Science Project: How to Add Vector Toys

Vector toys, or ramp walkers, walk to the end of a ramp and then stop just before falling off. A weight, attached by a string, hangs over the edge of the ramp and pulls the toy forward. The force consists of two vectors: one vector pulls the toy forward and the other pulls straight down, causing friction. As the toy gets closer to the edge, the vector pulling forward diminishes and the vector pulling down increases. Eventually, the force pulling the walker forward is less than the drag of friction caused by the downward vector, and the toy stops, right at the edge. Adding vector skills is suitable for grades seven through ten.

Things You'll Need

• Ramp walker toy
• String
• Weight
• Scissors
• Ramp
• Protractor
• Scale
• Calculator

Instructions

Making the Toy Walk

1. Tie a weight to a string. The minimum weight will be determined by experimentation later, but for demonstration purposes, try something roughly half the weight of the toy or lighter. Binder clips, pencils and erasers work well.

2. Hold the string up to the top of the of the desk surface allowing the weight to hang down. Adjust the length of the string so that the weight hangs an inch off the floor. Cut the string at that length.

3. Tie the string to the front of the vector toy.

4. Place the ramp walker as far away from the edge as possible and still allow the weight to hang freely. Release the ramp walker and watch it stop at the edge of the desk.

Calculate the Minimum Required Mass

1. Untie the string from the front of the ramp walker.

2. Place the ramp walker on a ramp. Raise the ramp until the walker starts moving forward.

3. Measure the angle between the ramp and the desk with a protractor.

4. Calculate the sine of the ramp angle using the scientific calculator.

5. Weigh the ramp walker on a gram scale.

6. Calculate the friction force by multiplying the weight of the toy times the force of gravity; for this purpose, use 10 meters per seconds squared as the force of gravity.

7. Calculate the pulling force generated by the angle of the ramp in Newtons by multiplying the friction force by the sine of the ramp angle.

8. Calculate the weight required to pull the toy forward on a flat surface, against the force of friction. You want the toy to stop before falling off the edge so use the string angle of 4 degrees. If the toy gets any closer to the edge before the pulling stops, momentum may carry it over the edge. The string angle is the angle between the string and the body of the ramp walker toy.

9. Use the friction force calculated for the toy's weight previously; multiply the friction force by the sine of 4 degrees to get the pulling force required. Divide the pulling force by the force of gravity, 10 meters per second squared, to find the weight needed, in kilograms, to exert the required force.

References

• Exploratorium: Vector Toy

Resources

• Physics Classroom: Describing Motion with Words