It is always fun to think up new activities for my second year AP Physics students. We do 55 labs in the first year course, so the second year is spent mostly solving problems.
Today, I told them to jump off the force plate, find the impulse the plate exerted on them, calculate how long they should spend in the air, and compare this calculated time with the measured value. I told them that they could have one person jump or they could all jump themselves or some combination.
I was pleased with this activity for many reasons.
- I told the students what to do, but not how to do it.
- The students immediately began discussing it AMONG THEMSELVES!
- I was able to sit back and listen to their conversation and look for opportunities to ask probing and irritating questions to check their understanding.
After their first attempt, the students calculated a 35% relative error. They actually asked me if that was “good enough”. High school students can be so amusing. I withheld comment except to challenge them to do better.
Here are some things that we learned.
1. The force that the force plate exerts upon you is not the critical value, but rather the net force. The force sensor can be “zeroed” with nothing on it or with the person standing on it. At first, the students tried to subtract the effect of gravity from the calculations. On the second try, they zeroed the scale with the person standing on it to get the force plate to read net force (no subtraction necessary).
2. Jumping is a complex motion. You lower yourself by bending your knees and then jump into the air by straightening your legs. The graph below shows what happens if the students begin collecting data before they lower themselves for the jump. There is an additional section of the graph that dips below the x-axis (near 0.6 seconds in this example). This is confusing to students and introduces the possibility that the rebound of the scale will affect the reading.
Data showing up and down motion of the jump.
Once they had some good data, zeroed the force plate while standing on it, and lowered themselves before collecting data, this is the analysis.
First, determine the impulse by highlighting the time interval and selecting the INTEGRAL button.
Determine the weight of the person from the graph and calculate their mass.
Use these values to calculate the launch velocity.
Determine the calculated “time of flight”.
Compare the calculated time with the time from the graph.
Determining Time of Flight
Deciding exactly where to place the brackets for this time interval led to an interesting discussion. We decided to place them as the force value passed through zero. This led to very good results but I am not sure this was the best choice. There seems to be some “rebound” action going on with the sensor. My force plate is quite old. You can see from the graph that had we placed the brackets as they reached the -603 N mark, our measured time would have been shorter. We read the time interval from the delta t in parentheses in the lower left corner of the graph.
The value of t=0.40 matched our predicted time of flight very well.
The activity led to lots of good discussion and was reasonably good in terms of error. What else could you wish from a physics lab?
As always, your helpful comments are always welcome.