x = 0 m, mass = 0 g, Force= 0 N x = 0.039 m, mass = 40 g, Force = 0.392 N x = 0.

Question

x = 0 m, mass = 0 g, Force= 0 N
x = 0.039 m, mass = 40 g, Force = 0.392 N
x = 0.08 m, mass = 80 g, Force = 0.784 N
x = 0.12 m, mass = 120 g, Force = 1.176 N
x = 0.16 m, mass = 160 g, Force = 1.568 N
x = 0.20 m, mass = 200 g, Force = 1.96 N

spring constant (k) = 9.7788 N/m

A) How much variation is there in the distance the spring stretches each time you add 40g? (This is the variation in the change of x each time you add 40g.)

B) If x = 0 is the point where a spring of your spring constant is unstretched, how much work would it take to stretch the spring from x=0.1m to x=0.2m? (Show work, please.)

Explanation / Answer

A) The variation in the value of ' x ' when each time you add 40 g mass is given by 0.20 - 0.16 = 0.16 - 0.12 = 0.12 - 0.08 = 0.4 ˜ 0.08 - 0.039 So the change in the value of ' x ' in each time is 0.4 m B) The spring constant, K = 9.7788 N/m The initial value fo x, x1 = 0.1 m The final value of x, x2 = 0.2 m So the total expansion, x = x2 - x1 = 0.1 m The work would it take to stretch the spring is given by the formula W = (1/2)kx^2 = 0.5 * 9.7788 * 0.1 * 0.1 = 0.048894 So the work done is given by the value, W = 0.049 J B) The spring constant, K = 9.7788 N/m The initial value fo x, x1 = 0.1 m The final value of x, x2 = 0.2 m So the total expansion, x = x2 - x1 = 0.1 m The work would it take to stretch the spring is given by the formula W = (1/2)kx^2 = 0.5 * 9.7788 * 0.1 * 0.1 = 0.048894 So the work done is given by the value, W = 0.049 J

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