Spring Constant Practicum Challenge

Practicum Challenge: Physicists Nikki and Hank

How much does the spring have to be compressed in order for the carts to go at the same velocity?

Our group had to solve for where the two carts needed to be placed to that the carts came out with the same velocity.

Mass:

Blue= .5394 kg

Red= .55 kg

(Note: Our group weighed both carts on a scale in grams, then converted all of the measurements to kilograms)

Spring Constant:

Red= 84 N/m

Blue: 112 N/m

The following are the equations for finding the placement of where to put the blue and red carts.

Blue:

Ek=Eel

1.2mv^2= ½ kx^2

 ½ (.5394)5^2= ½ (112)x^2

.067425=56x^2

.001204m =x^2

.03469m = x

.035m or 3.5 cm=x

3.5 cm is the distance the spring is compressed for the blue and 4 cm is the distance the spring was compressed for the red. Our group solved for x by setting the Ek and Eel equations equal to each other.

Red:

Ek=Eel

1.2mv^2= ½ kx^2

½ (84)x^2=1/2 (.55)5^2

42x^2= .275

x^2= .0016369 m

x= .04045868

x= .04m or 4cm

We went to test the percent error, and the recorded velocity of both carts was .44m/s. The carts went exactly the same velocity with the distances we predicted, meaning we had a 0% trial error. :) This challenge taught us how to use formulas to solve for a variable and how to manipulate data. Hank and I solved for the distance, converted units, found the mass, and applied to Ek and Eel formulas we learned in the FINAL challenge of the year.