On this challenge, we were tasked with trying to launch two carts with different spring constants at the same velocity. To do this we had to thoroughly understand the conceptual elements of energy conservation.
We began by determining the energy conservation equation.
Eel = Ek
We then manipulated the equation:
1/2kx^2 = 1/2mv^2
Through given information and initial calculations, we gathered the following information:
Red Spring Constant: 84Nm
Blue Spring Constant: 112Nm
Mass of cart: .542Kg
We knew that we had to get the same velocity for both carts so we decided to use .5m/s for our intended velocity. From there it was a plug and chug problem for both carts to find the x value.
Red Cart:
1/2kx^2 = 1/2mv^2
1/2(84)x^2 = 1/2(.542)(.5)^2
x^2 = .0016
x = 4cm
Blue Cart:
1/2kx^2 = 1/2mv^2
1/2(112)x^2 = 1/2(.542)(.5)^2
x^2 = .012
x = 3.5cm
From here, we tested our predictions on the track. The velocity of the red cart was .44m/s and the blue cart was .45m/s. These numbers left us with just a 2% margin of error, one of our lowest ones yet!
