pool billiard can be viewed as elastic collision in 1d if balls are hit head on. professional tables...
DESCRIPTION
Choose your system Is momentum conserved, i.e. are only internal forces acting on the system’s constituents? Draw two diagrams: initial and final situation Choose a coordinate system, in particular + and – directions Apply monetum conservation equations If elastic collision: apply kinetic energy conservation equation Solve for unknowns Check results (reasonable?) Collision Problem SolvingTRANSCRIPT
![Page 1: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/1.jpg)
Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white ball
hits the 8 ball head on (ignore friction)? • White ball slows down, both balls move after collision• White ball stops, 8 ball moves with white ball’s velocity • White bounced back ( neg. velocity), 8 ball moves forward
slowly• White ball stops, 8 ball moves forward with less than
white ball’s velocity
![Page 2: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/2.jpg)
Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Bar tables have a heavier white ball.
What happens if the white ball hits the 8 ball head on (ignore friction)?
• White ball slows down, both balls move after collision• White ball stops, 8 ball moves with white ball’s velocity • White bounced back ( neg. velocity), 8 ball moves forward
slowly• White ball stops, 8 ball moves forward with less than
white ball’s velocity
![Page 3: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/3.jpg)
• Choose your system• Is momentum conserved, i.e. are only internal forces
acting on the system’s constituents?• Draw two diagrams: initial and final situation• Choose a coordinate system, in particular + and –
directions• Apply monetum conservation equations• If elastic collision: apply kinetic energy conservation
equation• Solve for unknowns• Check results (reasonable?)
Collision Problem Solving
![Page 4: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/4.jpg)
Example: Inelastic collision
• Two balls of clay with velocities v1 and v2 collide. After collision they are stuck together, what is their velocity?
![Page 5: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/5.jpg)
Example: Elastic collision
• A white billiard ball of 100g and v=2m/s collides head-on with the 8-ball of 90g at rest.
• What are the velocities of the balls right after the collision?
![Page 6: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/6.jpg)
Example: Collision in 2D
• Neutron hits Helium target elastically with v=6.2 10^5 m/s and Helium off at an angle of 45 degrees.
• What are the velocities (vectors!) of the protons after the collision?
![Page 7: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/7.jpg)
A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug
sits halfway between her and the axis of rotation. The merry-go-round makes a complete revolution once each second.
The gentleman bug’s angular speed is …• … half the ladybug’s. • … the same as the ladybug’s.• … twice the ladybug’s.• … impossible to determine.
![Page 8: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/8.jpg)
A ladybug sits at the outer edge of a merry-go-round, that is turning and slowing down. The vector representing her angular velocity is in
the …
• -z direction• +z direction • +y direction • zero
z
x
y
![Page 9: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/9.jpg)
A ladybug sits at the outer edge of a merry-go-round, that is turning and slowing down.
At the instant shown, the radial component of the bug’s (Cartesian) acceleration is in the …
• -x direction• +y direction • +z direction • Zero
z
x
y
![Page 10: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/10.jpg)
A ladybug sits at the outer edge of a merry-go-round, that is turning and slowing down. At
the instant shown, the bug’s angular acceleration is in the …
• -z direction• -y direction • +y direction • +z direction
z
x
y
![Page 11: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/11.jpg)
A ladybug sits at the outer edge of a merry-go-round, that is turning and slowing down due to
a force exerted on its edge. At the instant shown, the torque on the disc is pointing in …
• -z direction• -y direction • +y direction • +z direction
z
x
yF
![Page 12: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/12.jpg)
A ladybug sits at the outer edge of a merry-go-round, that is turning and slowing down due to
a force exerted on its edge. The angular momentum of the bug is pointing in …
• -z direction• -y direction • +y direction • +z direction
z
x
yF
![Page 13: Pool Billiard can be viewed as elastic collision in 1D if balls are hit head on. Professional tables have balls of equal mass. What happens if the white](https://reader036.vdocuments.us/reader036/viewer/2022082908/5a4d1b307f8b9ab05999b065/html5/thumbnails/13.jpg)
What is A x A ?
• Zero• A• -A• A2