This activity was inspired by an outreach activity for high school girls by Liz Holden in Wisconsin. Initial tinkering by Eric Freudenthal. Refinements due to suggestions and criticism from Adrian Veliz, Vladik Kreinovich, and Gabby Gandara.
Precursor activity:students should be introduced line drawing and ball bounce simulation using summation in f#. Link to web-based impact-f# environment: http://tinyurl.com/impact-fsharp
- Determine student weight in Newtons
- Discuss how you have the same “mass” in kilograms, on the moon. But you weigh less. That weight is called force, and is measured in Newtons.
- The gravity on earth (to convert to “Newtons”) is 9.8. It’s less on the moon.
- Weigh student, mulitply, and post g, both mass (explicitly in kg) and weight (in N), and equation F=mg.
- Determine & post rope length in meters. Ideally the rope has a swing-seat at bottom hung from a tension scale in Newtons.
- Attach tension scale using 2nd rope near end of vertical rope (at connection between scale & seat).
- Examine force to pull student from resting position by pulling tension scale.
- Student hangs on rope (or sits in swing seat; if if hung from a tension scale in N, use it to verify earlier calculation). Mark rest position with tape on floor.
- Another student pulls her 1/10 of the rope’s length off center by pulling tension scale horizontally. Measure force. Notice that it’s 1/10 of her weight
- If the vertical rope also includes a tension scale, then expose students to vector decomposition by observing that ropeTension2 = weight2 + horizontalTension2 and relating this to the pythagorean theorem.
- Now 1/5 of rope’s length. Notice same ratio.
- Post equation F = m * p / l
- Reflection: Draw circle and mention that this nice ratio only works near the bottom (examine absurdity at ¼ revolution)
- Let girl swing as pendulum and measure period
- Measure time for 10 full swings and divide. Measure & record for large and small amplitude. Notice same period.
- Measure with 2 girls on rope (also know their mass & weight). Measure & record longer period.
- Now simulate
- Indicate f=ma. Discuss how related to f=mg (where g=accel of gravity from ball bounce simulation).
- Work through piecewise approximaton idea
- v=velocity, p=position
- from earlier experiement (posted), we know that we can compute force from position, weight, and rope length
- f=w*p/l (where w=weight, l = rope length and p = position from resting spot)
- we can compute acceleration from force
- acceleration = force/mass.
- so, for every 1/10 second
- change in velocity = acceleration / 10
- change in position = velocity / 10
- so we can repeatedly compute
- velocity = velocity + changeInVelocity
- positoin = position + changeInPosition
- Set parameters and build program quickly referencing these results
- Plot only position v. time; measure period. (have students predict first) Check that matches measurements
- Plot position and velocity v. time. (have students predict first) Notice relationship in time.
- Plot position v. velocity (hove students predict first). Notice that elipse. Discuss why.
p <- 1.0 // inhtial horizontal position
v <- 0.0 // initial velocity
t <- 0.0 // initial time
m <- 50.0 // kg
g <- 9.8 // acceleration of gravity
l <- 7.0 // rope length
w <- m * g // weight, in Newtons
let dt = 0.1
while t < 10. do
dot (t*10.,v*50.0) green // velocity
dot (t*10.,p*50.0) orange // position
dot (v*50.0, p*50.0) red // an elipse!!
f <- -w * p / l // force in horizontal direction (Newtons)
a <- f / m // acceleration in (horizontal direction)
v <- v + a*dt // next velocity
p <- p + v*dt // next position
t <- t + dt // next time