My PBL Project

Materials

This demonstration is very simple. All that is required is the loop the loop machinery which is a specialized product and different ball sizes as long as they fit on the ramp.

Scientific Principle and Formulas

This project deals with conservation of mechanical energy by using the laws of the centripetal force. To prove the required height, we can use the formulas of centripetal force and the law of conversation of energy.

Starting with the law of centripetal force, we need to calculate a speed at the top of the loop that produces an acceleration equal to gravity (9.81 m/s/s). v^2/r=g which means v^2=rg

From the law of conservation of energy the loss of gravitational potential energy as the ball descends is equal to its gain in kinetic energy. mgh=1/2mv^2

Substituting for v2 in the energy equation results in: mgh=1/2mgr

Therefore: h=1/2r

As seen in the above calculations the mass of the ball cancels out and therefore is not a factor. This can be demonstrated by using a ball of a different mass. Since there is some friction involved, you will need to start the ball slightly higher the predicted calculation

Main Concept:

Force and Motion

Deeper Concept:

Transfer between potential and kinetic energy

Newton’s Second Law of Motion

Key Words and Units:

Energy: joule, see the transfer of energy when going up and down the loop

Diameter: meters, distance in circle from radius to endpoint to see size of circle

Force: newton, how much of a force is applied when throwing object down

Height: meters, how high of a distance is the object from the bridge when released

Procedures

As said earlier, this demonstration is very simple. Once the materials are gathered, you will pick a ball and let go of it from different heights by starting from the lowest point. You might ascend an inch or more depending on the size of the loop the loop and will note the point where the ball starts circling the loop entirely. After that, you might want to try different sizes of balls to prove if the mass of the ball has an impact on whether the ball circles the loop the loop.