Practice Problems ...for those of you up to the challenge

Problem 1:    A SlinkyŽ is hung from a desk and a student places three different weights on the slinky and measures the results.                Weight             Displacement                 .10kg                      .25 m                 .15kg                      .35 m                 .20kg                      .45 m                 .25kg                      .55 m    What is the value of K for this experiment? Units? Is K positive or negative? Why?

Problem 2:    The regression for the graph of a Force vs. Displacement graph of a spring produces the following regression:                            y=(1.35) x + 10     What is the elastic constant of the spring?     If the spring experienced a displacement of .2 meters, what is the Force active on the spring?

Answers Problem1:   K will be the slope of the linear graph. Keep in mind that Force equals mass times acceleration or mass times -9.8m/s^2 (approx. 10m/s^2)         m= (y(2) - y(1))/(x(2) - x(1)         m= (2.5 - 2)/(.55 - .50)         m=    1 If Force is in Newtons, then F=ks and k=F/s   so k is a Newton/meter The acceleration of the object is towards the ground and negative, thus making K negative. Problem 2:   The elastic constant of the spring or "K" will be the slope that function.         y=(1.35) x+10        y'=1.35   The elastic constant of the spring is 1.35 N/m Since we are given the "x" in the equation, all that is necessary is to plug in the displacement.      y=(1.35) x+10      y=(1.35)(.2)+10      y=10.27      Force= 10.27 N