AP Physics C lab involving incline planes featuring motion laws

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SUMMARY

The forum discussion centers on a physics problem involving a ping pong ball rolling off an incline plane and hitting a specific target on the floor. The setup includes a table 90cm tall and a horizontal distance of 46cm from the ball's starting point. Key equations discussed include the conservation of energy, specifically mgh = (1/2)mv^2, and the need to calculate the appropriate ramp height for the ball to land on a 2cm diameter dot. The participants emphasize the importance of determining the angle and velocity of the ball's trajectory to solve for the ramp height effectively.

PREREQUISITES
  • Understanding of basic kinematics and projectile motion
  • Familiarity with conservation of energy principles
  • Knowledge of rotational mechanics and moment of inertia
  • Ability to apply mathematical equations to physical scenarios
NEXT STEPS
  • Study the principles of projectile motion to determine the trajectory of the ping pong ball
  • Learn about the conservation of energy in mechanical systems
  • Explore the calculations for moment of inertia and angular velocity
  • Investigate the effects of mass on the motion of rolling objects
USEFUL FOR

Students studying AP Physics, educators teaching mechanics, and anyone interested in practical applications of physics concepts involving motion and energy conservation.

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Homework Statement



A dot on the floor with a diameter of 2cm.

A table that is at a distance of 46cm horizontally from the center of said dot.

The table is 90cm tall.

The meat of the problem: A ping pong ball rolls off an incline plane (a wooden board) that is on top of the table. The incline plane must be some height. The ball must hit the table before it flies off the edge of the table. The ping pong ball must hit the dot on the floor.

Homework Equations



These are the formulas I believe to lead me to the answer:Rotational energy: 1/2(moment of inertia)(angular velocity)^2

mgh = (1/2)mv^2

The Attempt at a Solution



At first I thought a simple formula of v=2√(height1)(height2) would solve it, until I realized that it is only for objects having no mass...

I am stumped on how to go about finding the appropriate variables in finding the height of the ramp.

Primarily finding angular velocity
 
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Unless I am misunderstanding the setup, it seems to me rotational mechanics won't do you much good.

Wouldn't it be better to find the velocity/angle that the ping pong ball would have to bounce off the table to land on the dot and then work backwards to figure out the ramp height?
 
Dont I have to account for the mass of the ping pong ball?
 

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