FINAL CHALLENGE

In our FINAL challenge of the year, Ally and I teamed up to predict where to compress two different springs so that 2 carts of equal mass would come off with the same velocity. This challenge was riveting as we racked our brains to try and figure out how to use different equations we've learned this past unit. 

Spring Constants

Red cart= 84N/M

Blue cart=112 N/M

Mass

Red cart= .55kg

blue cart= .542 kg

Initially, we plugged in 1m/s for the velocity in the equation: Ek=1/2mv^2 but our numbers were off so instead we tried .5 m/s and it was much more accurate. 

Red Cart

Ek=1/2mv^2

Ek=1/2 (.551)(.5)^2

Ek=.2755J

Blue Cart

Ek=1/2mv^2

Ek=1/2(.542)(.5)^2

Ek=.07J

B=.271

.005=x^2

B=.069 m

R=.2755=1/2(84)x^2

x=.08m

Test for red: 1m/1sec

Test for blue: 1m/1sec

Ally and I fired up the old Capstone, arranged the motion detectors, and tested our predictions. For the red cart we pulled the spring back .08m and for the blue cart we pulled it back .069m. 

We were right on the money!

The velocities were the exact same and Ally & I were no longer amateur physicists. This final challenge was incredibly rewarding because right from the get go, we knew how to incorporate familiar equations and convert cm to meters and grams to kg. It was a great challenge to end on.