AP Physics - Collisions in Multiple Dimensions

Dan Fullerton
16 Oct 201207:52
EducationalLearning
32 Likes 10 Comments

TLDRIn the video, Dan Fullerton discusses a two-dimensional collision problem involving a Q ball (mass 0.17 kg) and an eight ball (mass 0.16 kg). Initially, the Q ball has a velocity of 3 m/s in the X direction, while the eight ball is at rest. After the collision, the Q ball is deflected 30° and the eight ball 45°. Using the conservation of momentum and trigonometry, Fullerton calculates the post-collision velocities: the Q ball at 2.14 m/s and the eight ball at 2.06 m/s. This comprehensive analysis demonstrates how to handle multi-dimensional collision problems effectively.

Takeaways
  • 📌 The problem discussed is a two-dimensional collision involving two balls, the Q ball and the eight ball.
  • 📐 The Q ball has a mass of 0.17 kg and is given an initial velocity of 3 m/s in the X direction.
  • ⚽️ The eight ball has a mass of 0.16 kg and is initially at rest before the collision.
  • 🔄 After the collision, the Q ball is deflected 30° in the opposite direction, and the eight ball is deflected 45° from the Q ball's original path.
  • 🎯 To solve the problem, a momentum table is set up for both the X and Y directions, considering the unknown velocities after the collision.
  • 📈 The X momentum of the Q ball before the collision is 0.51 kg·m/s, and the eight ball's initial momentum is zero.
  • 📊 The conservation of momentum law is applied to establish equations for both the X and Y components of the balls' velocities after the collision.
  • 🔢 The Y momentum equations are used to derive a relationship between the velocities of the Q and eight balls.
  • 🧠 By solving the system of equations, the final velocities of both balls after the collision are determined: the eight ball at 2.06 m/s and the Q ball at 2.14 m/s.
  • 📚 The process involves using trigonometric functions to calculate the X and Y components of the velocities after the collision.
  • 🌐 For further help or information on analyzing collisions in multiple dimensions, A+ Physics website is recommended.
Q & A

  • What is the main topic of the video?

    -The main topic of the video is the analysis of collisions in multiple dimensions, specifically a two-dimensional collision between a Q ball and an eight ball.

  • What are the masses of the Q ball and the eight ball?

    -The mass of the Q ball is 0.17 kg, and the mass of the eight ball is 0.16 kg.

  • What is the initial velocity of the Q ball before the collision?

    -The initial velocity of the Q ball before the collision is 3 m/s in the X direction.

  • How are the balls deflected after the collision?

    -After the collision, the Q ball is deflected 30° in the opposite direction, and the eight ball is deflected 45° from the Q ball's previous path.

  • What is the law used to solve for the velocities of the balls after the collision?

    -The law of conservation of momentum is used to solve for the velocities of the balls after the collision.

  • What is the significance of setting up a momentum table for the X and Y directions?

    -Setting up a momentum table for the X and Y directions helps to organize the known and unknown values for each direction, allowing for a systematic approach to solving the problem.

  • How is trigonometry used in this problem?

    -Trigonometry is used to determine the X and Y components of the balls' velocities after the collision, taking into account the angles of deflection.

  • What are the initial momenta of the Q ball and the eight ball before the collision?

    -The initial momentum of the Q ball before the collision is 0.51 kg·m/s, while the eight ball, being at rest, has an initial momentum of 0.

  • What are the final velocities of the Q ball and the eight ball after the collision?

    -After the collision, the Q ball has a velocity of 2.14 m/s, and the eight ball has a velocity of 2.06 m/s.

  • How does the video demonstrate the conservation of momentum?

    -The video demonstrates the conservation of momentum by showing that the total momentum before the collision equals the total momentum after the collision, both in the X direction and the Y direction.

  • What resource is recommended for more help or information on analyzing collisions in multiple dimensions?

    -For more help or information on analyzing collisions in multiple dimensions, the video recommends checking out A+ Physics.com.

Outlines
00:00
📚 Introduction to Multidimensional Collisions

In this segment, Dan Fullerton introduces the concept of collisions in multiple dimensions, specifically focusing on a two-dimensional collision problem. The scenario involves Bert striking a Q ball of mass 17 kg, giving it a velocity of 3 m/s in the X direction, which then collides with an 8 ball of mass 16 kg that was initially at rest. After the collision, the Q ball is deflected 30° in the opposite direction, and the 8 ball is deflected 45° from the Q ball's original path. The task is to find the velocities of both the Q and 8 balls after the collision. Dan begins by setting up a momentum table for the X direction, using the given masses and velocities to calculate the initial momentum of the balls. He then explains the need to use trigonometry to determine the X components of the balls' velocities after the collision. The process is repeated for the Y direction, emphasizing the conservation of momentum in both dimensions.

05:01
🧮 Solving the Collision Problem

In this part, Dan Fullerton continues the problem-solving process by diving into the algebra and mathematics required to find the velocities of the Q and 8 balls after the collision. He starts by setting up equations based on the conservation of momentum in both the X and Y directions, using the previously calculated momentum components. Dan then solves the Y momentum equation for the Q ball's velocity (VC), finding a relationship between VC and the 8 ball's velocity (V8). With this relationship, he substitutes VC into the X momentum equation to solve for V8, determining the velocity of the 8 ball to be 2.06 m/s. Using this result, Dan calculates the velocity of the Q ball to be 2.14 m/s after the collision. The segment concludes with Dan emphasizing the importance of using the law of conservation of momentum and keeping track of the X and Y components when analyzing collisions in multiple dimensions. He encourages viewers to seek further help or information at A+ Physics.com and wishes them a great day, highlighting his commitment to educational support.

Mindmap
Keywords
💡collisions
Collisions, in the context of the video, refer to the impact between two balls, specifically a Q ball and an eight ball, in a two-dimensional space. The concept is central to understanding the changes in momentum and velocity that occur when objects interact. The video uses the example of a Q ball striking an eight ball to illustrate how collisions can alter the direction and speed of the objects involved.
💡momentum
Momentum is a physical quantity that represents the motion of an object, defined as the product of an object's mass and velocity. In the video, the conservation of momentum is a fundamental principle used to solve for the unknown velocities of the Q ball and the eight ball after the collision. The concept is applied in both the X and Y directions to account for the two-dimensional nature of the collision.
💡dimensions
Dimensions refer to the number of degrees of freedom in the motion of objects. In the video, the term 'multiple dimensions' is used to describe the two-dimensional plane in which the collision occurs, meaning that the motion and collision are analyzed in both the X and Y directions. This allows for a more comprehensive understanding of the collision effects, as objects can move and collide in different directions horizontally and vertically.
💡mass
Mass is a measure of the amount of matter in an object, and it is a crucial factor in determining the momentum and behavior of objects during collisions. In the video, the masses of the Q ball (0.17 kg) and the eight ball (0.16 kg) are given, and they are used in calculations to determine the velocities of the balls after the collision.
💡velocity
Velocity is a vector quantity that describes the speed of an object in a specific direction. In the context of the video, the velocities of the Q ball and the eight ball before and after the collision are key to understanding the dynamics of the event. The video involves calculating the final velocities of both balls after the collision using the conservation of momentum principle.
💡conservation of momentum
The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In the video, this principle is used to set up equations that allow the calculation of the unknown velocities of the balls after the collision. By ensuring that the total momentum before the collision equals the total momentum after the collision, the problem can be solved for the unknown quantities.
💡trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, and it is used in the video to determine the components of the velocities in the X and Y directions after the collision. By applying trigonometric functions like cosine and sine, the video calculates the X and Y components of the velocities of the Q ball and the eight ball.
💡components
In the context of the video, components refer to the individual parts of a vector quantity that are analyzed separately along different axes. The components of the velocities of the Q ball and the eight ball in the X and Y directions are calculated to understand the effects of the collision in a two-dimensional space.
💡system of equations
A system of equations is a set of mathematical equations that are solved simultaneously. In the video, the conservation of momentum in both the X and Y directions results in a system of two equations with two unknowns (the velocities of the Q ball and the eight ball after the collision). By solving this system, the unknown velocities can be determined.
💡A+ Physics
A+ Physics is a reference to a resource mentioned in the video for those seeking further help or information on the topic of collisions in multiple dimensions. It suggests a website or educational material that provides additional learning material on physics concepts, including the analysis of collisions.
Highlights

Dan Fullerton discusses collisions in multiple dimensions.

A problem involving a two-dimensional collision is presented.

Bert strikes a Q ball of mass 0.17 kg, giving it a velocity of 3 m/s in the X direction.

The Q ball then strikes an 8 ball of mass 0.16 kg, which was previously at rest.

After the collision, the 8 ball is deflected 45° from the Q Ball's previous path.

The Q ball is deflected 30° in the opposite direction after the collision.

The goal is to find the velocity of the Q ball and the 8 ball after the collision.

Momentum table is set up to solve the problem, starting with the X direction.

Trigonometry is used to determine the X components of the balls' velocities after the collision.

The total momentum before and after the collision must be the same due to the law of conservation of momentum.

The Y momentum is also considered, as the balls may have velocities in the Y direction after the collision.

Two equations are derived from the conservation of momentum in both the X and Y directions.

The system of equations is solved to find the unknown velocities of the Q and 8 balls.

The final velocities are calculated to be 2.06 m/s for the 8 ball and 2.14 m/s for the Q ball.

The method demonstrates how to analyze collisions in multiple dimensions using conservation of momentum.

For more help or information, A+ Physics is recommended as a resource.

The presentation is engaging and informative for those interested in physics problems.

Transcripts

Browse More Related Video

AP Physics Workbook 5.J Explosions

AP PHYSICS 1: Unit 5 FRQ 2 (AP Physics Classroom)

AP Physics B Kinematics Presentation #77

AP Physics B Kinematics Presentation #35

Two Dimensional Motion Problems - Physics

AP Physics B Kinematics Presentation #32

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Physics EducationCollision DynamicsMomentum ConservationVector AnalysisProblem SolvingTwo-DimensionalEducational ContentTechnical ExplanationPhysics ProblemLearning Resource