Trinity Walton Club Activity Archive

Photo by Stas Knop: https://www.pexels.com/photo/red-roller-coaster-1208055/

You are a team of engineers and scientists who are in the process of designing Dublin’s exciting new
rollercoaster attraction “Breakneck”. This ride involves a roller-coaster-like car that can hold 8 passengers, with a mass of 700 kg. This car starts by effectively free falling 60m. The track curves at the bottom so that the car can slide up an 8-m-high hill before hitting a horizontal straightaway 50m long. In the middle of the straightaway is a section of track that is used to slow the car down. You can have the car brake over any or all of the 10m length of that section. Then at the end of the straightaway, a spring-like device hooks under the car. This device changes the car’s
direction just in time to prevent it from apparently falling over the end of the track, sending it back over the braking section again, stopping neatly at the end of the braking area. The car should stop at the end of the braking section, on the way back towards the launch pad.

Your tasks are…

(a) to decide on an appropriate braking force and length of the braking region needed on the
straightaway to stop the car at the right location.

(b) the effective spring constant of the turnaround device.

The car has special accelerometers mounted which relay that information and adjust the braking
force to provide the acceleration you request.

The most important piece of information for these devices is that a person can safely sustain acceleration of 3-4 “g’s” for a brief time, but not more than that.

Materials Needed:

• A string (about 1 meter long)
• A small weight (like a metal washer or a small pendulum bob)
• A protractor
• A ruler or measuring tape
• A stopwatch
• A clamp or a stable support to hang the pendulum from
• Graph paper (optional)

Procedure:

1. Setup the Pendulum: 

• Attach the weight to one end of the string. 

• Secure the other end of the string to a stable support so that it can swing freely. 

2. Measure the Length: 

• Measure the length of the string from the point of suspension to the center of the weight. Record this length as it will be important for calculating potential energy. 

3. Initial Potential Energy: 

• Pull the weight to one side and measure the height from the lowest point of the swing (the point where the weight would be directly below the support) to the initial position. This height will be used to calculate the initial potential energy. 

4. Release and Timing: 

• Release the pendulum without pushing it (let it fall freely). 

• Use the stopwatch to measure the time it takes for the pendulum to complete one full swing (back and forth). 

5. Calculate Potential and Kinetic Energy: 

• The potential energy (PE) at the highest point can be calculated using the formula: 

PE=mgh 

where m is the mass of the weight, g is the acceleration due to gravity (9.81 m/s²), and h is the height measured. 

• The kinetic energy (KE) at the lowest point can be calculated using the formula: 

Ke = 1/2 mv² 

where m is the mass of the weight and v is the velocity of the weight at the lowest point. The velocity can be approximated by measuring the speed of the pendulum bob at the lowest point using the time period of the swing. 

6. Observation and Analysis: 

• Observe that at the highest points of the swing, the pendulum has maximum potential energy and minimal kinetic energy. 

• At the lowest point of the swing, the pendulum has maximum kinetic energy and minimal potential energy. 

• Note how energy is conserved and converted between potential and kinetic forms throughout the motion. 

7. Optional: Graphical Representation: 

• Plot a graph of the pendulum’s height versus time or its speed versus time to visually represent the energy conversion.