1 / 9

Understanding Center of Mass: Insights from Baseball Bats and Particles Motion

This module explores the concept of the center of mass through engaging Concept Tests. Learn how the center of mass of a baseball bat is influenced by its mass distribution and how it is affected during interactions between two equal-mass particles. Additionally, discover scenarios involving the stacking of blocks, where maintaining the center of mass is essential for stability. This content emphasizes the understanding of motion and mass distribution, making it an essential topic in physics.

kanoa
Télécharger la présentation

Understanding Center of Mass: Insights from Baseball Bats and Particles Motion

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Module 6, Recitation 4 • Concept Problems, Center of Mass

  2. ConcepTest Baseball Bat 1) at the midpoint 2) closer to the thick end 3) closer to the thin end (near handle) 4) it depends on how heavy the bat is Where is center of mass of a baseball bat located?

  3. ConcepTest Baseball Bat 1) at the midpoint 2) closer to the thick end 3) closer to the thin end (near handle) 4) it depends on how heavy the bat is Where is center of mass of a baseball bat located? Since most of the mass of the bat is at the thick end, this is where the center of mass is located. Only if the bat were like a uniform rod would its center of mass be in the middle.

  4. ConcepTest Motion of CM Two equal-mass particles (A and B) are located at some distance from each other. Particle A is held stationary while B is moved away at speed v. What happens to the center of mass of the two-particle system? 1) it does not move 2) it moves away from A with speed v 3) it moves toward A with speed v 4) it moves away from A with speed ½v 5) it moves toward A with speed ½v

  5. ConcepTest Motion of CM Two equal-mass particles (A and B) are located at some distance from each other. Particle A is held stationary while B is moved away at speed v. What happens to the center of mass of the two-particle system? 1) it does not move 2) it moves away from A with speed v 3) it moves toward A with speed v 4) it moves away from A with speed ½v 5) it moves toward A with speed ½v Let’s say that A is at the origin (x = 0) and B is at some position x. Then the center of mass is at x/2 because A and B have the same mass. If v = Dx/Dt tells us how fast the position of B is changing, then the position of the center of mass must be changing like D(x/2)/Dt, which is simply 1/2 v.

  6. ConcepTest Center of Mass (1) (2) XCM 1) higher 2) lower 3) at the same place 4) there is no definable CM in this case The disk shown below in (1) clearly has its center of mass at the center. Suppose the disk is cut in half and the pieces arranged as shown in (2). Where is the center of mass of(2) ascompared to(1) ?

  7. ConcepTest Center of Mass (1) (2) XCM 1) higher 2) lower 3) at the same place 4) there is no definable CM in this case The disk shown below in (1) clearly has its center of mass at the center. Suppose the disk is cut in half and the pieces arranged as shown in (2). Where is the center of mass of(2) ascompared to(1) ? The CM of each half is closer to the top of the semi-circle than the bottom. The CM of the whole system is located at the midpoint of the two semi-circle CM’s, which is higher than the yellow line. CM

  8. Stacking blocks • Key to problem • Keep center of mass of group of blocks within area of lowest block • Might be easiest to start from top and “add” blocks at bottom • Add block at bottom with maximum offset of 1/(2n) • First block at half-block • Second block at quarter-block

  9. 0.5 Stacking blocks 1 2 0.25 3 0.167 4 0.125 5 0.10 6 Offset block by 1/(2n)

More Related