(A, B\) and \(C\) of equal mass are moving with the same velocity \(v\) along the medians of an equilateral triangle. These particle collide at the centre \(G\) of triangle. After collision \(A\) becomes stationary, \(B\) retraces its path with velocity \(v\) then the magnitude and direction of velocity of \(C\) will be adeep Kshetrapal for students at genius academu, Mexwell classes Korba, Gupta classes Kusmumdo

A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical power output will be proportional to (a) \(v\) (b) \(v^{2}\) (c) \(v^{3}\) (d) \(v^{4}\)

A ball \(B_{1}\) of mass \(M\) moving northwards with velocity \(v\) collides elastically with another ball \(B_{2}\) of same mass but moving eastwards with the same velocity \(v\). Which of the following statements will be true (a) \(B_{1}\) comes to rest but \(B_{2}\) moves with velocity \(\sqrt{2} v\) (b) \(B_{1}\) moves with velocity \(\sqrt{2} v\) but \(B_{2}\) comes to rest (c) Both move with velocity \(v / \sqrt{2}\) in north east direction (d) \(B_{1}\) moves eastwards and \(B_{2}\) moves north wards
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Wave Optics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Engineering Physics

Read Explanation

Magnetism

Read Explanation

Famous Physicists

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.